MATHSBOX - Secondary - Christmas Trial
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4 Questions
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2 Questions
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Up to 10 questions
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Exit tickets
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Worksheet
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Relay Maker
Up to 20 cards
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Number
Algebra
Proportion
Geometry
Statistics
Bidmas
Decimals
Directed Numbers
Equivalence
Estimation
Finance
Fractions
Indices
Integers
Place Value
Product rule
Standard Form
Types of numbers
Surds
Using a calculator
BIDMAS
Positive Integers
Order of operations (1): \( a - b + c \times d \)
Order of operations (2): \( a + b + c \times d \)
Order of operations (3): \( a + b \times c \)
Order of operations (4): \( a - b \times c \)
Order of operations (5): \( a + b \div c \)
Order of operations (6): \( a - b \div c \)
Order of operations (7): \( a \times b - c \times d \)
Order of operations (8): \( a \times b + c \times d \)
Order of operations (9): \( a + (b + c ) \times d \)
Order of operations (10): \( (a + b) \times c \)
Order of operations (11): \( (a - b) \times c \)
Order of operations (12): \( a - (b + c ) \times d \)
Positive integers
Order of operations (13): \( a \times (b - c) \)
Order of operations (14): \( (a - b) \times c \)
Order of operations (15): \( (a + b) \div c \)
Order of operations (16): \( a \div (b + c) \)
Order of operations (17): \( (a - b) \div c \)
Order of operations (18): \( a \div (b - c) \)
Order of operations (19): \( a(b - c) + d \)
Order of operations (20): \( a(b + c) + d \)
Order of operations (21): \( a \times (b - c)^2 \)
Order of operations (22): \( (a - b)^2 \)
Order of operations (23): \( (a + b)^2 \)
Order of operations (24): \( a \times (b - c) \times d \)
Directed numbers
Order of operations - directed numbers mixture
Order of operations(1): \( a - b + c \times d \)
Order of operations(2): \( a - (b + c ) \times d \)
Order of operations(3): \( a + b + c \times d \)
Order of operations(4): \( a + (b + c ) \times d \)
Order of operations(5): \( a \times (b - c)^2 \)
Order of operations(6): \( a - b^2 \)
Order of operations(7): \( a + b^2 \)
Order of operations(8): \( a \times (b - c) \times d \)
Order of operations(9): \( a \times b - c \times d \)
Directed numbers
Order of operations(10): \( a \times b + c \times d \)
Order of operations(11): \( (a + b) \times c \)
Order of operations(12): \( a \times (b - c) \)
Order of operations(13): \( (a - b ) \times c \)
Order of operations(14): \( a \div (b + c) \)
Order of operations(15): \( a \div (b - c) \)
Order of operations(16): \( a + b \times c \)
Order of operations(17): \( a - b \times c \)
Order of operations(18): \( a + b \div c \)
Decimals
Complements
Complements to 1 - hundredths
Complements to 1 - tenths and hundredths
Complements to 1 - thousandths
Addition
Add decimals across 1
Counting in tenths
Add decimals - hundredths
Add decimals - tenths and hundredths
Add decimals - same number of d.p
Add decimals (up to 2 d.p)
Add decimals (up to 3 d.p)
Ordering and comparing
Comparing tens and tenths
Ordering decimals (up to 2 d.p.)
Subtraction
Subtract decimals within 1 (hundredths)
Subtract decimals within 1 (tenths and hundredths)
Subtract decimals across 1
Subtract decimals (same d.p)
Subtract decimals (up to 2 d.p.)
Subtract decimals (up to 3 d.p.)
Multiplication
Multiplying by 10
Multiplying by 100
Multiplying by 1000
Multiplying by 10,100,1000 missing values
Multiplying a decimal by an integer
Multiplying by multiples of 10 or decimals
Use known facts - multiplication (inc decimals)
Multiplying decimals (written methods)
Division
Dividing a 1 digit number by 10
Dividing a 2 digit number by 10
Dividing a 1 digit number by 100
Dividing a 2 digit number by 100
Dividing (up to 3 digit number) by 10
Dividing (up to 3 digit number) by 100
Dividing (up to 3 digit number) by 1000
Dividing by 10 (including decimals)
Dividing by 100 (including decimals)
Dividing by 1000 (including decimals)
Missing values ÷ 10, 100, 1000
Dividing a decimal by and integer
Division decimal by a decimal
Division - mixture
Directed Numbers
Temperatures and Ordering
Comparing temperatures
Comparing directed numbers
Ordering temperatures
Calculating temperature after an increase
Calculating temperature after a decrease
Finding the difference between two temperatures
Arithmetic
Counting in 1's (negative numbers)
Counting in 2,3,4 5 etc
Addition crossing zero
Directed numbers \( a + -b \)
Subtraction crossing zero
Directed numbers \( a - -b \)
Finding more of less
Directed numbers \( \pm a \times \pm b \)
Directed numbers \( \pm a \div \pm b \)
Order of operations
Order of operations - directed numbers mixture
Order of operations(1): \( a - b + c \times d \)
Order of operations(2): \( a - (b + c ) \times d \)
Order of operations(3): \( a + b + c \times d \)
Order of operations(4): \( a + (b + c ) \times d \)
Order of operations(5): \( a \times (b - c)^2 \)
Order of operations(6): \( a - b^2 \)
Order of operations(7): \( a + b^2 \)
Order of operations(8): \( a \times (b - c) \times d \)
Order of operations(9): \( a \times b - c \times d \)
Order of operations(10): \( a \times b + c \times d \)
Order of operations(11): \( (a + b) \times c \)
Order of operations(12): \( a \times (b - c) \)
Order of operations(13): \( (a - b ) \times c \)
Order of operations(14): \( a \div (b + c) \)
Order of operations(15): \( a \div (b - c) \)
Order of operations(16): \( a + b \times c \)
Order of operations(17): \( a - b \times c \)
Order of operations(18): \( a + b \div c \)
Missing numbers
Missing numbers: (1) \( \fbox{} - a = b \)
Missing numbers: (2) \( \fbox{} - a = b \)
Missing numbers: (3) \( \fbox{} + a = b \)
Missing numbers: (4) \( \fbox{} - - a = b \)
Missing numbers: (5) \( a - \fbox{} = b \)
Missing numbers: (6) \( a \div \fbox{} = b \)
Missing numbers: (7) \( a \times \fbox{} = b \)
Missing numbers mixture
Equivalence
Decimals and fractions
Decimals as fractions
Fraction as a decimal (1)
Fraction as decimal (2)
Decimals and fractions - tenths
Decimals and fractions - hundredths
Write division as a fraction
Use division - fraction as a decimal
Decimals and percentages
Decimal as a percentage less than 100
Decimal as a percentage greater than 100
Percentage as a decimal less than 100
Percentage as a decimal greater than 100
Mixture less than 100
Mixture greater than 100
Recurring decimals to fractions
Recurring decimals as fractions
Decimals and fractions
Fractions as percentages
Percentages to fractions (<100)
Percentages to fractions (>100)
Ratios and fractions
Expressing a ratio as a fraction
Expressing a fraction as a ratio
Mixture
Fractions, decimals and percentages
Estimation
Rounding to the nearest
Rounding to the nearest 10
Rounding to the nearest 100
Rounding to the nearest 1000
Mixed Rounding up to 10,000
Round within 1,000,000
Round within 1,000,000,000
Mixed rounding up to 10000000
Rounding to the nearest integer
Rounding to the nearest tenth
Rounding to the nearest hundredth
Significant figures
Rounding to 1 significant figure (integers)
Rounding to 1 significant figure (decimals)
Rounding to 1 significant figure
Rounding to 2 significant figure (integers)
Rounding to 2 significant figure (decimals)
Rounding to 2 significant figures
Rounding to 3 significant figure (integers)
Rounding to 3 significant figure (decimals)
Rounding to 3 significant figures
Rounding-significant figures (integers)
Rounding-significant figures (decimals)
Decimal places
Rounding to 1 decimal place
Rounding to 2 decimal places
Rounding to 1 or 2 decimal places
Truncating
(1) Truncating to thousands
(2) Truncating to hundreds
(3) Truncating to tens
(4) Truncating to an integer
Mixture (1 - 4)
Truncating
(5) Truncating to 1 d.p.
(6) Truncating to 2 d.p.
Mixture (5 - 6)
(7) Truncating to 1 s.f (integers)
(8) Truncating to 1 s.f (decimals)
(9) Truncating to 2 s.f (integers)
(10) Truncating to 2 s.f (decimals)
Mixture (7-12)
Error intervals
Error intervals - numbers - nearest integer
Error intervals - numbers - 1 d.p.
Error intervals - numbers - 2 d.p.
Error intervals - numbers - mixture
Error intervals - measures -nearest integer
Error intervals - measures -1 d.p.
Error intervals - measures -nearest 10
Error intervals - measures -nearest 100
Error intervals - measures -nearest 1000
Error intervals - measures -mixture
Error intervals - truncated numbers
(1) Truncating to thousands
(2) Truncating to hundreds
(3) Truncating to tens
(4) Truncating to an integer
Mixture (1 - 4)
(5) Truncating to 1 d.p.
(6) Truncating to 2 d.p.
Mixture (5 - 6)
(7) Truncating to 1 s.f (integers)
(8) Truncating to 1 s.f (decimals)
(9) Truncating to 2 s.f (integers)
(10) Truncating to 2 s.f (decimals)
Mixture (7-12)
Estimating answers
Estimation (1): \( \frac{a + b }{c} \)
Estimation (2): \( \frac{a - b }{c} \)
Estimation (3): \( \frac{a \times b }{c} \)
Estimation (4): \( a \times b \)
Estimation (5): \( a + b \)
Estimation (6): \( a - b \)
Mixture
Bounds
Min/max radius
Min/max perimeter
Min/max containers
Calculations involving bounds -mixture (1)
Min/max (1): \( \frac{A \times B}{C} \)
Min/max (2):\( \frac{A}{B \times C} \)
Min/max (3):\( A + B - C \)
Min/max (4):\( C(A - B) \)
Calculations involving bounds mixture(2)
Calculations involving bounds - Mixture (1 & 2)
Types of numbers
Identifying Integers
Identifying Positive Integers
Identifying Negative Integers
Identifying Integers
Odd and even numbers
Listing even numbers
Listing odd numbers
Factors
Finding factors
Using factor pairs
Finding common factors
Finding the HCF
Multiples
Listing multiples of 2
Listing multiples of 5 and 10
Listing multiples of 2
Finding multiples of a number
Listing multiples - mixture
Finding common multiples
Finding the lowest common multiple
Prime numbers
Listing prime numbers
Expressing as a product of prime factors
Reciprocals
Finding the reciprocal
Square and cubes
Listing square numbers
Cube numbers
Cube and square numbers
Square roots and intervals
Finance
Working with money (non decimal)
Pence and pounds (755p = £7 and 55p)
Adding money (within a pound)
Adding money
Subtracting money (within a pound)
Subtracting money
Calculating change from £1
Calculating change from £5
Calculating change from £10
Working with money (decimal)
Adding money - decimals
Subtracting money - decimals
Addition and Subtraction - mixture
Calculating change from £1 as a decimal
Calculating change from £5 as a decimal
Calculating change from £10 as a decimal
Calculating change mixture
Problems in context
Multiplication problems
Finding the difference
Totals and change
Tickets and change
Multiply and divide in context
Problem solving with money
Simple Interest
Simple interest - calculating the total
Simple interest - calculating the interest
Simple interest mixture
VAT and Income tax
Calculating the price including VAT
Calculating the price before VAT
Working with VAT - mixture
Calculating Income tax
Fractions
Equivalence and simplifying
Find fractions equivalent to a unit fraction
Find fractions equivalent to a non-unit fraction
Comparing and ordering
Comparing unit fractions
Comparing non-unit fractions
Comparing fractions less than 1
Ordering fractions less than 1
Comparing fractions greater than 1
Order unit fractions
Order non-unit fractions
Compare Mixed numbers
Mixed Numbers and Improper fractions
Count beyond 1 (unit fractions)
Count beyond 1 (increasing)
Count beyond 1 (decreasing)
Partition a mixed number
Improper fractions equivalent to whole(s)
Mixed numbers to improper fractions
Improper fractions to mixed numbers
Order Mixed numbers
Fraction of a quantity
Unit fraction of a quantity (up to × 12 )
Unit fraction of a quantity
Non-unit fraction of a quantity
Comparing fractions quantities
Find the whole - given a unit fraction
Find the whole - given a fraction
Addition
Partition the whole (1): \( \frac{2}{5}+\frac{?}{5} = 1 \)
Partition the whole (2):\( \frac{2}{5}+\frac{1}{5}+\frac{?}{5} = 1 \)
Add fractions within 1
Add fractions total greater than 1
Add any two proper fractions
Add a proper fraction to a mixed number
Adding mixed numbers (1) - same den
Adding mixed numbers (2) - common multiple
Adding mixed numbers (3)
Subtraction
Subtracting fractions from a whole
Subtracting fractions - same denominator
Subtract fractions (common multiple den)
Subtract fractions
Subtract a whole from a mixed number
Fraction from a mixed number (1)
Fraction from a mixed number (2)
Fraction from a mixed number (3)(across a whole)
Subtract mixed numbers (1)
Subtract mixed numbers (2)
Addition and Subtraction
Fractions and decimals - tenths and hundredth
Fractions (common multiple denominators)
Fractions
Mixed numbers (common multiple denominators)
Mixed numbers
Fractions and decimals (answer as a fraction)
Fractions and decimals (answer as a decimal)
Multiplication
Multiply - Unit fraction by an integer
Find the product of a pair of unit fractions
Multiply - fraction by an integer
Find the product of a pair of proper fractions
Multiply - mixed number by an integer
Multiply mixed numbers
Division
Dividing a unit fraction by an integer
Divide an integer by a fraction
Dividing a fraction by an integer
Divide a fraction by a unit fraction
Divide any pair of fractions
Divide mixed numbers
Indices
Evaluating - positive integer powers
Evaluating - negative integer powers
Evaluating - fractional powers \( \frac{1}{2} \) and \( \frac{1}{3} \)
Evaluating - fractional powers \( \frac{n}{m} \)
Evaluating - negative fractional powers \( \frac{1}{2} \) and \( \frac{1}{3} \)
Evaluating - negative fractional powers \( \frac{n}{m} \)
Solving equations
Solving (1) \( \fbox{?}^{\frac{n}{2}} = \frac{1}{m} \)
Solving (2) \( \fbox{?}^{\frac{n}{2}} = m \)
Solving (3) \( \fbox{?}^{\frac{n}{3}} = \frac{1}{m} \)
Solving (4) \( \fbox{?}^{\frac{n}{2}} = m \)
Solving (5) \( \fbox{?}^{-{\frac{n}{2}}} = m \)
Solving (6) \( \fbox{?}^{-{\frac{n}{3}}} = m \)
Solving (7) \( a^m \times b^{\fbox{?}} = m \)
Integers
Add/Subtract 1's ,10's ,100's
Number bonds to 10(0)
Add 1's
Subtract 1's across 10
Add and subtract 1's - missing values
Add 10's
Subtract 10's
Add and subtract 10's
Add and subtract 100's
Add and subtract 1's 10's or 100's
Addition
Add a 2 digit to a 3 digit number
Add two 3 digit numbers (no exchanges)
Add two 3 digit numbers (across 10)
Add two 3 digit numbers across a 10 and/or 100
Add two 3 digit numbers
Add up to 4-digit numbers – no exchange
Add up to 4-digit numbers – one exchange
Add two 4-digit numbers – more than one exchange
Addition - More than 4 digits
Addition - up to 1000000
Subtraction
Subtract a 2 digit from a 3 digit numbers
Subtract two 3 digit numbers (no exchanges)
Subtract two 3 digit numbers across a 10
Subtract two 3 digit numbers across a 100
Subtract two 3 digit numbers across a 10 or 100
Subtract two 4-digit numbers – no exchange
Subtract two 4-digit numbers – (1 exchange)
Subtract two 4-digit numbers – (1+ exchange)
Subtraction - More than 4 digits
Subtraction - numbers up to 1000000
Times Tables
Multiplying by 3
Dividing by 3
Multiplying by 4
Dividing by 4
Multiplying by 8
Dividing by 8
Divide a number by 1 and itself
Multiply by 1 and 0
Multiply and divide by 6
Multiply and divide by 9
Multiply and divide by 7
Multiply and divide by 11
Multiply and divide by 12
Comparing single digit multiplication calculations
Multiply 3 numbers
Multiplication
Using factor pairs
Multiplying - 2 digit by a single digit
Comparing calculation involving multiples of 10
Multiply a 2 digit by a 1 digit number - no exchange
Multiply a 2 digit by a 1 digit number - with exchange
Multiply a 3 digit by a 1 digit number
Multiply a 4 digit by a 1 digit number
Multiply - by 10
Multiply by 100
Multiply by 10,100 or 1000
Multiply by 0.1 or 0.01
Multiply - 2 digit by 2 digit
Multiply - 3 digit by 2 digit
Multiply - 4 digit by 2 digit
Multiplication - by multiples of 10,100,1000
Use factors to simplify multiplication calculations
Comparing related products
Division
Division - related calculations
Dividing by 10
Dividing by 100
Dividing by 10,100 or 1000
Division - by multiples of 10,100,1000
2-digit ÷ 1-digit - no exchange
2-digit ÷ 1-digit- with exchange
2-digit ÷ 1-digit- with remainders
3-digit ÷ 1-digit
3-digit ÷ 1-digit- with remainders
Division - 3 or 2 digit by 1 digit
Division - 3 or 4 digit by 1 digit (with remainders as decimals)
Division - 3 or 4 digit by 1 digit (with remainders as fractions)
Division - 4 digit by 1 digit (no remainders)
Division - 4 digit by 1 digit (with remainders)
Division - 3 or 4 digit by 2 digit numbers
Inverse operations and language
Addition up to 100 (1)
Addition up to 1000 (2)
Addition up to 10000 (3)
Subtraction up to 100 (4)
Subtraction up to 1000 (5)
Subtraction up to 10000 (6)
Finding the sum
Finding the product
Finding the difference
Mixture
Comparing calculations - addition and subtraction
Inverse operations - addition and subtraction
Missing numbers in equivalent calculations
Complements to 100
Multiplication and Division - by multiples of 10
Comparing multiplication and division calculations
Multiplication and division - multiple powers of 10
Related calculations - multiplication and division
Place Value
Roman numerals
Roman numerals to figures (12)
Figures to Roman numerals (12)
Roman numbers to figures (100)
Roman numbers to figures (1000)
Reading and writing numbers
Words to figures up to 1000
Making large and small numbers (5 digits)
Words to figures to 1,000
Words to figures to 100,000
Words to figures up to 1,000,000
Words to figures up to 1 billion in figures
Place value and partitioning
Partition numbers up to 100
Hundreds and tens - equivalence
Place value in numbers up to 1000
Partition numbers to 1000
1's, 10's, 100's, 1000's equivalence
Partition numbers up to 10,000
Flexible partitioning of numbers to 10,000
Place value in numbers up to 1,000,000
Partition numbers up to 1,000,000
Place value within 1
Place value - integers and decimals
Place value - decimals (up to 3 d.p.)
Ordering and comparing
Compare numbers up to 1000
Comparing numbers up to 1000 using < or >
Comparing numbers up to 10,000 using < or >
Comparing numbers up to 100,000
Comparing numbers up to 1,000,000
Order numbers up to 1000
Order numbers up to 10,000
Order numbers up to 100,000
Order numbers up to 1,000,000
Order numbers up to 10,000,000
Order numbers up to 100,000,000
More or less
Finding 10 or 100 more than a number
Finding 10 or 100 less than a number
Finding 10, 100 or 1000 more (1,000)
Finding 10, 100 or 1000 less (1,000)
Finding 10, 100 or 1000 more (10,000)
Finding 10, 100 or 1000 less (10,000)
Finding 10, 100 or 1000 more (1,000,000)
Finding 10, 100 or 1000 less (1,000,000)
Multiples of powers of 10 more than a number
Multiples of powers of 10 less than a number
More or less
Finding 1 more or less than a number
Finding 10 more or less than a number
Finding 100 more or less than a number
Finding 10 or 100 more or less than a number
Powers of 10 more/less
Multiples of powers of 10 more/less
Related Calculations
(1)Finding \( 10a \times b \)
(2)Finding \( a \times 10b \)
(3)Finding \( a \div 10 \times b \)
(4)Finding \( a \times b \div 10 \)
(5)Finding \( a \div 10 \times b \div 10 \)
(6)Finding \( a \div 10 \times 10b \)
(7)Finding \( 10a \times b \div 10 \)
(8)Finding \( a \div 100 \times b \)
(9)Finding \( a \times b \div 100 \)
(10)Finding \( a \div 100 \times 10b \)
(11)Finding \( 10a \times b \div 100 \)
(12)Finding \( a \times (b+1) \)
(13)Finding \( (a+1) \times b \)
(14)Finding \( a \times (b-1) \)
(15)Finding \( (a-1) \times b \)
Related Calculations
(16)Finding \( 2a \times b \)
(17)Finding \( a \times 2b \)
(18)Finding \( (a-1) \div 10 \times b \)
(19)Finding \( a \times (b-1) \div 10 \)
(20)Finding \( (a+1) \div 10 \times b \)
(21)Finding \( a \times (b+1) \div 10 \)
(22)Finding \( (a-1) \div 100 \times b \)
(23)Finding \( a \times (b-1) \div 100 \)
(24)Finding \( (a+1) \div 100 \times b \)
(25)Finding \( a \times (b+1) \div 100 \)
(26)Finding \( a \div 10 \times (b+1) \div 10 \)
(27)Finding \( a \div 10 \times (b-1) \div 10 \)
(28)Finding \( (a+1) \div 10 \times b \div 10 \)
(29)Finding \( (a-1) \div 10 \times b \div 10 \)
Standard Form
Powers of 10
Multiplying positive powers of 10
Dividing positive powers of 10
Multiplying and Dividing positive powers of 10
Expressing negative powers of 10 as a decimal
Ordering
Order numbers in standard form
Compare numbers in standard form
Expressing in standard form
Wrtiting in standard form 0 < n < 1
Writing in ordinary form 0 < n < 1
Standard form and ordinary form mixed
Writing in standard form - integers
Writing in ordinary form - integers
Standard form and ordinary form mixed
Addition and subtraction
Addition - decimals
Addition - integers
Subtraction - decimals
Subtraction - integers
Mixture + and - decimals
Mixture + and - decimals
Addition and subtraction - same power
Addition - decimals
Addition - integers
Subtraction - decimals
Subtraction - integers
Multiplication and division
Multiply a number in standard form by an integer
Divide a number in standard form by an integer
Multiply numbers in standard form
Divide numbers in standard form
Multiplication and division - same power
Multiply numbers in standard form
Calculators and standard form
Standard form - mixed arithmetic (calculator)
Standard form - addition - calculator
Standard form - subtraction - calculator
Standard form - multiplication - calculator
Standard form - division - calculator
Standard form - × and ÷ - calculator
Standard form - mixed arithmetic (calculator)
Surds
Simplifying
Simplifying (1):\( \sqrt{a} \)
Simplifying (2):\(\sqrt{a} \pm b + \sqrt{a} \pm c\)
Simplifying (3):\( n\sqrt{a} \pm b + m\sqrt{a} \pm c\)
Simplifying (4):\( n\sqrt{a} + \sqrt{b} \)
Simplifying (5):\( n\sqrt{a} \times m\sqrt{a} \)
Simplifying (6):\( \sqrt{a} \times \sqrt{b} \)
Simplifying (7):\( m\sqrt{a} \times n\sqrt{b} \)
Simplifying expressions involving surds
Expanding brackets
Expanding brackets (1):\( \sqrt{a}(a\sqrt{b} \pm c ) \)
Expanding brackets (2): \( \sqrt{a}(b \pm \sqrt{a} ) \)
Expanding brackets (3):\( a\sqrt{b}(c\sqrt{d} \pm e ) \)
Expanding brackets (4): \( (\sqrt{a} \pm b)( \sqrt{a} \pm c ) \)
Expanding brackets (5): \( (a\sqrt{b} \pm c)( d\sqrt{b} \pm e )\)
Expanding mixture
Rationalising the denominator
Rationalising the denominator (1):\( \frac{a}{\sqrt{b}} \)
Rationalising the denominator (2):\(\frac{a}{c \pm \sqrt{b}} \)
Rationalising the denominator (3):\(\frac{a \pm \sqrt{b}}{c \pm \sqrt{b}} \)
Rationalising the denominator mixture
Using a calculator
Positive values
Squares and square roots mixture
Using a calculator (1): \( a \times \sqrt{b} \)
Using a calculator (2): \( a \times \sqrt{b} + \sqrt{c} \)
Using a calculator (3): \( a \times b^2 + \sqrt{b} \)
Using a calculator (4): \( a \times b^2 + \sqrt{c \times d } \)
Using a calculator (5): \( \sqrt{a} \times b + c \times \sqrt{d} \)
Using a calculator (6): \( \sqrt{a \times b^2} + c \times \sqrt{d} \)
Using a calculator (7): \( a \times \sqrt{b} - \sqrt{c} \)
Using a calculator (8):\( a \times b^2 - \sqrt{c} \)
Using a calculator (9): \( a \times b^2 - \sqrt{c\times d} \)
Using a calculator (10): \( \sqrt{a \times b} - c \times \sqrt{d} \)
Using a calculator (11):\( \sqrt{a \times b^2} - c \times \sqrt{d} \)
Using a calculator (12):\( a - \frac{b}{c} \)
Using a calculator (13):\( \sqrt{a - b} + c\)
Using a calculator (14):\( \sqrt{a^2 - b} - \sqrt{c} \)
Using a calculator (15):\( \sqrt[3]{a+\frac{c}{b}} \)
Using a calculator (16):\( \sqrt[3]\frac{a}{b}+ c^3 \)
Using a calculator (17):\( a^2 + b^3 + c^4 \)
Using a calculator (18):\( \frac{b}{a} \times 10^3 \)
Using a calculator (19):\( \frac{a}{b+c}\)
Directed numbers
Directed numbers (1):\( -a \times -b -c \)
Directed numbers (2): \( -a + - b + c \)
Directed numbers (3): \( -(a)^2 + -b + c \)
Directed numbers (4): \((-a)^2 + -b + c \)
Directed numbers (5): \((-a)^2 - -b + -c \)
Directed numbers (6): \((-a)^2 - -b - -c \)
Product rule for counting
Dials
(1) : Dials
(2) : Dials - multiples of 5 or 10
(3) : Dials - Odd and even
Menu Choices
(1) : Menu - 3 course selection
(2) : Menu - 2 course selection
Selecting cards
(1) - Cards - Different numbers
(2) - Cards - Different pairs
Fractions
Changing the subject
Linear Equations (1)
Linear Equations (2)
Quadratic Equations
Simultaneous Equations
Expanding Brackets
Factorising
Functions
Function Machines
Linear Graphs
Other Graphs
Indices
Inequalities
Sequences
Simplifying
Substitution
Fractions
Simplifying - Addition and Subtraction
Simplify (1):\( \frac{x}{a}+ \frac{x}{b} \)
Simplify (2):\( \frac{x}{a}- \frac{x}{b} \)
Simplify (3):\( \frac{ax}{b} + \frac{cx}{d} \)
Simplify (4):\( \frac{ax}{b} - \frac{cx}{d} \)
Simplify (5):\( \frac{x+a}{b} + \frac{x+c}{d} \)
Simplify (6):\( \frac{x+a}{b} - \frac{x+c}{d} \)
Simplify (7):\( \frac{x+a}{b} - \frac{x-c}{d} \)
Simplify (8):\( \frac{x-a}{b} - \frac{x+c}{d} \)
Simplify (9):\( \frac{x-a}{b} - \frac{x-c}{d} \)
Simplify (10):\( \frac{x-a}{b} + \frac{x-c}{d} \)
Simplify (11):\( \frac{x+a}{b} - \frac{x-c}{d} \)
Simplify Mixture
Simplifying - Multiplication and division
Multiply algebraic fractions
Divide algebraic fractions
Equations with fractions (quadratic formula needed)
Equations - fractions: \( \frac{a}{x}+ \frac{b}{x+c}= d \)
Equations - fractions :\( \frac{a}{x}- \frac{b}{x+c}= d \)
Equations - fractions :\( \frac{a}{x}+ \frac{b}{x-c}= d \)
Equations - fractions :\( \frac{a}{x-c}- \frac{b}{x}= d \)
Equations - fractions: \( \frac{a}{x+b}+ \frac{c}{x+d}= e \)
Equations - fractions :\( \frac{a}{x+b}- \frac{c}{x+d}= e \)
Equations - fractions :\( \frac{a}{x-b}- \frac{c}{x+d}= e \)
Equations - fractions :\( \frac{a}{x-b}- \frac{c}{x-d}= e \)
Changing the subject
One-step formula
Change the subject - 1 step (1): \( y = x + a \)
Change the subject - 1 step (2) \( y = x - a \)
Change the subject - 1 step (3) \( y = ax \)
Change the subject - 1 step (4) \( y= \frac{a}{x} \)
Change the subject - 1 step (5) \( y = \frac{x}{a} \)
Change the subject - 1 step (6) \( y= a - x \)
Change the subject - mixture
Two-step formula
Rearranging to the form y = mx + c
Rearrange two step (1): \( y= \frac{x}{a} + b \)
Rearrange two step (2): \( y= \frac{x}{a} - b \)
Rearrange two step (3): \( y= \frac{x + a}{b} \)
Rearrange two step (4): \( y= \frac{x - a}{b} \)
Rearrange two step - mixture
Complex formula
Rearrange complex (1): - \( y = \sqrt{x + a} \)
Rearrange complex (2): \( y = \sqrt{x - a} \)
Rearrange complex (3): \( y = \sqrt{a - x} \)
Rearrange complex (4): \( y = \frac{\sqrt{x}}{a} \)
Rearrange complex (5): \( y = \frac{a}{\sqrt{x}} \)
Rearrange complex (6): \( y = \sqrt{\frac{a}{x}} \)
Rearrange complex (7): \( y = \sqrt{\frac{x}{a}} \)
Rearrange complex (8): \( y = \sqrt{x} + a \)
Rearrange complex (9): \( y = \sqrt{x} -a \)
Rearrange complex (10): \( y = - \sqrt{x} \)
Rearrange complex formula :mixture
Variable appears more than once
Subject appears twice (1) \( ax = bx + c \)
Subject appears twice (2) \( ax = c - bx \)
Subject appears twice (3) \( ax + b = cx + d \)
Subject appears twice (4) \( ax - b = cx + d\)
Subject appears twice (5) \( ax - b = d - cx \)
Subject appears twice (6) \( ax + b = d - cx \)
Subject appears twice (7) \( \frac{x+a}{x+b} = c\)
Subject appears twice (8) \( \frac{x-a}{x+b} = c\)
Subject appears twice (9) \( \frac{x+a}{x-b} = c\)
Subject appears twice (10) \( ax - b = cd - d\)
Subject appears twice (11) \( \frac{x}{x-b} = c\)
Subject appears twice (12) \( \frac{x}{x+b} = c\)
Subject appears twice (13) \( \frac{ax+b}{cx + d} = e\)
Subject appears twice (14) \( \frac{ax-b}{cx + d} = e\)
Subject appears twice (15) \( \frac{ax-b}{cx-d} = e\)
Subject appears twice - mixture
Linear Equations
Forming equations and expressions
Forming single step expressions
Forming equations 1 step
Forming equations 2 step
Forming and solving equations
One-step equations
One step equations (1): \( x + a = b \)
One step equations (2): \( x - a = b \)
One step equations (3): \( a - x = b \)
One step equations (4): \( ax = b \)
One step equations (5): \( \frac{x}{a} = b \)
One step equations Mixture
Two step equations
Positive solutions (1): \( ax + b = c \)
Positive solutions (2): \( ax - b = c \)
Positive solutions (3): \( a - bx = c \)
Negative solutions (4): \( ax + b = c \)
Negative solutions (5): \( ax - b = c \)
Negative solutions (6):\( a - bx = c \)
Postive mixture
Postive/Negative mixture
Fractions (1)
Equations with fractions (1):\( \frac{x}{a} - b = c \)
Equations with fractions (2):\( \frac{x}{a} + b = c \)
Equations with fractions (3):\( \frac{x + a}{b} = c \)
Equations with fractions (4):\( \frac{x - a}{b} = c \)
Equations with fractions (5) \( a - \frac{x}{b} = c \)
Equations with fractions - mixture
Brackets
Solving (1) :\( a(bx + c) = d \)
Solving (2) :\( a(bx - c) = d \)
Solving (3) :\( a(c - bx) = d \)
Mixture (1) - (3)
Solving (4) :\( a( bx + c) + d = e \)
Solving (5) :\( a( bx - c) + d = e \)
Solving (6) :\( a( bx + c) - d = e \)
Solving (7) : \( a( bx - c) - d = e \)
Solving (8) :\( a( b - cx) + d = e \)
Solving (9) :\( a( b - cx) - d = e \)
Equations with brackets - mixture
Unknown on both sides - positive solutions only
Both sides (1a) : \( ax + b = cx + d \)
Both sides (2a) : \( ax - b = cx + d \)
Both sides (3a) : \( ax - b = cx - d \)
Unknown on both sides
Both sides (1) : \( ax + b = x + c \)
Both sides (2) : \( ax - b = x + c \)
Both sides (3) : \( ax + b = x - c \)
Both sides (4) : \( ax - b = x - c \)
Both sides (5) : \( ax + b = c - x \)
Both sides (6) : \( ax - b = c - x \)
Both sides (7) : \( ax + b = cx + d \)
Both sides (8) : \( ax - b = cx + d \)
Both sides (9) : \( ax + b = cx - d \)
Both sides (10) : \( ax - b = cx - d \)
Both sides (11) : \( ax + b = d - cx \)
Both sides (12) : \( ax - b = d - cx \)
Both sides mixture (1) - (12)
Both sides (13) : \( a(bx + c) = dx + e \)
Both sides (14) : \( a(bx - c) =dx + e \)
Both sides (15) : \( a(bx + c) = dx - e \)
Both sides (16) : \( a(bx - c) = dx - e \)
Both sides (17) : \( a(c - bx) + =dx + e \)
Both sides (18) : \( a(c - bx) = dx - e \
Both sides - mixture (1) - (18)
Equations with fractions (2)
Equations with fractions (6) \(\\\frac{x}{a} + b = cx + d \)
Equations with fractions (7) \(\\\frac{x}{a} - b = cx + d \)
Equations with fractions (8) \(\\\frac{x}{a} + b = cx - d \)
Equations with fractions (9) \(\\\frac{x}{a} - b = cx - d \)
Equations with fractions (10) \(b - \\\frac{x}{a} = cx + d \)
Equations with fractions (11) \(b - \\\frac{x}{a} = cx + d \)
Equations with fractions (12) \(\\\frac{x}{a} + b = \\\frac{x}{c} + d \)
Equations with fractions (13) \(\\\frac{x}{a} - b = \\\frac{x}{c} + d \)
Equations with fractions (14) \(\\\frac{x}{a} + b = \\\frac{x}{c} - d \)
Equations with fractions (15) \(\\\frac{x}{a} - b = \\\frac{x}{c} - d \)
Equations with fractions (2)
Equations with fractions (16) \(\\\frac{x}{a} + b = d - \\\frac{x}{c} \)
Equations with fractions (17) \(\\\frac{x}{a} - b = d -\\\frac{x}{c} \)
Equations with fractions (18) \(\\\frac{x}{a} + \\\frac{x}{b} = c \)
Equations with fractions (19) \(\\\frac{x}{a} - \\\frac{x}{b} = c \)
Equations with fractions (20) \(\\\frac{x}{a} + \\\frac{x}{b} = cx + d \)
Equations with fractions (21) \(\\\frac{x}{a} - \\\frac{x}{b} = cx + d \)
Equations with fractions (22) \(\\\frac{x}{a} + \\\frac{x}{b} = cx - d \)
Equations with fractions (23) \(\\\frac{x}{a} - \\\frac{x}{b} = cx - d \)
Equations with fractions (24) \(\\\frac{x}{a} + \\\frac{x}{b} = e - dx \)
Equations with fractions (25) \(\\\frac{x}{a} - \\\frac{x}{b} = e - dx \)
Equations with fractions - mixture
Linear Equations - alternative forms
Integer Solutions
One step equations (1): \( b = x + a \\\ \\\ b = a + x \)
One step equations (2): \( b = x - a \)
One step equations (3): \( b = a - x \)
One step equations (4): \( b = \frac{x}{a} \)
Integer Solutions
Two step equations (1): \( b = ax + b \)
Two step equations (2): \( b = ax - b \)
Two step equations (3): \( b = a - bx \)
Integer Solutions
Fractions (1): \( c = \frac{x}{a}+b \)
Fractions (2): \( c= \frac{x}{a} - b \)
Fractions (3): \( c= a - \frac{x}{b} \)
Fractions (4): \( c = \frac{x+a}{b} \)
Fractions (5): \( c = \frac{x-a}{b} \)
Integer Solutions
Brackets (1): \( d =a(bx+c) \)
Brackets (2): \( d=a(bx-c) \)
Brackets (3): \( d=a(c-bx) \)
Fraction - Solutions
Fractions (6): \( d = \frac{ax}{b}+c \)
Fractions (7): \( d= \frac{ax}{b} - c \)
Fractions (8): \( d= c - \frac{ax}{b} \)
Fractions (9): \( d = \frac{ax+b}{c} \)
Fractions (10): \( d = \frac{ax-b}{c} \)
Integer Solutions
Brackets (4): \( d =a(bx+c) \)
Brackets (5): \( d=a(bx-c) \)
Brackets (6): \( d=a(c-bx) \)
Quadratic Equations
Factorise and solve (1)
Factorise and solve \(x^2 + ax = 0 \)
Factorise and solve (1): \(x^2 - ax = 0 \)
Factorise and solve (2):\( ax^2 + bx = 0 \)
Factorise and solve (3):\( ax^2 - bx = 0 \)
Factorise and solve Mixture
Expressing in completed square form
Expressing in the form (1): \( (x \pm a)^2 \pm b \)
Expressing in the form (2): \( (ax \pm b)^2 \pm c \)
Completed square form mixture
Factorise and solve (2)
Factorise and solve (1): \( x^2 + bx + c = 0 \)
Factorise and solve (2): \( x^2 \pm bx - c = 0 \)
Factorise and solve (3): \(x^2 \pm bx + c = 0 \)
Factorise and solve (4): \(x^2 \pm bx + c = 0 \) (x = a)
Factorise and solve mixture (1) - (4)
Difference of 2 squares
Factorise and solve (4a): \( x^2 - b^2 = 0 \)
Factorise and solve (4b): \( a^2x^2 - b^2 = 0 \)
Factorise and solve (2)
Factorise and solve (5): \( ax^2 + bx + c = 0 \)
Factorise and solve (6): \( ax^2 \pm bx - c = 0 \)
Factorise and solve (7): \( ax^2 - bx + c = 0 \)
Factorise and solve (8): \( ax^2 \pm 2abx + b^2 = 0 \)
Factorise and solve mixture (5)-(8)
Factorise and solve mixture (1)-(8)
Rearrange before factorising
Rearrange and solve (1)
Rearrange and solve (2)
Quadratic formula
Find the discriminant
Solve \(x \pm bx \pm c = 0 \)
Solve \(ax \pm bx \pm c = 0 \)
Rearrange and solve
Equations with fractions (quadratic formula needed)
Equations - fractions: \( \frac{a}{x}+ \frac{b}{x+c}= d \)
Equations - fractions :\( \frac{a}{x}- \frac{b}{x+c}= d \)
Equations - fractions :\( \frac{a}{x}+ \frac{b}{x-c}= d \)
Equations - fractions :\( \frac{a}{x-c}- \frac{b}{x}= d \)
Equations - fractions: \( \frac{a}{x+b}+ \frac{c}{x+d}= e \)
Equations - fractions :\( \frac{a}{x+b}- \frac{c}{x+d}= e \)
Equations - fractions :\( \frac{a}{x-b}- \frac{c}{x+d}= e \)
Equations - fractions :\( \frac{a}{x-b}- \frac{c}{x-d}= e \)
Simultaneous Equations
Linear
Find pairs of values
Solve problems with two unknowns
(1): \( x + y = r \) and \( x - y = s \)
(2): \( ax + by = r \) and \( ax - y = s \)
(3): \( ax + by = r \) and \( ax + y = s \)
(4): \( ax - by = r \) and \( ax - y = s \)
(5): \( ax + by = r \) and \( x - by = s \)
(6):\( ax - by = r \) and \( x - by = s \)
(7): \( ax + by = r \) and \( x + by = s \)
Mixed questions (1 - 7)
Linear
(8):\( x + by = r \) and \( cx + dy = s \)
(9):\( x - by = r \) and \( cx + dy = s \)
(10):\( x + by = r \) and \( cx - dy = s \)
(11):\( x - by = r \) and \( cx - dy = s \)
(12):\( ax + y = r \) and \( cx + dy = s \)
(13):\( ax - y = r \) and \( cx + dy = s \)
(14):\( ax + y = r \) and \( cx - dy = s \)
(15):\( ax + y = r \) and \( cx - dy = s \)
Mixture (8 - 15)
Expanding Brackets
Single brackets
Expanding (1): \( a(bx + c) \)
Expanding (2): \( a(bx - c) \)
Expanding (3): \( a(b - cx ) \)
Expanding (4): \( ax(bx + c) \)
Expanding (5): \( ax(bx - c) \)
Expanding (6): \( ax(b - cx ) \)
Expanding mixture ( 1 - 6)
Multiple, single brackets
Expanding (1): \( a( bx + c) + d(ex + f) \)
Expanding (2): \( a( bx - c) + d(ex + f) \)
Expanding (3): \( a( bx + c) + d(ex - f) \)
Expanding (4): \( a( bx - c) + d(ex - f) \)
Expanding Mixture (1 - 4)
Expanding (5): \( a( bx + c) - d(ex + f) \)
Expanding (6): \( a( bx - c) - d(ex + f) \)
Expanding (7): \( a( bx + c) - d(ex - f) \)
Expanding (8): \( a( bx - c) - d(ex - f) \)
Expanding Mixture (5 - 8)
Expanding Mixture (1 - 8)
Double brackets (1)
Expanding (1): \( (x + a)(x + b) \)
Expanding (2): \( (x - a)(x - b) \)
Expanding (3): \( (x + a)(x - b) \)
Expanding (4): \( (x - a)(x + b) \)
Expanding (5): \( (x + a)^2 \)
Expanding (6): \( (x - a)^2 \)
Expanding (7): \( (x - a)(x + a) \)
Expanding Mixture ( 1 - 7)
Double Brackets (2)
Expanding (8): \( (ax + b)(cx + d) \)
Expanding (9): \( (ax - b)(cx + d) \)
Expanding (10): \( (ax + b)(cx - d) \)
Expanding (11): \( (ax - b)(cx - d) \)
Expanding (12): \( (ax + b)^2 \)
Expanding (13): \( (ax - b)^2 \)
Expanding Mixture ( 8 - 13)
Expanding Mixture ( 1 - 13)
3 brackets
Expanding 3 brackets
Factorising
Single bracket
Factorising (1): \( ax + b \)
Factorising (2): \( ax - b \)
Factorising (3): \( a - bx \)
Factorising Mixture (1 - 3)
Single bracket
Factorising (4): \( ax^2 + bx \)
Factorising (5): \( ax^2 - bx \)
Factorising (6): \( bx - ax^2 \)
Factorising Mixture (4 - 6)
Factorising Mixture (1 - 6)
2 brackets
Factorising (1): \(x^2 + bx + c\)
Factorising (2): \(x^2 ± bx - c\)
Factorising (3): \(x^2 - bx + c\)
Factorising (4): \( x^2 ± 2ax + a^2 \)
Factorising Mixture (1 - 4)
Difference of 2 squares
Factorising (4a): \( x^2 - b^2 \)
Factorising (4b): \( a^2x^2 - b^2 \)
2 brackets
Factorising (5): \( ax^2 + bx + c \)
Factorising (6): \( ax^2 \pm bx - c \)
Factorising (7): \( ax^2 - bx + c \)
Factorising to (8): \( (ax + b)^2 \)
Factorising to (9): \( (ax - b)^2 \)
Factorising Mixture (5 - 9)
Factorising Mixture (1 - 9)
Functions
Evaluating functions
Evalutating functions (1) : \( ax^2 - b \)
Evalutating functions (2) : \( b - ax^2 \)
Evalutating functions (3) : \( (ax)^2 + b \)
Evalutating functions (4) : \( \frac{ax^2}{b} \)
Evalutating functions (5) : \( \frac{ax^2}{b} + c \)
Evalutating functions (6) : \( \frac{ax^2}{b} - c \)
Evalutating functions (7) : \( \sqrt{ax+b} \)
Evalutating functions (8) : \( \sqrt{b-ax} \)
Evaluating functions
Evalutating functions (9) : \( \sqrt{\frac{x+a}{b}} \)
Evalutating functions (10) : \( x^2 + x \)
Evalutating functions (11) : \( ax^2 \pm x \)
Evalutating functions (12) : \( x^2 \pm ax \)
Evalutating functions (13) : \( ax^2 \pm bx \)
Evalutating functions (14) : \( ax - bx^2 \pm c \)
Evalutating functions (15) : \( ax^3 \pm bx^2 \)
Evalutating functions (16) : \( ax^3 \pm bx^2 \pm cx \pm d \)
Inverse functions
Inverse functions (1) : \( x - a \)
Inverse functions (2) : \( x + a \)
Inverse functions (3) : \( a - x \)
Inverse functions (4) : \( ax \)
Inverse functions (5) : \( \frac{x}{a} \)
Inverse functions (6) : \( \frac{a}{x} \)
Inverse functions (7) : \( ax + b \)
Inverse functions (8) : \( b - ax \)
Inverse functions (9) : \(ax - b \)
Inverse functions (10) : \( \frac{x+b}{a} \)
Inverse functions (11) : \( \frac{x-b}{a} \)
Inverse functions (12) : \( \frac{b-x}{a} \)
Inverse functions (13) : \( \frac{a}{x + b} \)
Inverse functions (14) : \( \frac{a}{x - b} \)
Inverse functions (15) : \( \frac{x}{a} + b \)
Inverse functions (16) : \( \frac{x}{a} - b \)
Inverse functions (17) : \( \sqrt{x} \)
Inverse functions (18) : \( a \sqrt{x} \)
Inverse functions (19) : \( \sqrt{x + a } \)
Inverse functions (20) : \( \sqrt{x - a } \)
Inverse functions (21) : \( \sqrt{a - x} \)
Inverse functions (22) : \( \frac{ \sqrt{x}}{a} \)
Inverse functions (23) : \( \frac{a}{\sqrt{x}} \)
Inverse functions (24) : \( \sqrt{ \frac{a}{x} } \)
Inverse functions (25) : \( \sqrt{\frac{x}{a}} \)
Inverse functions (26) : \( \sqrt{x} + a \)
Inverse functions (27) : \( \sqrt{x} - a \)
Inverse functions (28) : \( a - \sqrt{x} \)
Inverse functions (29) : \( a \sqrt{x + b} \)
Inverse functions (30) : \( a \sqrt{x - b} \)
Inverse functions (31) : \( a + \sqrt{x - b} \)
Inverse functions (32) : \( a - \sqrt{x - b} \)
Inverse functions (33) : \( a - \sqrt{x + b} \)
Inverse functions (34) : \( \frac{\sqrt{x + b}}{a} \)
Inverse functions (35) : \( \sqrt{ \frac{x-b}{a}} \)
Inverse functions (36) : \( \sqrt{ \frac{x+b}{a}} \)
Inverse functions (37) : \( \frac{\sqrt{x}}{a}+b \)
Inverse functions (38) : \( \frac{\sqrt{x}}{a}-b \)
Inverse functions (39) : \( b - \frac{\sqrt{x}}{a} \)
Inverse functions (40) : \( \sqrt{ax + b} \)
Inverse functions (41) : \( \sqrt{ax - b} \)
Inverse functions (42) : \( \sqrt{b - ax} \)
Inverse functions (43) : \( \frac{ \sqrt{x}}{a} + b \)
Inverse functions mixture
Forming composite functions
(1) : \( fg(x) \\ f(x) = ax \pm b \\\ \\\ g(x) = cx \pm d \)
(2) : \( gf(x) \\\ f(x) = ax \pm b \\\ \\\ g(x) = cx \pm d \)
(3) : \( fg(x) \\\ f(x) = x^2 \\\ \\\ g(x) = ax \pm b \)
(4) : \( g(x) \\\ f(x) = x^2 \\\ \\\ g(x) = ax \pm b \)
(5) : \( fg(x) \\\ f(x) = ax^2 \\\ \\\ g(x) = bx \pm c \)
(6) : \( gf(x) \\\ f(x) = ax^2 \\\ \\\ g(x) = bx \pm c \)
(7) : \( fg(x) \\\ f(x) = x^2 \pm a \\\ \\\ g(x) = x \pm b \)
(8) : \( gf(x) \\\ f(x) = x^2 \pm a \\\ \\\ g(x) = x \pm b \)
(9) : \( fg(x) \\\ f(x) = a \pm bx \\\ \\\ g(x) = cx \pm d \)
(10): \( gf(x) \\\ f(x) = a \pm bx \\\ \\\ g(x) = cx \pm d \)
Composite functions - mixture
Function Machines
One-step finding the output
Find the output (1) : \( + a \)
Find the output (2) : \( - a \)
Find the output (3) : \( × a \)
Find the output (4) : \( ÷ a \)
One-step input mixture (1 - 4)
Find the output - decimals (5) : \( + a \)
Find the output - decimals (6) : \( - a \)
Find the output - decimals (7) : \( × a \)
Find the output - decimals (8) : \( ÷ a \)
One-step output mixture (4 - 8)
One-step finding the input
Find the input (1) : \( + a \)
Find the input (2) : \( - a \)
Find the input (3) : \( × a \)
Find the input (4) : \( ÷ a \)
One-step input mixture (1 - 4)
Two-step finding the output
Find the output (1) \( \times a + b \)
Find the output (2) \( \times a - b \)
Find the output (3) \( + a \times b \)
Find the output (4) \( \div a + b\)
Find the output (5) \( \div a - b \)
Find the output (6) \( + a \div b \)
Find the output (7) \( -a \div b \)
Find the output (8) \( -a \times b\)
Two-step output mixture
Two-step finding the input
Find the input (1) \( \times a + b \)
Find the input (2) \( \times a - b \)
Find the input (3) \( + a \times b \)
Find the input (4) \( \div a + b\)
Find the input (5) \( \div a - b \)
Find the input (6) \( + a \div b \)
Find the input (7) \( -a \div b \)
Find the input (8) \( -a \times b\)
Two-step input mixture
Expressions
Find an expression for the output
Find the function
Missing functions
Two-step - missing functions
Linear Graphs
Equations of \(x = a, \\\ y = b \\\ , y = \pm x \)
Lines parallel to the x-axis
Lines parallel to the x-axis (Diagram)
Lines parallel to the y-axis
Lines parallel to the y-axis (Diagram)
Lines parallel to the axes
Lines parallel to the axes (diagram)
2 coordinates given
Coordinates on lines
Does a point lie on \( y = mx \)
Does a point lie on \( y = mx \pm c \)
Complete a coordinate for \( y = x \pm c \)
Complete a coordinate for \( y = mx \)
Complete a coordinate for \( y = mx \pm c \)
Find the mid-point of a line segment
Identify equations of non-linear graphs
Finding the gradient
Determine which is the steeper line
Identify the gradient (diagram)
Identify the gradient of \( y = mx \pm c \)
Identify the gradient after rearranging
Finding the intercept
Identify the \( y \\\ axis \) intercept for \( y = x \pm a \)
Identify the \( x \\\ axis \) intercept for \( y = x \pm a \)
Identify the \( y \\\ axis \) intercept for \( y = mx \pm c \)
Identify the intercept after rearranging
Equation of a straight - words
Equation of a line - 2 function machines
Equation of a line - through (a,b) and (0,c)
Equation of a line - through (a,b) and (c,d)
Equation of a line - gradient and y-intercept
Equation of a straight - from diagrams
\( y=mx \pm c \) - positive gradient
\( y=mx \pm c \) - negative gradient
\( y = mx \pm c \)
\( ax + by = c \)
Equations of parallel lines
Equation of a line - through (0,a)
Equation of a line - through (0,a) (rearranging)
Equation of a line - through (a,b)
Equation of a line - through (a,b)(rearranging)
Parallel lines - mixture
Equations of perpendicular lines
Equation of a line - through (0,a)
Equation of a line - through (0,a) (rearranging)
Equation of a line - through (a,b)
Equation of a line - through (a,b) (rearranging)
Perpendicular lines mixture
Parallel and perpendiclar mixture
Equation of a tangent to a circle
Non-Linear graphs
Quadratic graphs
Sketching \(y = x^2 \pm bx \pm c \)
Quadratic graphs - points to plot
State the vertex of a quadratic graph
Complete the square and find the vertex (1)
Complete the square and find the vertex (2)
Symmetry (1) \( y= (x \pm a)(x\pm b) \)
Symmetry (2) \(y =x^2 \pm bx \pm c \)
Symmetry (3) \( y =ax^2 \pm bx \pm c \)
Roots (1) \(y =x^2 \pm bx \pm c \)
Roots (2) \( y =ax^2 \pm bx \pm c \)
Identify the roots from a graph
Identify the vertex from a graph
Solve \( x^2 \pm ax \pm b = \pm c \) from a graph
Equation of a circle
Finding the equation of a circle
Equation of a tangent to a circle
Trigonometry
Using the sine graph
Using the cosine graph
Sine and cosine graph
Indices
Simplifying
Multiplying terms \( ax^m \times b x^n \)
Dividing terms \( ax^n y^m \div cx \)
Simplifying \( (ax^n)^m \)
Simplifying -mixture
Missing powers (1)
Indices - Addition law - missing power \( x^n \times x^m = x^p \)
Indices - Subtraction law - missing power \( x^n \div x^m = x^p \)
Indices - raising to a power - missing power \( (x^n)^m = x^p \)
Missing powers - mixture
Solving equations
Solving (1) \( \fbox{?}^{\frac{n}{2}} = \frac{1}{m} \)
Solving (2) \( \fbox{?}^{\frac{n}{2}} = m \)
Solving (3) \( \fbox{?}^{\frac{n}{3}} = \frac{1}{m} \)
Solving (4) \( \fbox{?}^{\frac{n}{2}} = m \)
Solving (5) \( \fbox{?}^{-{\frac{n}{2}}} = m \)
Solving (6) \( \fbox{?}^{-{\frac{n}{3}}} = m \)
Solving (7) \( a^m \times b^{\fbox{?}} = m \)
Inequalities
Linear Inequalities - listing integer solutions
Inequalities (1) : \( a < x < b \)
Inequalities (2) : \( a \le x < b \)
Inequalities (3) : \( a < x \le b \)
Inequalities (4) : \( a \le x \le b \)
Inequalities mix (1 - 4)
Inequalities (5) : \( a < mx < b \)
Inequalities (6) : \( a \le mx < b \)
Inequalities (7) : \( a < mx \le b \)
Inequalities (8) : \( a \le mx \le b \)
Inequalities mix (5 - 8)
Inequalities (9) : \( a < mx + c < b \)
Inequalities (10) : \( a \le mx + c < b \)
Inequalities (11) : \( a < mx + c \le b \)
Inequalities (12) : \( a \le mx + c \le b \)
Inequalities mix (9 - 12)
Linear Inequalities - listing integer solutions
Inequalities (13) : \( a < mx - c < b \)
Inequalities (14) : \( a \le mx - c < b \)
Inequalities (15) : \( a < mx - c \le b \)
Inequalities (16) : \( a \le mx - c \le b \)
Inequalities mix (13 - 16)
Inequalities (17) : \( a < c - mx < b \)
Inequalities (18) : \( a \le c - mx < b \)
Inequalities (19) : \( a < c - mx \le b \)
Inequalities (20) : \( a \le c - mx \le b \)
Inequalities mix (17 - 20)
Inequalities mix (9 - 20)
Linear Inequalities - single integer solutions
Integers (1) : Smallest value\( ax + b > c \)
Integers (2) : Smallest value \( ax - b > c \)
Integers (3) : Largest value \( ax - b < c \)
Linear Inequalities - single integer solutions
Integers (4) : Largest value \( ax + b < c \)
Integer solutions - mixture
Linear Inequalities
Solving (1): \( x + a <> b \)
Solving (2): \( x - a <> b \)
Solving (3): \( x \pm a <> b \)
Solving (4): \( ax + b <> c \)
Solving (5): \( ax - b <> c \)
Solving (6): \( ax \pm b <> c \)
Solving (7): \( \frac{x}{a} - b <> c \)
Solving (8): \( \frac{x}{a} + b <> c \)
Solving (9): \( \frac{x + a}{b} <> c \)
Solving (10): \( \frac{x - a}{b} <> c \)
Solving (11):\( a(bx + c) <> d \)
Solving (12):\( a(bx - c) <> d \)
Solving (13):\( a(bx \pm c) <> d \)
Mixture (1) - (13)
Solving (14):\( a(b - cx) <> d \)
Solving (15):\( a - \frac{x}{a} <> d \)
Solving (16):\( \frac{a - x}{b} <> d \)
Solving mixture (14) - (16)
Solving mixture (1) - (16)
Linear Inequalities
Solving (1): \( a < bx + c < d \)
Solving (2): \( a < bx - c < d \)
Solving (3): \( a < b - cx < d \)
Inequalitites -defining shaded regions
Representing (1):\( y \le a \) or \( y \lt a \)
Representing (2):\( y \ge a \) or \( y \gt a \)
Representing (3):\( x \le a \) or \( x \lt a \)
Representing (4):\( x \ge a \) or \( x \gt a \)
Representing (5):\( ax+by \le c \) or \( ax+by \lt c \)
Representing (6):\( ax+by \ge c \) or \( ax+by \gt c \)
Representing (7):\( ax+by \le c \) and axes bounds
Representing (8):\( ax+by \ge c \\\ \)axes bounds
Representing (9):\( ax+by \le c \\\ x \ge p \\\ , \\\ y \ge 0 \)
Representing (10):\( ax+by \ge c \\\ x \le p \\\ , \\\ y \le 0 \)
Representing (11):\( ax+by \le c \\\ x \ge 0 \\\ , \\\ y \ge p \)
Representing (12):\( ax+by \ge c \\\ x \le 0 \\\ , \\\ y \le p \)
Representing (13):\( ax+by \le c \\\ x \ge p \\\ , \\\ y \ge q \)
Representing (14):\( ax+by \ge c \\\ x \le p \\\ , \\\ y \le q \)
Inequalitites -defining unshaded regions
Representing (15):\( y \ge a \) or \( y \gt a \)
Representing (16):\( y \le a \) or \( y \lt a \)
Representing (17):\( x \ge a \) or \( x \gt a \)
Representing (18):\( x \le a \) or \( x \lt a \)
Representing (19):\( ax+by \ge c \) or \( ax+by \gt c \)
Representing (20):\( ax+by \le c \) or \( ax+by \lt c \)
Representing (21):\( ax+by \ge c \\\ \) and axes bounds
Representing (22):\( ax+by \le c \\\ \) and axes bounds
Representing (23):\( ax+by \ge c \\\ x \le p \\\ , \\\ y \le 0 \)
Representing (24):\( ax+by \le c \\\ x \ge p \\\ , \\\ y \ge 0 \)
Representing (25):\( ax+by \ge c \\\ x \le 0 \\\ , \\\ y \le p \)
Representing (26):\( ax+by \le c \\\ x \ge 0 \\\ , \\\ y \ge p \)
Representing (27):\( ax+by \ge c \\\ x \le p \\\ , \\\ y \le q \)
Representing (28):\( ax+by \le c \\\ x \ge p \\\ , \\\ y \ge q \)
Quadratic inequalitites
Solving (1) :\(x^2 - bx + c \ge 0 \)
Solving (2) :\(x^2 - bx + c \le 0 \)
Solving (3) :\(x^2 - bx - c \ge 0 \)
Solving (4) :\(x^2 - bx - c \le 0 \)
Solving (5) :\( x^2 + bx - c \ge 0 \)
Quadratic inequalitites
Solving (6) :\( x^2 + bx - c \le 0 \)
Solving (7) :\( x^2 + bx + c \ge 0\)
Solving (8) :\( x^2 + bx + c \le 0\)
Solving Mixture
Sequences
Counting patterns and continuing
Counting in 50's
Contine a linear sequence (integers)
Counting in tenths
Counting in tenths hundredths
Directed numbers
Finding missing terms
Missing terms - linear sequences
Missing terms - tenths
Missing terms - hundredths
Missing terms - directed numbers
Generating sequences
Generate a sequence given the first term and rule
Generate sequences given an algebraic rule
Generate an increasing sequence - nth term
Generate a decreasing sequence - nth term
Generate a linear sequence - nth term
Generate a quadratic sequence - nth term
Finding the nth term
Find the nth term linear - inc
Find the nth term linear - dec
Find the nth term linear - mixture
Find the nth term quadratic
Find the 10th term - quadratic
Find the nth term mixture - lin/quad
Fractions sequences - nth term
Find the nth term mixture - lin/quad
Other sequences
Continue a fibonacci sequence
Continue a geometric sequence
Find missing terms in a geometric sequence
Recognise a linear sequence
Fractions and sequences
Algebraic sequences
Simplifying Expressions
Collecting like terms
Simplifying -addition - single variable
Collecting like terms - Single variable (1)
Collecting like terms - Single variable (2) (across 0)
Collecting like terms - Two variables
Collecting like powers of a variable
Multipication and division
Multiplying terms (1)
Multiplying terms (2): \( a \times x \times b \times x \)
Multiplying terms (3): \( ax \times bx \)
Dividing terms (1)
Dividing terms (2) :\( ax \div b \)
Expand and simplify
Expanding (1): \( a( bx + c) + d(ex + f) \)
Expanding (2): \( a( bx - c) + d(ex + f) \)
Expanding (3): \( a( bx + c) + d(ex - f) \)
Expanding (4): \( a( bx - c) + d(ex - f) \)
Expanding Mixture (1 - 4)
Expanding (5): \( a( bx + c) - d(ex + f) \)
Expanding (6): \( a( bx - c) - d(ex + f) \)
Expanding (7): \( a( bx + c) - d(ex - f) \)
Expanding (8): \( a( bx - c) - d(ex - f) \)
Expanding Mixture (5 - 8)
Expanding Mixture (1 - 8)
Fractions - Addition and Subtraction
Simplify (1):\( \frac{x}{a}+ \frac{x}{b} \)
Simplify (2):\( \frac{x}{a}- \frac{x}{b} \)
Simplify (3):\( \frac{ax}{b} + \frac{cx}{d} \)
Simplify (4):\( \frac{ax}{b} - \frac{cx}{d} \)
Simplify (5):\( \frac{x+a}{b} + \frac{x+c}{d} \)
Simplify (6):\( \frac{x+a}{b} - \frac{x+c}{d} \)
Simplify (7):\( \frac{x+a}{b} - \frac{x-c}{d} \)
Simplify (8):\( \frac{x-a}{b} - \frac{x+c}{d} \)
Simplify (9):\( \frac{x-a}{b} - \frac{x-c}{d} \)
Simplify (10):\( \frac{x-a}{b} + \frac{x-c}{d} \)
Simplify (11):\( \frac{x+a}{b} - \frac{x-c}{d} \)
Simplify Mixture
Fractions - Multiplication and division
Multiply algebraic fractions
Divide algebraic fractions
Substitution
Positive Integers
Substitution (1): \( x + a \)
Substitution (2): \( x - a \)
Substitution (3): \( ax \)
Substitution (4): \( \frac{a}{x} \)
Substitution (5): \( y = ax + b \)
Substitution (6): \( y = ax - b \)
Substitution (7): \( y =b - ax \)
Substitution (8): \( y = \frac{x}{a} + b \)
Substitution (9): \( y = \frac{x+a}{b} \)
Substitution (10): \( y = \frac{x-a}{b} \)
Substitution (11): \( y = \frac{ax + b}{c} \)
Substitution (12): \( y = \frac{ax - b}{c} \)
Substitution (13) : \( y = ax^2 \)
Substitution (14) : \( y = ax^2 + b \)
Substitution (15) : \( y = ax^2 - b \)
Substitution (16) : \( y = b - ax^2 \)
Substitution (17) : \( y = \frac{ax^2}{ b} \)
Substitution (18) : \( y = \frac{ax^2}{ b} + c \)
Substitution (19) : \( y = \frac{ax^2}{ b} - c \)
Substitution (20) : \( y= \sqrt{ax+b}\)
Substitution (21) : \( y= \sqrt{b-ax} \)
Substitution (22) : \( y = a\sqrt{x} + b \)
Substitution (23) : \( y = b - a\sqrt{x} \)
Substitution (24) : \( y = \sqrt{ \frac{x+a}{b}}ax^2 + b \)
Substitution (25) : \( y = \sqrt{ \frac{x+a}{b}}ax^2 - b \)
Substitution (26) : \( y = \sqrt{b(x+a)} \)
Substitution (27) : \( y = \frac{a}{ \sqrt{x+b}} \)
Substitution (28) : \( y = x^2 \pm x \)
Substitution (29) : \( y = ax^2 \pm x \)
Substitution (30) : \( y = x^2 \pm ax \)
Substitution (31) : \( y = ax^2 \pm bx \)
Substitution (32) : \( y= x^2 \pm bx + c \)
Substitution (33) : \( y = bx-ax^2 \pm c \)
Substitution (34) : \( y = ax^3 \pm bx^2 \)
Substitution (35) : \( y = ax^3 \pm bx^2 \pm cx \pm d\)
Negative Integers
Negative integers (1) : \(y = x + a \)
Negative integers (2) : \(y = x + a \)
Negative integers (3) : \(y = a - x \)
Negative integers (4) : \(y = ax \)
Negative integers (5) : \(y = \frac{x}{a} \)
Negative integers (6) : \(y = \frac{a}{x} \)
Negative integers (7) : \(y = ax + b \)
Negative integers (8) : \(y = ax - b \)
Negative integers (9) : \(y = b - ax \)
Negative integers (10) : \(y = \frac{x}{a} + b \)
Negative integers (11) : \(y = \frac{x+a}{b} \)
Negative integer{ (12) : \(y = \frac{x-a}{b} \)
Negative integers (13) : \(y = \frac{ax+b}{c} \)
Negative integers (14) : \(y = \frac{ax-b}{c} \)
Negative integers (15) : \(y = ax^2 \)
Negative integers (16) : \(y = ax^2 + b \)
Negative integers (17) : \(y = ax^2 - b \)
Negative integers (18) : \(y = b - ax^2 \)
Negative integers (19) : \(y = (ax)^2+b \)
Negative integers (20) : \(y = \frac{ax^2}{b} \)
Negative integers (21) : \(y = \frac{ax^2}{b} + c \)
Negative integers (22) : \(y = \frac{ax^2}{b} - c \)
Negative integers (23) : \(y = \sqrt{ax+b} \)
Negative integers (24) : \(y = \sqrt{b-ax} \)
Negative integers (25) : \(y = \sqrt{\frac{x+a}{b}} \)
Negative integers (26) : \(y = \sqrt{b(x-a)} \)
Negative integers (27) : \(y = \frac{a}{\sqrt{x+b}} \)
Negative integers (28) : \(y = x^2 \pm x \)
Negative integers (29) : \(y = ax^2 \pm x \)
Negative integers (30) : \(y = x^2 \pm ax \)
Negative integers (31) : \(y = ax^2 \pm bx \)
Negative integers (32) : \(y = x^2 \pm bx \pm c \)
Negative integers (33) : \(y = bx-ax^2\pm c \)
Negative integers (34) : \(y = ax^3 \pm bx^2 \)
Negative integers (35) :\(y = ax^3 \pm bx^2 \pm cx \pm d\)
Fractional values
Fractions (2) : \(y = b - ax \)
Fractions (3) : \(y = a(x \pm b) \)
Fractions (4) : \( y = ax^2 \pm b \)
Fractions (5) : \( y = ax^2 \pm bx \)
Using SUVAT formulae
SUVAT - Calculating the initial velocity \(v = u + at \)
SUVAT - Calculating the acceleration \(v = u + at \)
SUVAT - Calculating the time \(v = u + at \)
SUVAT - Calculating the velocity \(v = u + at \)
SUVAT - mixture \(v = u + at \)
SUVAT - Calculating the initial velocity \(s = ut + \frac{1}{2}at^2 \)
SUVAT - Calculating the displacement \(s = ut + \frac{1}{2}at^2 \)
SUVAT - mixture \(s = ut + \frac{1}{2}at^2 \)
SUVAT - Calculating the initial velocity \(v^2 = u^2 + 2as \)
SUVAT - Calculating the displacement \(v^2 = u^2 + 2as \)
SUVAT - Mixture \(v^2 = u^2 + 2as \)
Compound Measures
Proportion
Measures
Percentages - calculator
Percentages - non-calculator
Ratio
Compound Measures
Speed Distance Time
Speed Distance Time (1) - speed
Speed Distance Time (2) - distance
Speed Distance Time (3) - time
Speed Distance Time - Mixture
Average speed problems
Speed Distance Time - (easier)
Speed Distance Time (4) - speed
Speed Distance Time (5) - distance
Speed Distance Time (6) - time
Speed Distance Time - Mixture
Mass, Volume, Density
Density mass volume (1) - density
Density mass volume (2) - mass
Density mass volume (3) - volume
Density mass volume - Mixture
Force Area Pressure
Pressure Force and Area (1) - pressure
Pressure , Force and Area (2) - force
Pressure , Force and Area (3) - area
Pressure , Force and Area - mixture
Population Density Area
Population Density (1) - density
Population Density (2) - population
Population Density (3) - area
Population Density - mixture
Converting units - speed
Converting units of speed m/s to km/h (1)
Converting units of speed km/h to m/s (2)
Converting units of speed (1 & 2)
Converting units of speed km/h to mph (3)
Converting units of speed mhp to km/h (4)
Converting units of speed (3 & 4)
Converting units - density and flow
Converting units of density g/cm
3
to kg/m
3
(1)
Converting units of density kg/m
3
to g/cm
3
(2)
Converting units of density (1 & 2)
Converting units of rates of flow
Proportion
Mixed proportion problems
Solve problems involving scaling
Solve problems involving rates
Direct Proportion problems (£s)
Direct Proportion problems
Solving recipe problems
Calculating wages
Wages and overtime
Solving best buy problems
UK currency for foreign currency
Foreign currency to UK currency
Exchange rates - comparing prices
Inverse proportion problems
Forming and using formulae
Direct proportion (1) : \( y \propto kx \)
Direct proportion (2) : \( y \propto kx^2 \)
Direct proportion (3) : \( y \propto k \sqrt[3]{x} \)
Direct proportion (4) : \( y \propto kx^3 \)
Direct proportion (5) : \( y \propto \ k \sqrt{x} \)
Direct proportion - formula - mixture
Forming and using formulae
Inverse proportion (1) : \( y \propto \frac{k}{x} \)
Inverse proportion (2) : \( y \propto \frac{k}{x^2} \)
Inverse proportion (3) : \( y \propto \frac{k}{\sqrt{x}} \)
Inverse proportion - mixture
Proportion - mixture
Measures
Time
Time from a digital clock
am and pm when comparing times
Understanding the order of the months
Converting (1): years months days
Converting (2): weeks days hours
Converting (3): hours minutes
Converting time mixture
Minutes and seconds as seconds
Seconds as minutes and seconds
Comparing seconds and minutes and seconds
Time
Comparing time intervals
Calculate the time after - minutes
Calculate the time - before
Calculate the time Mixture
Calculating time intervals (1) (5 minutes)
Calculating time intervals (2)
Working out end times (3)
Working out start times (4)
Mixture (1) to (4)
Metric Measures - Length
Equivalence - km and m
Equivalence - m and cm
Equivalence -m and cm (decimals)
Equivalence - cm and mm
Equivalence - cm and mm (decimals))
Addition - mixed lengths
Subtraction - mixed lengths (1)
Subtraction - mixed lengths (2)
Comparing - km and m
Comparing - mixed units
Metric - Mass
Comparing - mixed measures
Addition - mixed measures
Subtraction - mixed measures
Metric - Capacity
Equivalence ml and litres
Addition- mixed measures
Subtraction - mixed measures
Metric - Area and volume
Metric units of area - \( mm^2 \) and \( cm^2 \)
Metric units of area - \( cm^2 \) and \( m^2 \)
Metric units of area - mixture
Metric units of volume - \( mm^3 \) and \( cm^3 \)
Metric units of volume - \( cm^3 \) and \( m^3 \)
Metric units of volume - mixture
Mixed metric measures
Mixed Equivalence - kg and km
Mixed Equivalence - ml and mm
Equivalence - mixed measures
Addition of mixed metric measures
Imperial Measures
Miles and km
Inches and cm
Kilograms and pounds
Pints and gallons
Mixed imperial measures
Error intervals for rounded measures
Error intervals for rounded measures
Percentages - calculator
Percentages with a calculator
Calculating a percentage of a quantity
Identifying multipliers for percentage increases
Identifying multixliers for percentage decreases
Increasing by a given percentage
Decreasing by a given percentage
Calculate the percentage increase
Calculate the percentage decrease
Calculate the percentage change
Expressing as a percentage
Finding the original < 100%
Finding the original > 100%
Repeated percentage change
Stating a formula for % increase
Stating a formula for % decrease
Identifying the interest rate
Identifying the rate of depreciation
Calculating compound interest
Compound interest - years
Compound interest - total
Population decrease - total
Population decrease - overall percentage decrease
Population Decrease - years
Calculate depreciation -car
Percentages non-calculator
Percentage of a quantity
Understanding percentages (35% = 3 x 10% + 5%)
50% of a quantity
25% and 50% of a quantity
10% of a quantity
10% and 20% of a quantity
20% of a quantity
10% and 5% of a quantity
Percentage of a quantity
5% of a quantity
5% 10% and 15% of quantity
5% 10% and 20% of a quantity
15% of a quantity
Multiples of 5%
Percentages - missing values
Mixed Questions
Expressing as a percentage
Calculate a percentage increase
Calculate a percentage decrease
Calculate a percentage change
Ratio
Simplifying and equivalence
Using ratio language
Using the ratio symbol
Simple ratio problems
Solve problems involving ratios of the form m : n
Simplifying ratios
Simplfying ratios (mixed units)
Expressing in the form 1:n or n:1
Expressing a ratio as a fraction
Expressing a fraction as a ratio
Dividing in a ratio
Dividing in a given ratio
Dividing in a given ratio - difference known
Dividing in a given ratio - one share known
Find the larger share - smaller known
Find the smaller share -larger known
Find the larger share - difference known
Find the smaller share - difference known
Mixed questions
Maps and scale
Using scale drawings
Interpret scale diagrams - model to real
Interpret scale diagrams - real to model to real
Interpret maps - map to real
Interpret maps - real to map
Combined ratios
a:b and b:c - find a:c (1)
a:b and b:c - express as a fraction (2)
a:b and b:c -calculate a quantity (3)
na =mb and b:c - find a:b:c (4)
na =mc and b:c - find a:c (5)
Angles
Area (polygons)
Area (circles)
Bearings
Coordinates
Measures
Perimeter
Pythagoras
Similarity
Surface area
Transformations
Trigonometry
Vectors
Volume
Angles
Classifying Angles and turns
Classifying angles
Angles (degrees) - clocks hands 5 mins intervals
Basic Angles Facts
Angles on a straight line (1)
Angles on a straight line (2)
Angles at a point (1)
Angles at a point (2)
Vertically Opposite Angles
Angles and parallel lines
(1) Corresponding angles
(2) Allied/co-interior angles
(3) Alternate angles
Basic Mixture (1-3)
Parallel lines (1)
Parallel lines (2)
Parallel lines (3)
Parallel lines (4)
Angles in Triangles
Angles in a triangle
Angles in an isosceles triangle (1)
Angles in an isosceles triangle (2)
Angles in a right angled triangle
Calculate missing angles triangles
Angles in polygons
Calculate angles in a quadrilateral
Interior angles - polygons
Exterior angles - polygons
Bearings
Bearings and compass directions
Compass directions and right angles
Bearings -words
Bearings - with diagrams
(1) : Bearings - from A to B
(2) : Bearings - from B to A
(3) : Bearings - from A to B
(4) : Bearings - from B to A
Area - Polygons
Non calculator
Squares with diagrams
(1) : Area of a square
(2) : Calculate the side length
(3) : Calculate the perimeter - area known
(4) : Calculate the area - perimeter known
Rectangles with diagrams
(5) : Area of a rectangle - non calc
(6) : Calculate the side length
(7) : Calculate the area - perimeter known
(8) : Calculate the perimeter - area known
Triangles with diagrams
(9) : Right angled triangle area
(10) : Right angled triangle base
(11) : Right angled triangle height
(12) : Non right-angled triangle area
(13) : Non right-angled triangle base
(14) : Non right-angled triangle height
(15) : Obtuse-angled triangle area
(16) : Obtuse-angled triangle base
(17) : Obtuse-angled triangle height
Parallelograms with diagrams
(18) : Parallelogram area
(19) : Parallelogram base
(20) : Parallelogram height
Trapeziums with diagrams
(21) : Trapezium area
(22) : Trapezium base
(23) : Trapezium height
Calculator
Squares With diagrams
(1c) : Area of a square
(2c) : Calculate the side length - area known
(3c) : Calculate the perimeter - area known
(4c) : Calculate the area - perimeter known
Rectangles with diagrams
(5c) : Area of a rectangle
(6c) : Calculate the side length
(7c) : Calculate the area - perimeter known
(8c) : Calculate the perimeter - area known - calc
Triangles with diagrams
(9c) : Right angled triangle area
(10c) : Right angled triangle base
(11c) : Right angled triangle height
(12c) : Non right-angled triangle area
(13c) : Non right-angled triangle base
(14c) : Non right-angled triangle height
(15c) : Obtuse-angled triangle area
(16c) : Obtuse-angled triangle base
(17c) : Obtuse-angled triangle height
Parallelograms with diagrams
(18) : Parallelogram area
(19) : Parallelogram base
(20) : Parallelogram height
Trapeziums with diagrams
(21c) : Trapezium area
(22c) : Trapezium base
(23c) : Trapezium height
Compound shapes - with diagrams
(24) : Compound shapes - missing length
(25) : Compound shapes - area
(26) : Compound shapes - area
Compound shapes - with diagrams
(24c) : Compound shapes - missing length
(25c) : Compound shapes - area
(26c) : Compound shapes - area
Non calculator
Area of polygons - no-diagrams
(27) : Area of a rectangle
(28) : Height of a rectangle
(29) : Area of a rectangle mixture
(30) :Area of a triangle
(31) : Area of a triangle - missing length
(32) : Area of a triangle - mixture
(33) : Area of a parallelogram
(34) : Area of a parallelogram - missing length
(35) : Area of a trapezium
(36) : Area of a trapezium - missing lengths
Calculator
Area of polygons - no diagrams
(27c) : Area of a rectangle
(28c) : Height of a rectangle
(29c) : Area of a rectangle mixture
(30c) : Area of a triangle
(31c) : Area of a triangle - missing length
(32c) : Area of a triangle - mixture
Area of circles and sectors
Non calculator
Area - with diagrams
(1) : Area of a circle - radius known
(2) : Area of a circle - diameter known
(3) : Area of a circle - mixture
(4) : Area of a semi-circle
(5) : Area of a sector
(6) : Area of a sector - angle
(7) : Area of a sector - radius
Area - without diagrams
(8) : Area of a circle - radius known
(9) : Area of a circle - diameter known
(10) : Area of a circle - mixture
(11) : Area of a sector
(12) : Area of a sector - radius
(13) : Area of a sector - angle
(14) : Area of a sector - mixture
Calculator
Area - with diagrams
(1c) : Area of a circle radius - calc (diagram)
(2c) : Area of a circle diameter - calc (diagram)
(3c) : Area of a circle -mixture - (diagram)
(4c) : Area of a semi-circle
(5c) : Area of a sector
(6c) : Area of a sector - radius
(7c) : Area of a sector - angle
Area - without diagrams
(8c) : Area of a circle - radius known
(9c) : Area of a circle - diameter known
(10c) : Area of a circle mixture
(11c) : Area of a sector - calc
(12c) : Area of a sector - radius
(13c) : Area of a sector - angle
(14c) : Area of a sector - mixture
Shaded area problems
Shaded Area 1
Shaded Area 2
Shaded Area 3
Shaded area problems
Shaded Area 4
Shaded Area 5
Shaded Area 6
Area and circumference mixtures
Non-calculator
Area and circumference of circles - non calc
Area and circumference mixtures
Calculator
Area and circumference of circles - calc
Coordinates
Coordinates
1st quadrant
2nd Quadrant
3rd Quadrant
4th Quadrant
All 4 Quadrants
Perimeter
Non calculator
Squares - with diagrams
(1) : Perimeter of a square
(2) : Area - perimeter known
(3) : Perimeter - area known
(4) : Side length - perimeter known
Rectangles - with diagrams
(5) : Perimeter of a rectangle
(6) : Area - perimeter known
(7) : Perimeter - area known
(8) : Side length - perimeter known
Rectangle - without diagrams
(9) : Perimeter of a rectangle
(10) : Side length - perimeter known
Mixed polygons - without diagrams
(11) : Perimeter - square, rectangle and equilateral triangle
(12) : Perimeter of regular polygons
(13) : Side length - perimeter known
Calculator
Squares - with diagrams
(1c) : Perimeter of a square
(2c) : Area - perimeter known
(3c) : Perimeter - area known
(4c) : Side length - perimeter known
Rectangles - with diagrams
(5c) : Perimeter of a rectangle
(6c) : Area - perimeter known
(7c) : Perimeter - area known
(8c) : Side length - perimeter known
Rectangle - without diagrams
(9c) : Perimeter of a rectangle
(10c) : Side length - perimeter known
Mixed polygons - without diagrams
(11c) : Perimeter - square, rectangle and equilateral triangle
(12c) : Perimeter of regular polygons
(13c) : Side length - perimeter known
Perimeter of compound shapes
(1) : Compound shapes - 1 length missing
(2) : Compound shapes - 2 lengths missing
(3) : Compound shapes - perimeter
Circumference and arcs - with diagrams
(1) Circumference - radius known
(2) Circumference - diameter known
(3) Circumference - mixture
(4) : Semi-circle - perimeter
(5) : Arc length
(6) : Arc length - radius
(7) : Arc length - angle
(8) : Arc length - mixture
Circumference and arcs - without diagrams
(9) Circumference - radius known
(10) Circumference - diameter known
(11) Circumference - mixture
(12) Arc length
Circumference and area
(13)Area and circumference of circles
Circumference and arcs - with diagrams
(1c) : Circumference
(2c) : Circumference - radius
(3c) : Circumference - diameter
(4c) : Semi-circle
(5c) : Calculate the arc length
(6c) : Arc length - radius
(7c) : Arc length - angle
(8c) : Arc length - mixture
Circumference and arcs - without diagrams
(9c) Circumference - radius known
(10c) Circumference - diameter known
(11c) Circumference - mixture
(12c) Arc length
Circumference and area
(13c) Area and circumference of circles
Pythagoras' Theorem
Question with diagrams
(1) : Pythagoras - hypotenuse
(2) : Pythagoras - shorter side
(3) Pythagoras - any side
(4) : Height - equilateral triangle
(5) : Slant height - isoscles triangle
(6) : Height - isosceles triangle
(7) : Perimeter - isosceles triangle
(8) : Area - isosceles triangle
(9) Length of a diagonal
(10) : Distance between 2 points
Question without diagrams
(11) : Calculating c in \( a^2 + b^2 =c^2 \)
(12) : Calculating a in \( a^2 + b^2 =c^2 \)
(13) : Calculating b in \( a^2 + b^2 =c^2 \)
(14) : Calculating the distance between 2 points
(15) : Compass directions and distance
(16) : Pythagoras - mixture
Non-calculator
(17) : Calculating any side - exact
Similarity
Length
Using scale factors - simple
Missing lengths - similar rectangles
Calculating missing sides in similar shapes
Enlargement - lengths mixture
Enlargement - finding the new length
Enlargement - finding the original length
Enlargement - mixture - length
Area
Enlargement - area - mixture
Enlargement - finding the new area
Enlargement - finding the original area
Enlargement - area mixture
Volume
Enlargement - finding the new volume
Enlargement - finding the original volume
Enlargement - volume mixture
Area and volume
Englargement - area and volume mixture
Englargement - mixture
Measures
Time
Time from a digital clock
am and pm when comparing times
Understanding the order of the months
Converting (1): years months days
Converting (2): weeks days hours
Converting (3): hours minutes
Converting time mixture
Minutes and seconds as seconds
Seconds as minutes and seconds
Comparing seconds and minutes and seconds
Time
Comparing time intervals
Calculate the time after - minutes
Calculate the time - before
Calculate the time Mixture
Calculating time intervals (1) (5 minutes)
Calculating time intervals (2)
Working out end times (3)
Working out start times (4)
Mixture (1) to (4)
Metric Measures - Length
Equivalence - km and m
Equivalence - m and cm
Equivalence -m and cm (decimals)
Equivalence - cm and mm
Equivalence - cm and mm (decimals))
Addition - mixed lengths
Subtraction - mixed lengths (1)
Subtraction - mixed lengths (2)
Comparing - km and m
Comparing - mixed units
Metric - Mass
Comparing - mixed measures
Addition - mixed measures
Subtraction - mixed measures
Metric - Capacity
Equivalence ml and litres
Addition- mixed measures
Subtraction - mixed measures
Metric - Area and volume
Metric units of area - \( mm^2 \) and \( cm^2 \)
Metric units of area - \( cm^2 \) and \( m^2 \)
Metric units of area - mixture
Metric units of volume - \( mm^3 \) and \( cm^3 \)
Metric units of volume - \( cm^3 \) and \( m^3 \)
Metric units of volume - mixture
Mixed metric measures
Mixed Equivalence - kg and km
Mixed Equivalence - ml and mm
Equivalence - mixed measures
Addition of mixed metric measures
Imperial Measures
Miles and km
Inches and cm
Kilograms and pounds
Pints and gallons
Mixed imperial measures
Error intervals for rounded measures
Error intervals for rounded measures
Trigonometry
The basics - identifying the correct sides
Identifying the sine ratio of an angle (1)
Identifying the sine ratio of an angle (2)
Identifying the sine ratio of an angle (mix)
Identifying the cosine ratio of an angle (1)
Identifying the cosine ratio of an angle (2)
Identifying the cosine ratio of an angle (mix)
Identifying the tangent ratio of an angle (1)
Identifying the tangent ratio of an angle (2)
Identifying the tangent ratio of an angle (mix)
Identifying mixed ratios of angles (1)
Identifying mixed ratios of angles (2)
Identifying mixed ratios of angles (mix)
The basics - using a calculator
Evaluating sin(x),cos(x) or tan(x)
Evaluating a × sin(x),a × cos(x),a × tan(x)
Evaluating a ÷ sin(x),a ÷ cos(x),a ÷ tan(x)
Sine ratio
Sine ratio - calculating the opposite(1)
Sine ratio - calculating the opposite(2)
Sine ratio - calculating the opposite(mix)
Sine ratio - calculating the hypotenuse (1)
Sine ratio - calculating the hypotenuse (2)
Sine ratio - calculating the hypotenuse (mix)
Sine ratio - calculating sides (1)
Sine ratio - calculating sides (2)
Sine ratio - calculating sides (mix)
Sine ratio
Sine ratio - calculating the angle (1)
Sine ratio - calculating the angle (2)
Sine ratio - calculating the angle (mix)
Sine ratio - calculating angles/sides (1)
Sine ratio - calculating angles/sides (2)
Sine ratio - calculating angles/sides (mix)
Cosine ratio
Cosine ratio - calculating the adjacent(1)
Cosine ratio - calculating the adjacent(2)
Cosine ratio - calculating the adjacent(mix)
Cosine ratio - calculating the hypotenuse (1)
Cosine ratio - calculating the hypotenuse (2)
Cosine ratio - calculating the hypotenuse (mix)
Cosine ratio - calculating sides (1)
Cosine ratio - calculating sides (2)
Cosine ratio - calculating sides (mix)
Cosine ratio
Cosine ratio - calculating the angle (1)
Cosine ratio - calculating the angle (2)
Cosine ratio - calculating the angle (mix)
Cosine ratio - calculating angles/sides (1)
Cosine ratio - calculating angles/sides (2)
Cosine ratio - calculating angles/sides (mix)
Tangent ratio
Tangent ratio - calculating the opposite (1)
Tangent ratio - calculating the opposite (2)
Tangent ratio - calculating the opposite (mix)
Tangent ratio - calculating the adjacent (1)
Tangent ratio - calculating the adjacent (2)
Tangent ratio - calculating the adjacent (mix)
Tangent ratio - calculating sides (1)
Tangent ratio - calculating sides (2)
Tangent ratio - calculating sides (mix)
Tangent ratio
Tangent ratio - calculating the angle (1)
Tangent ratio - calculating the angle (2)
Tangent ratio - calculating the angle (mix)
Tangent ratio - calculating angles and sides (1)
Tangent ratio - calculating angles and sides (2)
Tangent ratio - calculating angles and sides (mix)
Mixed ratios
Mixed ratios - calculating angles
Mixed ratios - calculating sides
Mixed ratios - calculating angles and sides
Trigonometry in 3D - Cuboid Problems
Trigonometry in 3D - Pyramid Problems
Trigonometry in 3D - mixed Problems
Trigonometry - Sine Rule
Sine rule - calculating an angle (1)
Sine rule - calculating an angle (2)
Sine rule - calculating an angle (mix)
Sine rule - calculating sides (1)
Sine rule - calculating sides (2)
Sine rule - calculating sides (mix)
Sine rule - calculating angles and sides
Trigonometry - Cosine Rule
Cosine rule - calculating an angle
Cosine rule - calculating sides
Cosine rule - calculating angles and sides
Sine and cosine rules calculating sides
Sine and cosine rules calculating an angle
Sine and cosine rules mixture
Sine and area
Calculating the area (1)
Calculating the area (2)
Calculating the area (1 & 2)
Calculating an angle
Calculating a side
Side and angle mixture
Mixture
Exact Values
Using Exact Trig Values
Vectors
Column Vectors
Column vectors - sum and difference
Column vectors - missing values
Column vectors mixture
Writing as a column vector
Vector geometry
Vector geometry
Transformations
Translation
Translations - x direction
Translations - y direction
Translations
Reflection
Reflection (1) : x = a
Reflection (2) : y = a
Reflection mix (1 & 2)
Reflection (3) : y = x
Reflection (4) : y = -x
Reflection mix (1 - 4)
Rotation
Rotation (1) : 90^o Clockwise
Rotation (2) : 90^o Clockwise
Rotation (3) : 180^o Anti-clockwise
Rotation Mixture
Enlargement
Enlargement (1) : scale factor 2
Enlargement (2) : scale factor 2
Enlargement (3) : scale factor 0.5
Enlargement mix (1 to 3)
Enlargement (4) :scale factor -2
Enlargement (5) :scale factor -0.5
Enlargement mix (4 to 5)
Enlargement mix (1 to 5)
Volume
Volume - with diagrams
Cuboids
(1) : Volume of a cuboid
(2) : Volume of a cuboid - missing lengths
Prisms
(3) : Triangular prism
(4) : Missing lengths
(5) :Missing width
Cylinders
(6) : Cylinder -radius known
(7) : Cylinder - diameter known
(8) : Find the radius
(9) : Find the height
Cones
(10) : Cone - height known
(11) : Cone - slant height known
(12) : Find the radius
(13) : Find the height
Pyramids
(14) : Square based pyramid volume
(15) : Square based pyramid volume - find the height
(16) : Square based pyramid volume - find the base
Spheres
(17) : Sphere - radius known
(18) : Sphere - diameter known
(19) : Find the radius
(20) : Find the diameter
Hemispheres
(21) : Hemisphere - radius known
(22) : Hemisphere -diameter known
(23) : Find the radius
(24) : Find the diameter
Volume - without diagrams
Cuboids
Volume of a cuboid
Cylinders
Volume of a cylinder - non calc
Volume of a cylinder - radius known - non calc
Volume of a cylinder -diameter known - non calc
Cones
Volume of a cone - radius and vertical height known
Volume of a cone -radius and slant height known
Volume of a cone - mixture
Prisms
Volume of a triangular prism (1)
Volume of a trapeziod prism(2)
Volume of prisms mixture(3)
Spheres
Volume of a sphere
Calculate the radius of a sphere given the volume
Volume of a sphere and radius mixture
Pyramids
Volume of a pyramid
Frustums
Volume of a frustum
Surface area
Questions with diagrams
Cuboids
(1) : Cuboid
Prisms
(2) : Trianguar prism
Cylinders
(3) : Curved SA - radius
(4) : Curved SA - diameter
(5) : Total SA - radius
(6) : Total SA - diameter
Cones
(7) : Cone - height known
(8) : Cone - slant height known
Spheres
(9) : Sphere - radius known
(10) : Sphere - diameter known
(11) : Sphere - find radius
(12) : Sphere - find diameter
Hemisphere
(13) : Hemisphere - radius known
(14) : Hemisphere - diameter known
(15) : Hemisphere - find radius
(16) : Hemisphere - find diameter
Questions without diagrams
Cuboids
(17) : Cuboid
Prisms
(18) : Triangular prism
(19) : Trapeziod prism prism
(20) : Prisms mixture
Cylinders
(21) : Cylinder - radius known
(22) : Cylinder - diameter known
(23) : Curved surface area - radius known
(24) Curved surface area - diameter known
Spheres
(25) :Sphere
(26) : Find the radius of a sphere
(27) : Sphere mixture
Averages
Collecting Data
Representing Data
Probability
Averages
Calculate the range
Calculate the mean - from a list
Mean given - find a missing value
Calculate the median
Find the mode
Collecting Data
Capture-recapture - estimating the population
Capture-recapture - calculating the sample size
Capture-recapture - calculating the number marked
Capture - recapture - mixture
Capture-recapture - mixture
Representing Data
Pie Charts - calculating angles
Probability
Calculated expected outcome
Calculating relative frequency
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 11
Term 1
Term 2
Term 3
Year 3 - Term 1
Place Value
Partition numbers up to 100
Hundreds and tens
Partition numbers up to 1000
Finding 1 more or less than a number
Finding 10 more or less than a number
Finding 100 more or less than a number
Finding 1,10 or 100 more or less
Compare numbers up to 1000
Counting in 50's
Addition
Number bonds within 10
Add 1's across 10
Add 10's across 100
Add two 3 digit numbers (no exchanges)
Add two 3 digit numbers (across 10)
Add two 3 digit numbers
Add two 3 digit numbers across a 10 and/or 100
Subtraction
Subtract 1's across 10
Subtract 10's across 100
Subtract two 3 digit numbers (no exchanges)
Subtract two 3 digit numbers across a 10
Subtract two 3 digit numbers across a 100
Subtract two 3 digit numbers across a 10 or 100
Subtract a 2 digit from a 3 digit numbers
Complements to 100
Addition and Subtraction
Add and subtract 1's
Add and subtract 10's
Add a 2 digit to a 3 digit number
Add and subtract a 2 digit from a 3 digit numbers
Add and subtract 100's
Add and subtract 1's 10's or 100's
Multiplication
Listing multiples of 2
Listing multiples of 5 and 10
Multiplying by 3
Multiplying by 4
Multiplying by 8
Division
Listing multiples of 2
Dividing by 3
Dividing by 4
Dividing by 8
Year 3 - Term 2
Multiplication
Multiplication - by 10
Comparing single digit multiplication calculations
Comparing calculation involving multiples of 10
2 digit by a 1 digit number - no exchange
2 digit by a 1 digit number - with exchange
Solve problems involving scaling
Division
Division - related calculations
Comparing multiplication and division calculations
2-dgit by a 1-digit number- no exchange
2-digit by a 1-digit number- with exchange
2-dgit by a 1-digit number- with remainders
Length and perimeter
Comparing measures in different units
Equivalent lengths (metres and centimetres)
Equivalent lengths (centimetres and millimetres)
Adding mixed lengths
Partition the whole \( \frac{2}{5}+\frac{?}{5} = 1 \)
Subtracting mixed lengths (1)
Subtracting mixed lengths (2)
Perimeters
Fractions A
Making a whole
Partition the whole \( \frac{2}{5}+\frac{?}{5} = 1 \)
Comparing unit fractions
Comparing non-unit fractions
Order unit fractions
Order non-unit fractions
Mass
Calculating the grams needed to complete a kg
Equivalent masses (kg and g)
Comparing mass
Mass - Addition of mixed measures
Mass - Subtraction of mixed measures
Capacity
Calculating the ml needed to make a litre
Capacity - Addition of mixed measures
Capacity - Subtraction of mixed measures
Year 3 - Term 3
Fractions B
Calculating a unit fraction of a quantity (up to x12)
Calculating a unit fraction of a quantity
Calculating a non-unit fraction of a quantity
Comparing fraction of a quantity calculations
Partition the whole \( \frac{2}{5}+\frac{?}{5} = 1 \)
Adding fractions - same denominator
Subtracting fractions from a whole
Subtracting fractions - same denominator
Money
Covert pence to pounds and pence 755p = £ and p
Adding money (within a pound)
Adding money
Subtracting money (within a pound)
Subtracting money
Calculating change from £1
Calculating change from £5
Calculating change from £10
Time
Roman numbers (up to 12) - write in figures
Read the time from a digital clock
Understand am and pm when comparing times
Understanding the order of the months of the year
Converting :years, months/days
Converting : weeks, days ,hours
Converting : hours, minutes
Expressing minutes and seconds as seconds
Expressing seconds as minutes and seconds
Comparing seconds and minutes and seconds
Time Calculations
Comparing time intervals
Calculating time intervals (5 minutes)
Calculating time intervals
Working out end times
Working out start times
Shape
Compass directions and right angles
Term 1
Term 2
Term 3
Year 4 - Term 1
Place Value
Ones, Tens, hundreds and thousands (equivalence)
Partition numbers up to 10000
Flexible partitioning of numbers to 10z000
Finding 1,10,100 or 1000 more or less
Ordering a comparing numbers up to 10000
Roman numbers (up to 100) - write in figures
Rounding to the nearest 10
Rounding to the nearest 100
Rounding to the nearest 1000
Addition
Add 1's 10's 100's and 1000's
Add 1's 10's 100's and 1000's
Up to 4-digit numbers – no exchange
4-digit numbers – one exchange
4-digit numbers – more than one exchange
Subtraction
Subtract 1's 10's 100's and 1000's
4-digit numbers – no exchange
4-digit numbers – one exchange
4-digit numbers – more than one exchange
Multiplication and division
Listing multiples of 2
Multiply and divide by 6
Multiply and divide by 9
Multiply and divide by 7
Multiply and divide by 11
Multiply and divide by 12
Multiply by 1 and 0
Divide a number by 1 and itself
Multiply 3 numbers
Year 4 - Term 2
Multiplication
Finding factors
Using factor pairs
Multiply by 10
Multiply by 100
Related calculations - multiplication and division
Multiplying - 2 digit by a single digit
Multiply a 3 digit by a 1 digit number
Division
Dividing by 10
Dividing by 100
Division - 2 digit by 1 digit (A)
Division - 2 digit by 1 digit (B)
Division - 3 digit by 1 digit
Length and perimeter
Comparing lengths in km and m
Equivalent lengths (km and metres))
Calculate the perimeter
Calculate a missing length given the perimeter
Calculate the perimeter of regular polygons
Calculate the side length of a regular polygon
Decimals A
Writing as a decimal
Counting in tenths
Dividing a 1 digit number by 10
Dividing a 2 digit number by 10
Dividing a 1 digit number by 100
Dividing a 2 digit number by 100
Comparing tenths and tens
Expressing tenths and hundredths as hundredths
Hundredths fractions/decimals
Fractions
Completing the whole
Count beyond 1 (unit fractions)
Count beyond 1 (increasing)
Count beyond 1 (decreasing)
Partition a mixed number
Order Mixed numbers
Compare Mixed numbers
Improper fractions equivalent to whole(s)
Mixed numbers to improper fractions
Improper fractions to mixed numbers
Adding fractions - same denominator/label>
Adding fractions crossing the whole
Adding mixed numbers - same denominator
Adding mixed numbers - crossing the whole
Subtract a whole from a mixed number
Subtract fractions - same denominator
Subtract fractions from a whole
Subtract a whole from a mixed number
Subtract a fraction from a mixed number
Year 4 - Term 3
Decimals B
Make a whole with tenths - decimals only
Make a whole with tenths
Make a whole with hundredths
Partition decimals
Identify place value of underlined digits
Flexible partition decimals
Compare decimals
Order Decimals
Round to the nearest whole number
Fractions as decimals
Money
Write money as decimals
Convert between pounds and pence
Compare amounts of money
Round to the nearest 10 pence
Round to the nearest pound
Subtracting amounts of money
Multiplying money
Dividing money
Time
Years months weeks and days
Hours minutes and seconds
Write as digital times
Time interval calculations
Convert to the 24-hour clock
Convert from 24-hour clock
Shape
Compass directions and right angles
Classifying triangles
Calculate the perimeter of regualar polygons
Calculate the side length of a regular polygon
Term 1
Term 2
Term 3
Year 5 - Term 1
Place Value
Roman numerals up to 1000
Numbers up to 10000 - more or less
Numbers up to 100000 - more or less
Numbers up to 1000000 - more or less
Identifying place value in numbers
Read and write numbers to 1000000
Making large and small numbers (5 digits)
Finding 1,100,1000,10000,100000 more or less
Partition numbers up to 1000000
Ordering a comparing numbers up to 100000
Round within 10,000
Round within 1,000,000
Addition and Subtraction
Addition - More than 4 digits
Subtraction - More than 4 digits
Inverse operations - addition and subtraction
Comparing calculations - addition and subtraction
Missing numbers in equivalent calculations
Multiplication and division (1)
Listing multiples
Finding common multiples
Finding common factors
Listing prime numbers
Listing square numbers
Cube numbers
Multiplication and division (2)
Multiply by 10,100 or 1000
Dividing by 10,100 or 1000
Multiplication - by multiples of 10,100,1000
Division - by multiples of 10,100,1000
Multiplication and Division - by multiples of 10
Fractions A (1)
Find fractions equivalent to a unit fraction
Find fractions equivalent to a non-unit fraction
Compare Mixed numbers
Improper fractions equaivalent to whole(s)
Comparing fractions less than 1
Ordering fractions less than 1
Comparing fractions greater than 1
Add fractions-same denominator
Add fractions within 1
Fractions A (2)
Add fractions total greater than 1
Add a proper fraction to a mixed number
Add two mixed numbers
Subtract fractions - same denominator
Subtract fractions
Subtract a fraction from a mixed number (1)
Subtract a fraction from a mixed number (2)
Subtract two mixed numbers
Year 5 - Term 2
Multiplication and division
Multiply a 3 digit by a 1 digit number
Multiply a 4 digit by a 1 digit number
Multiplication - 2 digit by 2 digit
Multiplication - 3 digit by 2 digit
Multiplication - 4 digit by 2 digit
Comparing related products
Division - 3 or 2 digit by 1 digit
Division - 4 digit by 1 digit (no remainders)
Division - 4 digit by 1 digit (with remainders)
Fractions
Calculate a unit fraction of a quantity
Calculate a fraction of a quantity
Multiply - Unit fraction by an integer
Multiply - fraction by an integer
Find the product of a pair of proper fractions
Multiply - mixed number by an integer
Find the whole -given a unit fraction
Find the whole -given a fraction
Area and Perimeter
Calculate the perimeter
Calculate a missing length given the perimeter
Calculate the perimeter of regular polygons
Calculate the side length of a regular polygon
Calculate the area of a rectangle
Area of a rectangle - missing length
Decimals and percentages (1)
Place value in Decimals (2 d.p)
Partitioning Decimals (2 d.p.)
Equivalent fractions and decimals (tenths)
Equivalent fractions and decimals (hundredths)
Thousandths as fractions
Thousandths as decimals
Compare and order decimals (1)
Compare and order decimals (2)
Decimals and percentages (2)
Round to the nearest whole number
Round to 1 decimal place
Understand percentages
Percentages as fractions
Fractions as percentages
Percentages as decimals
Decimals as percentages
Year 5 - Term 3
Shape
Calculate angle turns - minute hand 5 mins intervals
Calculate angle turns - minute hand 5 mins intervals
Decimals (1)
Add decimals within 1 (hundredths)
Add decimals within 1 (tenths and hundredths)
Subtract decimals within 1 (hundredths)
Subtract decimals within 1 (tenths and hundredths)
Complements to 1 - hundredths
Complements to 1 - tenths and hundredths
Complements to 1 - thousandths
Add decimals across 1
Subtract decimals across 1
Add decimals (same number of decimal places)
Subtract decimals (same number of decimal places)
Add decimals (up to 2 d.p)
Subtract decimals (up to 2 d.p.)
Decimals (2)
Tenths - increasing and decreasing
Hundredths - increasing and decreasing
Missing terms - tenths
Missing terms - hundredths
Multiplying by 10
Multiplying by 100
Multiplying by 1000
Dividing (up to 3 digit number) by 10
Dividing (up to 3 digit number) by 100
Dividing (up to 3 digit number) by 1000
Multiplying by 10 100 1000 - missing values
Dividing by 10 100 1000 - missing values
Negative Numbers
Calculating temperature after an increase
Calculating temperature after a decrease
Counting in 1's (negative numbers)
Counting in 2,3,4 5 etc
Directed numbers
Comparing temperatures
Ordering temperatures
Finding the difference between two temperatures
Converting Units
kg and km
ml and mm
cm and mm
cm and m
Inches and cm
Kilograms and pounds
Pints and gallons
Converting between units of time mixture
Calculating time intervals
Term 1
Term 2
Term 3
Year 6 - Term 1
Place Value
Place value in numbers up to 1000000
Numbers up to 10000000
Identifying place value in numbers upt 10000000
Writing numbers in figures up to 10000000
Multiplication and division - multiple powers of 10
Comparing numbers up to 10000000 using < or >
Rounding integers to a power of 10
Missing terms - directed numbers
Finding more of less - directed numbers
Mixed arithmetic
Addition - up to 1000000
Subtraction - numbers up to 1000000
Division - 3 digit by 1 digit
Division - 3 or 4 digit by 2 digit numbers
Finding common multiples
Finding common factors
Listing prime numbers
Cube and square numbers
Order of operations
Order of operations (1): \( a - b + c \times d \)
Order of operations (2): \( a + b + c \times d \)
Order of operations (3): \( a + b \times c \)
Order of operations (4): \( a - b \times c \)
Order of operations (5): \( a + b \div c \)
Order of operations (6): \( a - b \div c \)
Order of operations (7): \( a \times b - c \times d \)
Order of operations (8): \( a \times b + c \times d \)
Order of operations (9): \( a + (b + c ) \times d \)
Order of operations (10): \( (a + b) \times c \)
Order of operations (11): \( (a - b) \times c \)
Order of operations (12): \( a - (b + c ) \times d \)
Order of operations (13): \( a \times (b - c) \)
Order of operations (14): \( (a - b) \times c \)
Order of operations (15): \( (a + b) \div c \)
Order of operations (16): \( a \div (b + c) \)
Order of operations (17): \( (a - b) \div c \)
Order of operations (18): \( a \div (b - c) \)
Order of operations (19): \( a(b - c) + d \)
Order of operations (20): \( a(b + c) + d \)
Order of operations (21): \( a \times (b - c)^2 \)
Order of operations (22): \( (a - b)^2 \)
Order of operations (23): \( (a + b)^2 \)
Order of operations (24): \( a \times (b - c) \times d \)
Fractions A (1)
Simplifying a fraction
Equivalent fractions
Comparing fractions less than 1
Ordering fractions less than 1
Adding and subtracting fractions (1)
Adding and subtracting fractions(2)
Adding mixed numbers
Subtracting mixed number
Fractions A (2)
Multiply - fraction by an integer
Multiply - fractions
Dividing a unit fraction by an integer
Dividing a fraction by an integer
Calculate a fraction of a quantity
Find the whole -given a fraction
Converting units
Length - mixed measures
Addition of mixed metric measures
Miles and km
Mixed imperial measures
Year 6 - Term 2
Ratio
Using ratio language
Using the ratio symbol
Expressing a ratio as a fraction
Using scale drawings
Using scale factors - simple
Missing lengths - similar rectangles
Simple ratio problems
Direct Proportion problems (£s)
Solving recipe problems
Equivalence
Fractions as decimals
Write division as a fraction
Use division to write a fraction as a decimal
Fraction as division (mixture)
Fractions as percentages
Fraction as a decimal
Decimals as fractions
Algebra
One-step - find the output
One-step - find the input
One-step - find the output - decimals
Find the output \( \times a + b \)
Find the output \( \times a - b \)
Find the output \( + a \times b \)
Find the output \( \div a + b\)
Find the output \( \div a - b \)
Find the output \( + a \div b \)
Find the output \( -a \div b \)
Find the output \( -a \\times b\)
Two-step - find the output mixture
Find the input \( \times a + b \)
Find the input \( \times a - b \)
Find the input \( + a \times b \)
Find the input \( \ div a + b\)
Find the input \( \div a - b \)
Find the input \( + a \div b \)
Find the input \( -a \div b \)
Find the input \( -a \times b\)
Two-step - find the input
Two-step - missing functions
Algebra
Substitution : \( x + a \)
Substitution : \( x - a \)
Substitution : \( ax \)
Substitution : \( \frac{a}{x} \)
Substitution : one-step mixture
Substitution : \( y = ax + b \)
Substitution : \( y = ax - b \)
Substitution : \( y =b - ax \)
Forming equations -one step function machines
Forming equations -two step function machines
One step equations : \( x + a = b \)
One step equations : \( x - a = b \)
One step equations : \( ax = b \)
One step equations : \( \frac{x}{a} = b \)
Two step equations : \( ax + b = c \)
Two step equations : \( ax - b = c \)
Find pairs of values
Solve problems with two unknowns
Decimals
Place value within 1
Place value - integers and decimals
Rounding to the nearest integer
Rounding to the nearest tenth
Rounding to the nearest hundredth
Add decimals (up to 3 d.p)
Subtract decimals (up to 3 d.p.)
Multiply by 10
Multiply by 100
Multiply by 1000
Dividing by 10 (including decimals)
Dividing by 100 (including decimals)
Dividing by 1000 (including decimals)
Multiply a decimal by an integer
Dividing a decimal by and integer
Multiply and divide decimals in context
Percentages
Percentages to 100 (shaded/unshaded percentage)
Understanding percentages (35% = 3 x 10% + 5%)
Understanding percentages (35% = 3 x 10% + 5%)
50% of a quantity - non calculator
25% and 50% of a quantity - non -calculator
10% of a quantity - non-calculator
10% and 20% of a quantity - non-calculator
20% of a quantity - non-calculator
10% and 5% of a quantity - non-calculator
5% of a quantity - non-calculator
5% 10% and 15% of quantity - non-calculator
5% 10% and 20% of a quantity - non-calculator
15% of a quantity - non-calculator
Multiples of 5% - non-calculator
Percentages of quantities - missing values
Area and Perimeter
Calculate the area of a rectangle
Area of a rectangle - missing length
Area of a triangle - (non-calc)
Area of a parallelogram
Volume of a cuboid
Averages
Calculate the mean - from a list
Find the mode
Year 6 - Term 3
Shape
Classifying angles
Calculate missing angles triangles
Calculate angles in a quadrilateral
Radius and diameter calculations
Interior angles in polygons
Term 1
Term 2
Term 3
Year 7 - Term 1
Sequences
Recognise a linear sequence
Continue a linear sequence
Find missing terms in a linear sequence
Continue a geometric sequence
Continue a fibonacci sequence
Find missing terms in a geometric sequence
Algebra
One step equations : \( x + a = b \)
One step equations : \( x - a = b \)
One step equations : \( ax = b \)
One step equations : \( \frac{x}{a} = b \)
Collecting like terms - Single variable
Collecting like terms - Two variables
Algebraic Notation
Find the output of a single function machine
Use inverse operations to find the input
Multiplying terms
Dividing terms
Simplifying -addition - single variable
Find an expression for the output
Find the function
Substitution mixture
Substitution : \( y = \frac{x}{a} + b \)
Substitution : \( y = \frac{x+a}{b} \)
Substitution : \( y = \frac{x-a}{b} \)
Substitution : \( y = \frac{ax + b}{c} \)
Substitution : \( y = \frac{ax - b}{c} \)
Generate sequences given an algebraic rule
Place Value
Place value up to one billion
More of less in numbers up to 1 billion
Writing numbers up to 1 billion in figures
Round within 1,000,000,000
Ordering numbers up to 100000000
Calculate the range
Calculate the median
Understand place value of decimals (3 d.p.)
Rounding to 1 significant figure (integers)
Rounding to 1 significant figure (decimals)
Rounding to 1 significant figure
Writing integers in standard form
Writing decimals <1 in standard form
Equivalence
Express a fraction as a decimal
Express a decimal as a fraction
Fractions and decimals - fifths and quarters
Adding and subtracting fractions and decimals -
Simple fractions, decimals and percentages
Mixed numbers to improper fractions
Improper fractions to mixed numbers
Year 7 - Term 2
Addition and subtraction
Addition - Mentally
Addition - large numbers
Addition - Decimals
Subtraction - large numbers
Subtraction - Decimals
Adding money - decimals
Subtracting money - decimals
Adding and subtracting money - decimals
Add numbers in standard form
Subtract numbers in standard form (
Add and Subtract numbers in standard form
Writing integers in standard form
Writing decimals in standard form
Fractions and Percentages
Calculate a fraction of a quantity
Find the whole -given a fraction
Multiples of 5% - non-calculator
Calculating a percentage of a quantity (calc)
Percentages to fractions (>100)
Fractions - Addition and Subtraction
Subtract fractions from integers
Equivalent fractions
Add fractions - common multiples
Subtract fractions - common multiples
Add fractions
Subtract fractions
Adding mixed numbers (1)
Subtracting mixed numbers (1)
Adding mixed numbers
Subtracting mixed numbers
Add/subtract fractions and decimals (1)
Add/subtract fractions and decimals (2)
Directed numbers -mixture
Multiplication and Division
Finding factors
Listing multiples
Multiplying by powers of 10
Dividing by powers of 10
Length - mixed measures
Mass - mixed measures
Capacity - mixed measures
Multiplying by 0.1 and 0.01
Multiplying integers
Multiplying decimals by an integer(written methods)
Dividing integers
Dividing decimals
Order of operations (1): \( a - b + c \times d \)
Order of operations (2): \( a + b + c \times d \)
Order of operations (3): \( a + b \times c \)
Order of operations (4): \( a - b \times c \)
Order of operations (5): \( a + b \div c \)
Order of operations (6): \( a - b \div c \)
Order of operations (7): \( a \times b - c \times d \)
Order of operations (8): \( a \times b + c \times d \)
Order of operations (9): \( a + (b + c ) \times d \)
Order of operations (10): \( (a + b) \times c \)
Order of operations (11): \( (a - b) \times c \)
Multiplication and Division
Order of operations (12): \( a - (b + c ) \times d \)
Order of operations (13): \( a \times (b - c) \)
Order of operations (14): \( (a - b) \times c \)
Order of operations (15): \( (a + b) \div c \)
Order of operations (16): \( a \div (b + c) \)
Order of operations (17): \( (a - b) \div c \)
Order of operations (18): \( a \div (b - c) \)
Order of operations (19): \( a(b - c) + d \)
Order of operations (20): \( a(b + c) + d \)
Order of operations (21): \( a \times (b - c)^2 \)
Order of operations (22): \( (a - b)^2 \)
Order of operations (23): \( (a + b)^2 \)
Order of operations (24): \( a \times (b - c) \times d \)
Missing length- rectangle
Missing length - parallelogram
Missing length - triangle
Area of trapeziums
Mean given - find a missing value
Multiplying terms \( ax \times bx \)
Dividing terms \( ax \div b \)
Directed Numbers
Addition crossing zero
Subtraction crossing zero
Directed numbers \( a + -b \)
Directed numbers \( a - -b \)
Directed numbers \( \pm a \times \pm b \)
Directed numbers \( \pm a \div \pm b \)
Directed numbers \( -a \times -b -c \)
Directed numbers \( -a + - b + c \)
Directed numbers \( -(a)^2 + -b + c \)
Directed numbers \((-a)^2 + -b + c \)
Directed numbers \((-a)^2 - -b + -c \)
Directed numbers \((-a)^2 - -b - -c \)
Directed numbers -mixture
Collecting like terms - Single variable (across 0)
Substituting negative values -mixture
Substitution : \( a - b \)
+ b\)
Substitution : \( a(b - c) \)
Substitution : \( a - b^2 \)
Substitution : \( a^2 - b \)
Solving : \( ax + b = c \)
Solving : \( ax - b = c \)
Solving : \( a - bx = c \)
Equations Mixture
Solving : \( \frac{x}{a} - b = c \)
Directed Numbers
Solving : \( \frac{x}{a} + b = c \)
Solving : \( \frac{x + a}{b} = c \)
Solving : \( \frac{x - a}{b} = c \)
Mixture of equations with fractions
Order of operations - \( a - b + c \times d \)
Order of operations - \( a - (b + c ) \times d \)
Order of operations - \( a + b + c \times d \)
Order of operations - \( a + (b + c ) \times d \)
Order of operations - \( a \times (b - c)^2 \)
Order of operations - \( a - b^2 \)
Order of operations - \( a + b^2 \)
Order of operations - \( a \times (b - c) \times d \)
Order of operations - \( a \times b - c \times d \)
Order of operations - \( a \times b + c \times d \)
Order of operations - \( (a + b) \times c \)
Order of operations - \( a \times (b - c) \)
Order of operations - \( (a - b ) \times c \)
Order of operations - \( a \div (b + c) \)
Order of operations - \( a \div (b - c) \)
Order of operations - \( a + b \times c \)
Order of operations - \( a - b \times c \)
Order of operations - \( a + b \div c \)
Mixture order of operations
Identifying intervals for square roots
Evaluating - positive integer powers
Year 7 - Term 3
Angles
Compass directions and right angles
Classifying angles
Pie Charts - calculating angles
Calculate missing angles triangles
Calculate angles in a quadrilateral
Prime Numbers
Finding multiples of a number
Finding factors
Listing prime numbers
Finding the HCF
Finding the lowest common multiple
Expressing as a product of prime factors
Number sense
Addition - large numbers
Addition - Decimals
Subtraction - large numbers
Multiplication - Integers
Division - Integers
Calculating change from £1 as a decimal
Calculating change from £5 as a decimal
Calculating change from £10 as a decimal
Calculating change nixture
Multiplying by multiples of 10 or decimals
Number sense
Use factors ot simplify multiplication calculations
Estimation \( \frac{a + b }{c} \)
Estimation \( \frac{a - b }{c} \)
Estimation \( \frac{a \times b }{c} \)
Estimation \( a \times b \)
Estimation \( a + b \)
Estimation \( a - b \)
Mixture
Use known facts - multiplication (inc decimals)
Term 1
Term 2
Term 3
Year 8 - Term 1
Ratio ande Scale
Ratios of the form 1:n or n:1
Ratios of the form m : n
Dividing in a given ratio
Simplifying ratios
Expressing in the form 1:n or n:1
Expressing a fraction as a ratio
Expressing a ratio as a fraction
Multiplicative change
Direct Proportion problems
UK currency for foreign currency
Foreign currency to UK currency
Interpret scale diagrams - model to real
Interpret scale diagrams - real to model to real
Interpret maps - map to real
Interpret maps - real to map
Multiplying and Dividing Fractions
Multiply - Unit fraction by an integer
Find the product of a pair of unit fractions
Divide an integer by a fraction
Dividing a fraction by an integer
Divide a fraction by a unit fraction
Finding the reciprocal
Divide any pair of fractions
Multiply mixed numbers
Divide mixed numbers
Multiplying algebraic fractions
Divide algebraic fractions
Working in the caretsian plane
State equations of lines parallel to the axes
State equations of lines parallel to the x-axis
State equations of lines parallel to the y-axis
Points on a straight line graph \( y = mx \)
Steeper gradient \( y = ax \) or \( y = bx \)
Coordinate on \( y = x \pm c \)
Coordinate on \( y = mx \)
Coordinate on \( y = mx \pm c \)
\( y axis \) intercept for \( y = x \pm a \)
\( x axis \) intercept for \( y = x \pm a \)
\( y \) intercept for \( y = mx \pm c \)
Points a straight line graph \( y = mx \pm c \)
Identify equations of non-linear graphs
Find the mid-point of a line segment
Year 8 - Term 2
Brackets, Equations and Inequalities
Simplifying expressions
Forming single step expressions
Expanding \( a(bx \pm c) \) or \( a( b - cx ) \)
Expanding \( a(bx + c) \)
Expanding \( a(bx - c) \)
Expanding \( a(b - cx ) \)
Expanding \( ax(bx \pm c) \) or \( ax( b - cx ) \)
Expanding \( ax(bx + c) \)
Expanding \( ax(bx - c) \)
Expanding \( ax(b - cx ) \)
Factorising \( ax \pm b) \) or \(( a - bx ) \)
Factorising \( ax + b \)
Factorising \( ax - b \)
Factorising \( a - bx \)
Factorising \( ax^2 \pm bx \) or \( a - bx^2 \)
Factorising \( ax^2 + b \)
Factorising \( ax^2 - b \)
Factorising \( b - ax^2 \)
Expanding \( a( bx \pm c) + d(ex \pm f) \)
Expanding \( a( bx + c) + d(ex + f) \)
Expanding \( a( bx - c) + d(ex + f) \)
Expanding \( a( bx + c) + d(ex - f) \)
Expanding \( a( bx - c) + d(ex - f) \)
Expanding \( a( bx \pm c) - d(ex \pm f) \)
Expanding \( a( bx + c) - d(ex + f) \)
Expanding \( a( bx - c) - d(ex + f) \)
Expanding \( a( bx + c) - d(ex - f) \)
Expanding \( a( bx - c) - d(ex - f) \)
Brackets, Equations and Inequalities
Expanding \( a( bx \pm c) \pm d(ex \pm f) \)
Expanding \( (x \pm a)(x \pm b) \)
Expanding \( (x + a)(x + b) \)
Expanding \( (x - a)(x - b) \)
Expanding \( (x + a)(x - b) \)
Expanding \( (x - a)(x + b) \)
Expanding \( (x + a)^2 \)
Expanding \( (x - a)^2 \)
Expanding \( (x - a)(x + a) \)
Solving \( a(bx \pm c) = d \) or \( a(c - bx) = d \)
Solving \( a(bx + c) = d \)
Solving \( a(bx - c) = d \)
Solving \( a(c - bx) = d \)
Forming and solving equations involving brackets
Solving \( a( bx + c) + d = e \)
Solving \( a( bx - c) + d = e \)
Solving \( a( bx + c) - d = e \)
Solving \( a( bx - c) - d = e \)
Solving \( a( b - cx) + d = e \)
Solving \( a( b - cx) - d = e \)
Solving \( a( bx \pm cx) \pm d = e \)
Solving \( x + a <> b \)
Solving \( x - a <> b \)
Solving \( x \pm a <> b \)
Solving \( ax + b <> c \)
Solving \( ax - b <> c \)
Solving \( ax \pm b <> c \)
Sequences
Generate a sequence given the first term and rule
Generate an increasing sequence - nth term
Generate a decreasing sequence - nth term
Generate a linear sequence - nth term
Generate a quadratic sequence - nth term
Find the nth term - increasing only
Find the nth term - decreasing only
Find the nth term
Indices
Adding and subtracting powers of a variable
Multiplying terms \( a \times x \times b \times x \)
Multiplying terms with indices \( ax^m \times bx^n \)
Dividing terms \( ax^n y^m \div cx \)
Missing pwer \( x^n \times x^m = x^p \)
Missing power \( x^n \div x^m = x^p \)
Missing power \( (x^n)^m = x^p \)
Fractions and percentages (1)
Calculate a fraction of a quantity
Calculating a percentage of a quantity (calc)
Identifying multipliers for percentage increases
Identifying multipliers for percentage decreases
Increasing by a given percentage (calc)
Decreasing by a given percentage (calc)
Calculate the percentage increase
Calculate the percentage decrease
Calculate the percentage change
Finding the original < 100%
Finding the original > 100%
Expressing as a percentage - non calculator
Expressing as a percentage
Calculate a percentage increase - non calculator
Calculate a percentage decrease - non calculator
Calculate a percentage change
Standard Index Form
Multiplying positive powers of 10
Dividing positive powers of 10
Multiplying and Dividing positive powers of 10
Expressing negative powers of 10 as a
Standard Index Form
Wrtiting in standard form 0
Writing in ordinary form 0
Standard form and ordinary form 0
Wrtiting in standard form >1
Writing in ordinary form >1
standard form and ordinary form >1
Order numbers in standard form
Add numbers in standard form (integer)
Subtract numbers in standard form (integer)
Addition and subtraction in standard form (integers)
Multiply a number in standard from by an integer
Divide a number in standard from by an integer
Multiply numbers in standard form
Divide numbers in standard form
Standard form - mixed arithmetic (calculator)
Standard form - addition - calculator
Standard form - subtraction - calculator
Standard form - multiplication - calculator
Standard form - division - calculator
Multiplication and division mixture
Evaluating - negative integer powers
Evaluating - fractional powers \( \frac{1}{2} \) and \( \frac{1}{3} \)
Number Mixture
Rounding integers to a power of 10
Rounding to 1 significant figure
Rounding to 1 or 2 decimal places
Estimation \( \frac{a + b }{c} \)
Estimation \( \frac{a - b }{c} \)
Estimation \( \frac{a \times b }{c} \)
Estimation \( a \times b \)
Estimation \( a + b \)
Estimation \( a - b \)
Error intervals - numbers - nearest integer
Error intervals - numbers - 1 d.p.
Error intervals - numbers - 2 d.p.
Error intervals - numbers - mixture
Error intervals - measures -nearest integer
Error intervals - measures -1 d.p.
Number Mixture
Error intervals - measures -nearest 10
Error intervals - measures -nearest 100
Error intervals - measures -nearest 1000
Error intervals - measures -mixture
Identifying error intervals - mixture
Problem solving with money
Metric units of area - \( mm^2 \) and \( cm^2 \)
Metric units of area - \( cm^2 \) and \( m^2 \)
Metric units of area - mixture
Metric units of volume - \( mm^3 \) and \( cm^3 \)
Metric units of volume - \( cm^3 \) and \( m^3 \)
Metric units of volume - mixture
Calculate the time - before an event
Calculate the time - after an event
Calculate the time - mixture
Year 8 - Term 3
Angles in polygons
Exterior angles
Interior angles in polygons
Area
Missing length- rectangle
Area of a triangle - (non-calc)
Missing length - triangle
Area of a parallelogram
Missing length - parallelogram
Area of trapeziums
Area of trapeziums - finding missing lengths
Area of a circle in terms of \( \pi \)
Area of a circle - calculator
Measures of location
Calculate the mean - from a list
Mean given - find a missing value
Find the mode
Calculate the median
Term 1
Term 2
Term 3
Year 9 - Term 1
Straight Line graphs
Equations of lines parallel to the axes and (\ y = \pm x \) - 2 points given
Equation of a line - 2 function machines
Equation of a line given the gradient and y-intercept
Identify the y intercept of \( y = mx \pm c \) or \( y = c \pm mx \)
Identify the gradient of \( y = mx \pm c \) or \( y = c \pm mx \)
Identify the gradient after rearranging
Identify the intercept after rearranging
Equation of a line parallel to \( y = mx + c \) through (0,a)
Equation of a line parallel to \( y = mx + c \) through (0,a) - rearranging needed
Equation of a line parallel to \( y = mx + c \) through (a,b)
Equation of a line parallel to \( y = mx + c \) through (a,b) - rearranging needed
State equations of lines parallel to the axes and (\ y = \pm x \) - 2 points given
Equation of a line perpendicualar to \( y = mx + c \) through (0,a)
Equation of a line perpendicualar to \( y = mx + c \) through (0,a) -rearranging needed
Equation of a line perpendicular to \( y = mx + c \) through (a,b)
Equation of a line perpendicular to \( y = mx + c \) through (a,b) - rearranging needed
Solving equations
Solving : \( ax + b = c \)
Solving : \( ax - b = c \)
Solving : \( a - bx = c \)
Solving \( a(bx \pm c) = d \) or \( a(c - bx) = d \)
Solving \( a(bx + c) = d \)
Solving \( a(bx - c) = d \)
Solving \( a(c - bx) = d \)
Forming and solving equations involving brackets
Solving \( a( bx + c) + d = e \)
Solving \( a( bx - c) + d = e \)
Solving \( a( bx + c) - d = e \)
Solving \( a( bx - c) - d = e \)
Solving \( a( b - cx) + d = e \)
Solving \( a( b - cx) - d = e \)
Solving \( a( bx \pm cx) \pm d = e \)
Solving \( \frac{x}{a} - b = c \)
Solving \( \frac{x}{a} + b = c \)
Solving \( a - \frac{x}{b} = c \)
Solving \( \frac{x+a}{b} = c \)
Solving \( \frac{x-a}{b} = c \)
Solving \( \frac{a-x}{b} = c \)
Solving equations involving fractions - mixture
Solving inequalities
Solving \( x + a <> b \)
Solving \( x - a <> b \)
Solving \( x \pm a <> b \)
Solving \( ax + b <> c \)
Solving \( ax - b <> c \)
Solving \( ax \pm b <> c \)
Solving \( \frac{x}{a} - b <> c \)
Solving \( \frac{x}{a} + b <> c \)
Solving \( \frac{x + a}{b} <> c \)
Solving \( \frac{x - a}{b} <> c \)
Solving \( a(bx + c) <> d \)
Solving \( a(bx - c) <> d \)
Solving \( a(bx \pm c) <> d \)
Solving \( a(b - cx) <> d \)
Solving \( a - \frac{x}{a} <> d \)
Solving \( \frac{a - x} <> d \)
Solving mixture (involving reversing the inequalty sign)
Rearrangin formulae
Rearrange one step formulae - \( y = x + a \)
Rearrange one step formulae - \( y = x - a \)
Rearrange one step formulae - \( y = ax \)
Rearrange one step formulae - \( y= \frac{a}{x} \)
Rearrange one step formulae - \( y = \frac{x}{a} \)
Rearrange one step formulae - \( y= a - x \)
Rearranging to the form y = mx + c
Rearrange two step formulae - \( y= \frac{x}{a} + b \)
Rearrange two step formulae - \( y= \frac{x}{a} - b \)
Rearrange two step formulae - \( y= \frac{x + a}{b} \)
Rearrange two step formulae - \( y= \frac{x - a}{b} \)
Rearrange two step formulae - mixture
Rearrange complex formulae - \( y = \sqrt{x + a} \)
Rearrange complex formulae - \( y = \sqrt{x - a} \)
Rearrange complex formulae - \( y = \sqrt{a - x} \)
Rearrange complex formulae - \( y = \frac{\sqrt{x}}{a} \)
Rearrange complex formulae - \( y = \frac{a}{\sqrt{x}} \)
Rearrange complex formulae - \( y = \sqrt{\frac{a}{x}} \)
Rearrange complex formulae - \( y = \sqrt{\frac{x}{a}} \)
Rearrange complex formulae - \( y = \sqrt{x} + a \)
Rearrange complex formulae - \( y = \sqrt{x} -a \)
Rearrange complex formulae - \( y = - \sqrt{x} \)
Rearrange complex formulae - mixture
Substitution
Substitution (5): \( y = ax + b \)
Substitution (6): \( y = ax - b \)
Substitution (7): \( y =b - ax \)
Substitution (8): \( y = \frac{x}{a} + b \)
Substitution (9): \( y = \frac{x+a}{b} \)
Substitution (10): \( y = \frac{x-a}{b} \)
Substitution (11): \( y = \frac{ax + b}{c} \)
Substitution (12): \( y = \frac{ax - b}{c} \)
Substituion (13):\( ax^2 \pm bx \)
Substitution (14): \( a - b \) (neg values)
Substitution (15): \( a^2 + b\) (neg values)
Substitution (16): \( a(b - c) \) (neg values)
Substitution (17): \( a - b^2 \) (neg values)
Substitution (18): \( a^2 - b \) (neg values)
Testing conjectures
Finding multiples of a number
Finding factors
Listing prime numbers
Expanding \( (x \pm a)(x \pm b)
Expanding 3 brackets
Three dimensional shapes
Area of a circle in terms of \( \pi \)
Area of a circle - calculator
Calculate the surface area of a cuboid
Calculate the surface area of a cylinder
Calculate the curved surface area of a cylinder
Volume of a cylinder - in terms of pi
Volume of a cone -radius and vertical height known
Volume of a sphere
Volume of a pyramid
Year 9 - Term 2
Number Mixture
Simplifying surds
Addition - Decimals
Subtraction - large numbers
Multiplication - Integers
Division - Integers
Addition - decimals
Subtraction - decimals
Multiplication - Decimals
Division - Decimals
Finding the HCF
Finding the lowest common multiple
Expressing as a product of prime factors
Solving : \( \frac{x}{a} + b = c \)
Solving : \( \frac{x + a}{b} = c \)
Solving : \( \frac{x - a}{b} = c \)
Mixture of equations with fractions
Order of operations - \( a - b + c \times d \)
Order of operations - \( a - (b + c ) \times d \)
Number Mixture
Order of operations - \( a + b + c \times d \)
Order of operations - \( a + (b + c ) \times d \)
Order of operations - \( a \times (b - c)^2 \)
Order of operations - \( a - b^2 \)
Order of operations - \( a + b^2 \)
Order of operations - \( a \times (b - c) \times d \)
Order of operations - \( a \times b - c \times d \)
Order of operations - \( a \times b + c \times d \)
Order of operations - \( (a + b) \times c \)
Order of operations - \( a \times (b - c) \)
Order of operations - \( (a - b ) \times c \)
Order of operations - \( a \div (b + c) \)
Order of operations - \( a \div (b - c) \)
Order of operations - \( a + b \times c \)
Order of operations - \( a - b \times c \)
Order of operations - \( a + b \div c \)
Mixture order of operations
Fractions
Add fractions
Subtract fractions
Multiplying Fractions
Dividing fractions
Adding mixed numbers
Subtracting mixed number
Multiply mixed numbers
Divide mixed numbers
Standard Index Form
Wrtiting in standard form 0
Writing in ordinary form 0
Standard form and ordinary form 0
Wrtiting in standard form >1
Writing in ordinary form >1
Standard form - addition - calculator
Standard form - subtraction - calculator
Standard form - multiplication - calculator
Standard form - division - calculator
Percentages
Calculating a percentage of a quantity (calc)
Identifying multipliers for percentage increases
Identifying multipliers for percentage decreases
Increasing by a given percentage (calc)
Decreasing by a given percentage (calc)
Calculate the percentage increase
Calculate the percentage decrease
Calculate the percentage change
Calculating compound interest
Number of years (compound interest)
Calculate the total (compound interest)
Calculate depreciation
Finding the original < 100%
Finding the original > 100%
Calculate time to for a population to reduce to n
Money Calculations
Simple interest calculations
Simple interest - calculating the total
Simple interest - calculating the interest
Working with VAT
Calculating the price including VAT
Calculating the price before VAT
Wages and Taxes
Calculating Income tax
Solving best buy problems
Exchange rates - comparing prices
Pythagoras
Squares and square roots mixture
Calculating c in \( a^2 + b^2 =c^2 \)
Calculating a in \( a^2 + b^2 =c^2 \)
Calculating b in \( a^2 + b^2 =c^2 \)
Calculating any side - calculator
Pythagoras - height of an equilateral triangle
Pythagoras - height of an isosceles triangle
Pythagoras - length of a diagonal
Pythagoras - compass directions and distance
Pythagoras - mixture
Year 9 - Term 3
Enlargement and similarity
Calculating missing sides in similar shapes
Ratio and proportion
Direct Proportion problems (£s)
Solving recipe problems
Inverse proportion problems
Dividing in a given ratio
Dividing in a given ratio - difference known
Dividing in a given ratio - one share known
Rates
Speed Distance Time - Mixture
Speed Distance Time -Calculating speed
Speed Distance Time - Calculating distance
Speed Distance Time - Calculating time
Converting units of speed
Density mass volume - Mixture
Density mass volume - Calculating density
Density mass volume - Calculating mass
Density mass volume - Calculating volume
Solve problems involving rates
Converting units of rates of flow
Probability
Calculated expected outcome
Calculating relative frequency
Quadratic Graphs
Calculating coordinates
Term 1
Term 2
Term 3
Year 10 - Term 1
Similarity and Enlargement
Calculating missing sides in similar shapes
Using scale factors - simple
Enlargement - lengths mixture
Enlargement - finding the new length
Enlargement - finding the original length
Enlargement - mixture - length
Enlargement - area - mixture
Enlargement - finding the new area
Enlargement - finding the original area
Enlargement - volume - mixture
Enlargement - finding the new volume
Enlargement - area mixture
Enlargement - finding the original volume
Enlargement - volume mixture
Englargement - area and volume mixture
Englargement - mixture
Pythagoras
Calculating c in \( a^2 + b^2 =c^2 \)
Calculating a in \( a^2 + b^2 =c^2 \)
Calculating b in \( a^2 + b^2 =c^2 \)
Calculating the distance between 2 points
Calculating any side - calculator
Calculating any side - exact
Pythagoras - height of an equilateral triangle
Pythagoras - height of an isosceles triangle
Pythagoras - length of a diagonal
Pythagoras - compass directions and distance
Pythagoras - mixture
Trigonometry
Sine ratio - calculating the opposite
Sine ratio - calculating the hypotenuse
Sine ratio - calculating the angle
Sine ratio - calculating angles and sides
Cosine ratio - calculating the adjacent
Cosine ratio - calculating the hypotenuse
Cosine ratio - calculating the angle
Cosine ratio - calculating angles and sides
Tangent ratio - calculating the opposite
Tangent ratio - calculating the adjacent
Tangent ratio - calculating the angle
Tangent ratio - calculating angles and sides
Mixed ratios - calculating angles
Mixed ratios - calculating angles and sides
Trigonometry in 3D - Cuboid Problems
Trigonometry in 3D - Pyramid Problems
Trigonometry in 3D - mixed Problems
Trigonometry - Sine Rule
Sine rule - calculating an angle (1)
Sine rule - calculating an angle (2)
Sine rule - calculating an angle (mix)
Sine rule - calculating sides (1)
Sine rule - calculating sides (2)
Sine rule - calculating sides (mix)
Sine rule - calculating angles and sides
Trigonometry - Cosine Rule
Cosine rule - calculating angles and sides
Cosine rule - calculating an angle
Cosine rule - calculating sides
Sine and cosine rules calculating sides
Sine and cosine rules calculating an angle
Sine and cosine rules mixture
Forming equations and expressions
Forming single step expressions
Forming equations 1 step
Forming equations 2 step
Forming and solving equations
One-step equations
One step equations (1): \( x + a = b \)
One step equations (2): \( x - a = b \)
One step equations (3): \( a - x = b \)
One step equations (4): \( ax = b \)
One step equations (5): \( \frac{x}{a} = b \)
One step equations Mixture
Two step equations
Positive solutions (1): \( ax + b = c \)
Positive solutions (2): \( ax - b = c \)
Positive solutions (3): \( a - bx = c \)
Negative solutions (4): \( ax + b = c \)
Negative solutions (5): \( ax - b = c \)
Negative solutions (6):\( a - bx = c \)
Postive mixture
Postive/Negative mixture
Fractions (1)
Equations with fractions (1):\( \frac{x}{a} - b = c \)
Equations with fractions (2):\( \frac{x}{a} + b = c \)
Equations with fractions (3):\( \frac{x + a}{b} = c \)
Equations with fractions (4):\( \frac{x - a}{b} = c \)
Equations with fractions (5) \( a - \frac{x}{b} = c \)
Equations with fractions - mixture
Brackets
Solving (1) :\( a(bx + c) = d \)
Solving (2) :\( a(bx - c) = d \)
Solving (3) :\( a(c - bx) = d \)
Mixture (1) - (3)
Solving (4) :\( a( bx + c) + d = e \)
Solving (5) :\( a( bx - c) + d = e \)
Solving (6) :\( a( bx + c) - d = e \)
Solving (7) : \( a( bx - c) - d = e \)
Solving (8) :\( a( b - cx) + d = e \)
Solving (9) :\( a( b - cx) - d = e \)
Equations with brackets - mixture
Unknown on both sides
Both sides (1) : \( ax + b = x + c \)
Both sides (2) : \( ax - b = x + c \)
Both sides (3) : \( ax + b = x - c \)
Both sides (4) : \( ax - b = x - c \)
Both sides (5) : \( ax + b = c - x \)
Both sides (6) : \( ax - b = c - x \)
Both sides (7) : \( ax + b = cx + d \)
Both sides (8) : \( ax - b = cx + d \)
Both sides (9) : \( ax + b = cx - d \)
Both sides (10) : \( ax - b = cx - d \)
Both sides (11) : \( ax + b = d - cx \)
Both sides (12) : \( ax - b = d - cx \)
Both sides mixture (1) - (12)
Both sides (13) : \( a(bx + c) = dx + e \)
Both sides (14) : \( a(bx - c) =dx + e \)
Both sides (15) : \( a(bx + c) = dx - e \)
Both sides (16) : \( a(bx - c) = dx - e \)
Both sides (17) : \( a(c - bx) + =dx + e \)
Both sides (18) : \( a(c - bx) = dx - e \
Bothsides - mixture (1) - (18)
Equations with fractions (2)
Equations with fractions (6) \(\\\frac{x}{a} + b = cx + d \)
Equations with fractions (7) \(\\\frac{x}{a} - b = cx + d \)
Equations with fractions (8) \(\\\frac{x}{a} + b = cx - d \)
Equations with fractions (9) \(\\\frac{x}{a} - b = cx - d \)
Equations with fractions (10) \(b - \\\frac{x}{a} = cx + d \)
Equations with fractions (11) \(b - \\\frac{x}{a} = cx + d \)
Equations with fractions (12) \(\\\frac{x}{a} + b = \\\frac{x}{c} + d \)
Equations with fractions (13) \(\\\frac{x}{a} - b = \\\frac{x}{c} + d \)
Equations with fractions (14) \(\\\frac{x}{a} + b = \\\frac{x}{c} - d \)
Equations with fractions (15) \(\\\frac{x}{a} - b = \\\frac{x}{c} - d \)
Equations with fractions (16) \(\\\frac{x}{a} + b = d - \\\frac{x}{c} \)
Equations with fractions (17) \(\\\frac{x}{a} - b = d -\\\frac{x}{c} \)
Equations with fractions (18) \(\\\frac{x}{a} + \\\frac{x}{b} = c \)
Equations with fractions (19) \(\\\frac{x}{a} - \\\frac{x}{b} = c \)
Equations with fractions (20) \(\\\frac{x}{a} + \\\frac{x}{b} = cx + d \)
Equations with fractions (21) \(\\\frac{x}{a} - \\\frac{x}{b} = cx + d \)
Equations with fractions (22) \(\\\frac{x}{a} + \\\frac{x}{b} = cx - d \)
Equations with fractions (23) \(\\\frac{x}{a} - \\\frac{x}{b} = cx - d \)
Equations with fractions (24) \(\\\frac{x}{a} + \\\frac{x}{b} = e - dx \)
Equations with fractions (25) \(\\\frac{x}{a} - \\\frac{x}{b} = e - dx \)
Equations with fractions - mixture
Quadratic equations
Factorise and solve \(x^2 + ax = 0 \)
Factorise and solve \(x^2 - ax = 0 \)
Factorise and solve \( ax^2 + bx = 0 \)
Factorise and solve \( ax^2 - bx = 0 \)
Factorise and solve Mixture \( ax^2 \pm bx = 0 \)
Factorise and solve \( x^2 + bx + c = 0 \)
Factorise and solve \( x^2 \pm bx - c = 0 \)
Factorise and solve \(x^2 \pm bx + c = 0 \)
Factorise and solve \(x^2 \pm bx + c = 0 \) - repeated root
Factorise and solve mixture \( x^2 \pm bx \pm c= 0 \)
Factorise and solve \( ax^2 + bx + c = 0 \)
Factorise and solve \( ax^2 \pm bx - c = 0 \)
Factorise and solve \( ax^2 - bx + c = 0 \)
Factorise and solve \( ax^2 \pm 2abx + b^2 = 0 \)
Factorise and solve mixture \( ax^2 \pm bx \pm c = 0 \)
Linear Inequalities
Solving (1): \( x + a <> b \)
Solving (2): \( x - a <> b \)
Solving (3): \( x \pm a <> b \)
Solving (4): \( ax + b <> c \)
Solving (5): \( ax - b <> c \)
Solving (6): \( ax \pm b <> c \)
Mixture (1) - (6)
Solving (7): \( \frac{x}{a} - b <> c \)
Solving (8): \( \frac{x}{a} + b <> c \)
Solving (9): \( \frac{x + a}{b} <> c \)
Solving (10): \( \frac{x - a}{b} <> c \)
Solving (11):\( a(bx + c) <> d \)
Solving (12):\( a(bx - c) <> d \)
Solving (13):\( a(bx \pm c) <> d \)
Mixture (1) - (13)
Solving (14):\( a(b - cx) <> d \)
Solving (15):\( a - \frac{x}{a} <> d \)
Solving (16):\( \frac{a - x}{b} <> d \)
Solving mixture (14) - (16)
Solving mixture (1) - (16)
Linear Inequalities - integer solutions
Integers (1) : Smallest value\( ax + b > c \)
Integers (2) : Smallest value \( ax - b > c \)
Integers (3) : Largest value \( ax - b < c \)
Linear Inequalities - integer solutions
Integers (4) : Largest value \( ax + b < c \)
Integer solutions - mixture
Quadratic inequalitites
Solving (1) :\(x^2 - bx + c \ge 0 \)
Solving (2) :\(x^2 - bx + c \le 0 \)
Solving (3) :\(x^2 - bx - c \ge 0 \)
Solving (4) :\(x^2 - bx - c \le 0 \)
Solving (5) :\( x^2 + bx - c \ge 0 \)
Quadratic inequalitites
Solving (6) :\( x^2 + bx - c \le 0 \)
Solving (7) :\( x^2 + bx + c \ge 0\)
Solving (8) :\( x^2 + bx + c \le 0\)
Solving Mixture
Simultaneous Equations
Find pairs of values
Solve problems with two unknowns
Simultaneous Eqns (1): \( x + y = r \\\ \\\ x - y = s \)
Simultaneous Eqns (2): \( ax + by = r \\\ \\\ ax - y = s \)
Simultaneous Eqns (3): \( ax + by = r \\\ \\\ ax + y = s \)
Simultaneous Eqns (4): \( ax - by = r \\\ \\\ ax - y = s \)
Simultaneous Eqns (5): \( ax + by = r \\\ \\\ x - by = s \)
Simultaneous Eqns (6): \( ax - by = r \\\ \\\ x - by = s \)
Simultaneous Eqns (7): \( ax + by = r \\\ \\\ x + by = s \)
Simultaneous Eqns Mixture (1 - 7)
Simultaneous Eqns (8): \( ax + by = r \\\ \\\ cx + dy = s \)
Simultaneous Eqns (9): \( ax - by = r \\\ \\\ cx - dy = s \)
Simultaneous Eqns (10): \( ax - by = r \\\ \\\ cx + dy = s \)
Simultaneous Eqns Mixture (8 - 10)
Simultaneous Eqns Mixture (1 -10)
Quadratic/Linear :\(y= x^2 + bx + c \\\ \\\ y = dx + e \)
Year 10 - Term 2
Angles and Bearings
Bearings
Maps and scale
Using scale drawings
Interpret scale diagrams - model to real
Interpret scale diagrams - real to model to real
Interpret maps - map to real
Interpret maps - real to map
Working with circles - area and perimeter
Radius and diameter calculations
Circumference of a circle in terms of \( \pi \)
Circumference of a circle in terms of \( \pi \) - radius known
Circumference of a circle in terms of \( \pi \) - diameter known
Circumference of a circle (1 d.p.)
Circumference of a circle (1 d.p.) - radius known
Circumference of a circle (1 d.p.) - diameter known
Calculate the arc length ( 1 d.p.)
Calculate the arc length - in terms of \( \pi \)
Area of a circle in terms of \( \pi \)
Area of a circle in terms of \( \pi \) - radius known
Area of a circle in terms of \( \pi \) - diameter known
Area of a circle - calculator
Area of a sector (1 d.p.)
Area of a sector in terms of \( \pi \)
Sectors - calculate the radius given the area and angle - exact
Sectors - calculate the angle given the area and radius -exact
Sectors - mixture - exact values
Volume and Surface area
Volume of a cylinder - radius known - in terms of pi
Volume of a cylinder -diameter known - in terms of pi
Volume of a cone -radius and vertical height known
Volume of a cone -radius and slant height known
Volume of a cone - mixture
Volume of a sphere
Calculate the radius of a sphere given the volume
Volume of asphere and radius mixture
Calculate the surface area of a cylinder
Calculate the curved surface area of a cylinder
Surface area and radius of a sphere mixture
Calculate the surface area of a sphere
Calculate the radius of a sphere given the surface area
Column Vectors
Column vectors - sum and difference
Column vectors - missing values
Column vectors mixture
Vector geometry
Vector geometry
Ratios and fractions
Using ratio language
Using the ratio symbol
Simple ratio problems
Solve problems involving ratios of the form m : n
Simplifying ratios
Simplfying ratios (mixed units)
Expressing in the form 1:n or n:1
Solve problems involving ratios of the form 1:n or n:1
Expressing a ratio as a fraction
Expressing a fraction as a ratio
Dividing in a given ratio
Dividing in a given ratio
Find the total - difference known
Find the total - one share known
Find the larger share - smaller known
Find the smaller share -larger known
Find the larger share - difference known
Find thesmaller share - difference known
Mixed problens
Solving best buy problems
UK currency for foreign currency
Foreign currency to UK currency
Exchange rates - comparing prices
Map and scale
Using scale drawings
Interpret scale diagrams - model to real
Interpret scale diagrams - real to model to real
Interpret maps - map to real
Interpret maps - real to map
Equivalence - Decimals and fractions
Decimals as fractions
Fraction as a decimal (1)
Fraction as decimal (2)
Decimals and fractions - tenths
Decimals and fractions - hundredths
Write division as a fraction
Use division - fraction as a decimal
Equivalence - Decimals and percentages
Decimal as a percentage less than 100
Decimal as a percentage greater than 100
Percentage as a decimal less than 100
Percentage as a decimal greater than 100
Mixture less than 100
Mixture greater than 100
Recurring decimals to fractions
Recurring decimals as fractions
Equivalence - Decimals and fractions
Fractions as percentages
Percentages to fractions (<100)
Percentages to fractions (>100)
Ratios and fractions
Expressing a ratio as a fraction
Expressing a fraction as a ratio
Mixture
Fractions, decimals and percentages
Percentages and Interest
Calculating a percentage of a quantity (calc)
Identifying multipliers for percentage increases
Identifying multipliers for percentage decreases
Increasing by a given percentage (calc)
Decreasing by a given percentage (calc)
Calculate the percentage increase
Calculate the percentage decrease
Calculate the percentage change
Calculating compound interest
Calculating the number of years (compound interest)
Calculate the total (compound interest)
Calculate depreciation
Finding the original < 100%
Finding the original > 100%
Calculate time to for a population to reduce to n
Probability
Calculated expected outcome
Calculating relative frequency
Year 10 - Term 3
Averages
Calculate the range
Calculate the mean - from a list
Mean given - find a missing value
Calculate the median
Find the mode
Sampling
Capture-recapture - estimating the population
Capture-recapture - calculating the sample size
Capture-recapture - calculating the number marked
Capture - recapture - mixture
Pie Charts
Pie Charts - calculating angles
Addition and Subtraction - integers
Add a 2 digit to a 3 digit number
Add two 3 digit numbers
Add two 4-digit numbers – more than one exchange
Addition - More than 4 digits
Subtract a 2 digit from a 3 digit numbers
Subtract two 3 digit
Subtract two 4-digit numbers
Subtraction - More than 4 digits
Addition and Subtraction - decimals
Add decimals - same number of d.p
Add decimals (up to 2 d.p)
Add decimals (up to 3 d.p)
Subtract decimals (same d.p)
Subtract decimals (up to 2 d.p.)
Subtract decimals (up to 3 d.p.)
Multiplication and division - integers
Multiply a 2 digit by a 1 digit number
Multiply a 3 digit by a 1 digit number
Multiply a 4 digit by a 1 digit number
Multiply by 10,100 or 1000
Multiply by 0.1 or 0.01
Multiply - 2 digit by 2 digit
Multiply - 3 digit by 2 digit
Multiply - 4 digit by 2 digit
Multiplication - by multiples of 10,100,1000
Dividing by 10,100 or 1000
Division - by multiples of 10,100,1000
2-digit ÷ 1-digit- with remainders
3-digit ÷ 1-digit
Division - 3 or 2 digit by 1 digit
Division - 4 digit by 1 digit (with remainders)
Division - 3 or 4 digit by 2 digit numbers
Multiplication and division - decimals
Multiplying by 10
Multiplying by 100
Multiplying by 1000
Multiplying by 10,100,1000 missing values
Multiplying a decimal by an integer
Multiplying by multiples of 10 or decimals
Multiplying decimals (written methods)
Multiplication - Decimals
Dividing (up to 3 digit number) by 10
Dividing (up to 3 digit number) by 100
Dividing (up to 3 digit number) by 1000
Dividing by 10 (including decimals)
Dividing by 100 (including decimals)
Dividing by 1000 (including decimals)
Missing values ÷ 10, 100, 1000
Dividing a decimal by aninteger
Division - Decimals
Addition and Subtraction - fractions
Add fractions within 1
Add fractions total greater than 1
Add any two proper fractions
Subtract fractions (common multiple den)
Subtract fractions
Multiplication and division - fractions
Find the product of a pair of unit fractions
Multiply - fraction by an integer
Find the product of a pair of proper fractions
Multiply - mixed number by an integer
Divide an integer by a fraction
Dividing a fraction by an integer
Divide a fraction by a unit fraction
Divide any pair of fractions
Surds - Simplifying
Simplifying (1):\( \sqrt{a} \)
Simplifying (2):\(\sqrt{a} \pm b + \sqrt{a} \pm c\)
Simplifying (3):\( n\sqrt{a} \pm b + m\sqrt{a} \pm c\)
Simplifying (4):\( n\sqrt{a} + \sqrt{b} \)
Simplifying (5):\( n\sqrt{a} \times m\sqrt{a} \)
Simplifying (6):\( \sqrt{a} \times \sqrt{b} \)
Simplifying (7):\( m\sqrt{a} \times n\sqrt{b} \)
Simplifying expressions involving surds
Surds - Expanding brackets
Expanding brackets (1):\( \sqrt{a}(a\sqrt{b} \pm c ) \)
Expanding brackets (2): \( \sqrt{a}(b \pm \sqrt{a} ) \)
Expanding brackets (3):\( a\sqrt{b}(c\sqrt{d} \pm e ) \)
Expanding brackets (4): \( (\sqrt{a} \pm b)( \sqrt{a} \pm c ) \)
Expanding brackets (5): \( (a\sqrt{b} \pm c)( d\sqrt{b} \pm e )\)
Expanding mixture
Surds - Rationalising the denominator
Rationalising the denominator (1):\( \frac{a}{\sqrt{b}} \)
Rationalising the denominator (2):\(\frac{a}{c \pm \sqrt{b}} \)
Rationalising the denominator (3):\(\frac{a \pm \sqrt{b}}{c \pm \sqrt{b}} \)
Rationalising the denominator mixture
Rounding
Rounding to the nearest 10
Rounding to the nearest 100
Rounding to the nearest 1000
Rounding to the nearest integer
Rounding to 1 decimal place
Rounding to 2 decimal places
Rounding to 1 significant figure (integers)
Rounding to 1 significant figure (decimals)
Rounding to 2 significant figure (integers)
Rounding to 2 significant figure (decimals)
Rounding to 3 significant figure (integers)
Rounding to 3 significant figure (decimals)
Estimating
Estimation (1): \( \frac{a + b }{c} \)
Estimation (2): \( \frac{a - b }{c} \)
Estimation (3): \( \frac{a \times b }{c} \)
Estimation (4): \( a \times b \)
Estimation (5): \( a + b \)
Estimation (6): \( a - b \)
Mixture
Error intervals
Error intervals - numbers - nearest integer
Error intervals - numbers - 1 d.p.
Error intervals - numbers - 2 d.p.
Error intervals - numbers - mixture
Error intervals - measures -nearest integer
Error intervals - measures -1 d.p.
Error intervals - measures -nearest 10
Error intervals - measures -nearest 100
Error intervals - measures -nearest 1000
Error intervals - measures -mixture
Bounds
Min/max radius
Min/max perimeter
Min/max containers
Calculations involving bounds -mixture (1)
Min/max (1): \( \frac{A \times B}{C} \)
Min/max (2):\( \frac{A}{B \times C} \)
Min/max (3):\( A + B - C \)
Min/max (4):\( C(A - B) \)
Using given calculations
Using known calculations
Use known facts - multiplication (inc decimals)
Finance
Calculating change mixture
Problem solving with money
Multiply and divide in context
Simple interest - calculating the total
Simple interest - calculating the interest
Calculating the price including VAT
Calculating Income tax
Types of numbers
Prime Numbers
Finding multiples of a number
Finding factors
Listing prime numbers
Finding the HCF
Finding the lowest common multiple
Expressing as a product of prime factors
Generating sequences
Generate a sequence given the first term and rule
Generate sequences given an algebraic rule
Generate an increasing sequence - nth term
Generate a decreasing sequence - nth term
Generate a linear sequence - nth term
Generate a quadratic sequence - nth term
Finding the nth term
Find the nth term linear - inc
Find the nth term linear - dec
Find the nth term linear - mixture
Find the nth term quadratic
Find the 10th term - quadratic
Find the nth term mixture - lin/quad
Fractions sequences - nth term
Find the nth term mixture - lin/quad
Other sequences
Continue a fibonacci sequence
Continue a geometric sequence
Find missing terms in a geometric sequence
Recognise a linear sequence
Fractions and sequences
Algebraic sequences
Term 1
Term 2
Year 11 - Term 1
Gradients and Lines
Equations of \(x = a, \\\ y = b \\\ , y = \pm x \)
Lines parallel to the x-axis
Lines parallel to the x-axis (Diagram)
Lines parallel to the y-axis
Lines parallel to the y-axis (Diagram)
Lines parallel to the axes
Lines parallel to the axes (diagram)
2 coordinates given
Coordinates on lines
Does a point lie on \( y = mx \)
Does a point lie on \( y = mx \pm c \)
Complete a coordinate for \( y = x \pm c \)
Complete a coordinate for \( y = mx \)
Complete a coordinate for \( y = mx \pm c \)
Find the mid-point of a line segment
Identify equations of non-linear graphs
Finding the gradient
Determine which is the steeper line
Identify the gradient (diagram)
Identify the gradient of \( y = mx \pm c \)
Identify the gradient after rearranging
Finding the intercept
Identify the \( y \\\ axis \) intercept for \( y = x \pm a \)
Identify the \( x \\\ axis \) intercept for \( y = x \pm a \)
Identify the \( y \\\ axis \) intercept for \( y = mx \pm c \)
Identify the intercept after rearranging
Equation of a straight - words
Equation of a line - 2 function machines
Equation of a line - through (a,b) and (0,c)
Equation of a line - through (a,b) and (c,d)
Equation of a line - gradient and y-intercept
Equation of a straight - from diagrams
\( y=mx \pm c \) - positive gradient
\( y=mx \pm c \) - negative gradient
\( y = mx \pm c \)
\( ax + by = c \)
Equations of parallel lines
Equation of a line - through (0,a)
Equation of a line - through (0,a) (rearranging)
Equation of a line - through (a,b)
Equation of a line - through (a,b)(rearranging)
Parallel lines - mixture
Equations of perpendicular lines
Equation of a line - through (0,a)
Equation of a line - through (0,a) (rearranging)
Equation of a line - through (a,b)
Equation of a line - through (a,b) (rearranging)
Perpendicular lines mixture
Parallel and perpendiclar mixture
Equation of a tangent to a circle
Non-linear graphs
Quadratic graphs
Quadratic graphs - points to plot
State the vertex of a quadratic graph
Complete the square and find the vertex (1)
Complete the square and find the vertex (2)
Symmetry (1) \( y= (x \pm a)(x\pm b) \)
Symmetry (2) \(y =x^2 \pm bx \pm c \)
Symmetry (3) \( y =ax^2 \pm bx \pm c \)
Roots (1) \(y =x^2 \pm bx \pm c \)
Roots (2) \( y =ax^2 \pm bx \pm c \)
Identify the roots from a graph
Identify the vertex from a graph
Solve \( x^2 \pm ax \pm b = \pm c \) from a graph
Equation of a circle
Finding the equation of a circle
Equation of a tangent to a circle
Expanding and factorising
Expanding single brackets
Expanding (1): \( a(bx + c) \)
Expanding (2): \( a(bx - c) \)
Expanding (3): \( a(b - cx ) \)
Expanding (4): \( ax(bx + c) \)
Expanding (5): \( ax(bx - c) \)
Expanding (6): \( ax(b - cx ) \)
Factorising (single bracket)
Factorising (1): \( ax + b \)
Factorising (2): \( ax - b \)
Factorising (3): \( a - bx \)
Factorising (4): \( ax^2 + bx \)
Factorising (5): \( ax^2 - bx \)
Factorising (6): \( bx - ax^2 \)
Expanding binomials (1)
Expanding (1): \( (x + a)(x + b) \)
Expanding (2): \( (x - a)(x - b) \)
Expanding (3): \( (x + a)(x - b) \)
Expanding (4): \( (x - a)(x + b) \)
Expanding (5): \( (x + a)^2 \)
Expanding (6): \( (x - a)^2 \)
Expanding (7): \( (x - a)(x + a) \)
Expanding binomials (2)
Expanding (8): \( (ax + b)(cx + d) \)
Expanding (9): \( (ax - b)(cx + d) \)
Expanding (10): \( (ax + b)(cx - d) \)
Expanding (11): \( (ax - b)(cx - d) \)
Expanding (12): \( (ax + b)^2 \)
Expanding (13): \( (ax - b)^2 \)
Factorise Quadratic Expressions (1)
Factorising (1): \(x^2 + bx + c\)
Factorising (2): \(x^2 ± bx - c\)
Factorising (3): \(x^2 - bx + c\)
Factorising (4): \( x^2 ± 2ax + a^2 \)
Factorise Quadratic Expressions (2)
Factorising (5): \( ax^2 + bx + c \)
Factorising (6): \( ax^2 \pm bx - c \)
Factorising (7): \( ax^2 - bx + c \)
Factorising to (8): \( (ax + b)^2 \)
Factorising to (9): \( (ax - b)^2 \)
Solve quadratics by factorisation (1)
Factorise and solve \(x^2 + ax = 0 \)
Factorise and solve (1): \(x^2 - ax = 0 \)
Factorise and solve (2):\( ax^2 + bx = 0 \)
Factorise and solve (3):\( ax^2 - bx = 0 \)
Factorise and solve (1): \( x^2 + bx + c = 0 \)
Factorise and solve (2): \( x^2 \pm bx - c = 0 \)
Factorise and solve (3): \(x^2 \pm bx + c = 0 \)
Factorise and solve (4): \(x^2 \pm bx + c = 0 \) (x = a)
Factorise and solve (5): \( ax^2 + bx + c = 0 \)
Factorise and solve (6): \( ax^2 \pm bx - c = 0 \)
Factorise and solve (7): \( ax^2 - bx + c = 0 \)
Factorise and solve (8): \( ax^2 \pm 2abx + b^2 = 0 \)
Expressing in completed square form
Expressing in the form (1): \( (x \pm a)^2 + b \)
Expressing in the form (2): \( (x \pm a)^2 + b \)
Solving using the quadratic formula
Solving using the quadratic formula
Changing the subject
Solving equations
Equations (2 step)
Equations with fractions (1)
Equations with brackets
Variable on both sides
Equations with fractions (2)
Solving Inequalities
Simple inequalities
Listing integers solutions
Single integer solutions
Solving inequatitiles
Rearranging -One-step formula
Change the subject - 1 step (1): \( y = x + a \)
Change the subject - 1 step (2) \( y = x - a \)
Change the subject - 1 step (3) \( y = ax \)
Change the subject - 1 step (4) \( y= \frac{a}{x} \)
Change the subject - 1 step (5) \( y = \frac{x}{a} \)
Change the subject - 1 step (6) \( y= a - x \)
Change the subject - mixture
Rearranging - Two-step formula
Rearranging to the form y = mx + c
Rearrange two step (1): \( y= \frac{x}{a} + b \)
Rearrange two step (2): \( y= \frac{x}{a} - b \)
Rearrange two step (3): \( y= \frac{x + a}{b} \)
Rearrange two step (4): \( y= \frac{x - a}{b} \)
Rearrange two step - mixture
Rearranging -Complex formula
Rearrange complex (1): - \( y = \sqrt{x + a} \)
Rearrange complex (2): \( y = \sqrt{x - a} \)
Rearrange complex (3): \( y = \sqrt{a - x} \)
Rearrange complex (4): \( y = \frac{\sqrt{x}}{a} \)
Rearrange complex (5): \( y = \frac{a}{\sqrt{x}} \)
Rearrange complex (6): \( y = \sqrt{\frac{a}{x}} \)
Rearrange complex (7): \( y = \sqrt{\frac{x}{a}} \)
Rearrange complex (8): \( y = \sqrt{x} + a \)
Rearrange complex (9): \( y = \sqrt{x} -a \)
Rearrange complex (10): \( y = - \sqrt{x} \)
Rearrange complex formula :mixture
Rearranging - subject appears more than once
Subject appears twice (1) \( ax = bx + c \)
Subject appears twice (2) \( ax = c - bx \)
Subject appears twice (3) \( ax + b = cx + d \)
Subject appears twice (4) \( ax - b = cx + d\)
Subject appears twice (5) \( ax - b = d - cx \)
Subject appears twice (6) \( ax + b = d - cx \)
Subject appears twice (7) \( \frac{x+a}{x+b} = c\)
Subject appears twice (8) \( \frac{x-a}{x+b} = c\)
Subject appears twice (9) \( \frac{x+a}{x-b} = c\)
Subject appears twice (10) \( ax - b = cd - d\)
Subject appears twice (11) \( \frac{x}{x-b} = c\)
Subject appears twice (12) \( \frac{x}{x+b} = c\)
Subject appears twice (13) \( \frac{ax+b}{cx + d} = e\)
Subject appears twice (14) \( \frac{ax-b}{cx + d} = e\)
Subject appears twice (15) \( \frac{ax-b}{cx-d} = e\)
Subject appears twice - mixture
Functions
Substitution Positive Integers
Substitution (1): \( x + a \)
Substitution (2): \( x - a \)
Substitution (3): \( ax \)
Substitution (4): \( \frac{a}{x} \)
Substitution (5): \( y = ax + b \)
Substitution (6): \( y = ax - b \)
Substitution (7): \( y =b - ax \)
Substitution (8): \( y = \frac{x}{a} + b \)
Substitution (9): \( y = \frac{x+a}{b} \)
Substitution (10): \( y = \frac{x-a}{b} \)
Substitution (11): \( y = \frac{ax + b}{c} \)
Substitution (12): \( y = \frac{ax - b}{c} \)
Substitution (13) : \( y = ax^2 \)
Substitution (14) : \( y = ax^2 + b \)
Substitution (15) : \( y = ax^2 - b \)
Substitution (16) : \( y = b - ax^2 \)
Substitution (17) : \( y = \frac{ax^2}{ b} \)
Substitution (18) : \( y = \frac{ax^2}{ b} + c \)
Substitution (19) : \( y = \frac{ax^2}{ b} - c \)
Substitution (20) : \( y= \sqrt{ax+b}\)
Substitution (21) : \( y= \sqrt{b-ax} \)
Substitution (22) : \( y = a\sqrt{x} + b \)
Substitution (23) : \( y = b - a\sqrt{x} \)
Substitution (24) : \( y = \sqrt{ \frac{x+a}{b}}ax^2 + b \)
Substitution (25) : \( y = \sqrt{ \frac{x+a}{b}}ax^2 - b \)
Substitution (26) : \( y = \sqrt{b(x+a)} \)
Substitution (27) : \( y = \frac{a}{ \sqrt{x+b}} \)
Substitution (28) : \( y = x^2 \pm x \)
Substitution (29) : \( y = ax^2 \pm x \)
Substitution (30) : \( y = x^2 \pm ax \)
Substitution (31) : \( y = ax^2 \pm bx \)
Substitution (32) : \( y= x^2 \pm bx + c \)
Substitution (33) : \( y = bx-ax^2 \pm c \)
Substitution (34) : \( y = ax^3 \pm bx^2 \)
Substitution (35) : \( y = ax^3 \pm bx^2 \pm cx \pm d\)
Substitution Negative Integers
Negative integers (1) : \(y = x + a \)
Negative integers (2) : \(y = x + a \)
Negative integers (3) : \(y = a - x \)
Negative integers (4) : \(y = ax \)
Negative integers (5) : \(y = \frac{x}{a} \)
Negative integers (6) : \(y = \frac{a}{x} \)
Negative integers (7) : \(y = ax + b \)
Negative integers (8) : \(y = ax - b \)
Negative integers (9) : \(y = b - ax \)
Negative integers (10) : \(y = \frac{x}{a} + b \)
Negative integers (11) : \(y = \frac{x+a}{b} \)
Negative integers (12) : \(y = \frac{x-a}{b} \)
Negative integers (13) : \(y = \frac{ax+b}{c} \)
Negative integers (14) : \(y = \frac{ax-b}{c} \)
Negative integers (15) : \(y = ax^2 \)
Negative integers (16) : \(y = ax^2 + b \)
Negative integers (17) : \(y = ax^2 - b \)
Negative integers (18) : \(y = b - ax^2 \)
Negative integers (19) : \(y = (ax)^2+b \)
Negative integers (20) : \(y = \frac{ax^2}{b} \)
Negative integers (21) : \(y = \frac{ax^2}{b} + c \)
Negative integers (22) : \(y = \frac{ax^2}{b} - c \)
Negative integers (23) : \(y = \sqrt{ax+b} \)
Negative integers (24) : \(y = \sqrt{b-ax} \)
Negative integers (25) : \(y = \sqrt{\frac{x+a}{b}} \)
Negative integers (26) : \(y = \sqrt{b(x-a)} \)
Negative integers (27) : \(y = \frac{a}{\sqrt{x+b}} \)
Negative integers (28) : \(y = x^2 \pm x \)
Negative integers (29) : \(y = ax^2 \pm x \)
Negative integers (30) : \(y = x^2 \pm ax \)
Negative integers (31) : \(y = ax^2 \pm bx \)
Negative integers (32) : \(y = x^2 \pm bx \pm c \)
Negative integers (33) : \(y = bx-ax^2\pm c \)
Negative integers (34) : \(y = ax^3 \pm bx^2 \)
Negative integers (35) :\(y = ax^3 \pm bx^2 \pm cx \pm d\)
Function notation - Evaluating
Evalutating functions (1) : \( ax^2 - b \)
Evalutating functions (2) : \( b - ax^2 \)
Evalutating functions (3) : \( (ax)^2 + b \)
Evalutating functions (4) : \( \frac{ax^2}{b} \)
Evalutating functions (5) : \( \frac{ax^2}{b} + c \)
Evalutating functions (6) : \( \frac{ax^2}{b} - c \)
Evalutating functions (7) : \( \sqrt{ax+b} \)
Evalutating functions (8) : \( \sqrt{b-ax} \)
Function notation - Evaluating
Evalutating functions (9) : \( \sqrt{\frac{x+a}{b}} \)
Evalutating functions (10) : \( x^2 + x \)
Evalutating functions (11) : \( ax^2 \pm x \)
Evalutating functions (12) : \( x^2 \pm ax \)
Evalutating functions (13) : \( ax^2 \pm bx \)
Evalutating functions (14) : \( ax - bx^2 \pm c \)
Evalutating functions (15) : \( ax^3 \pm bx^2 \)
Evalutating functions (16) : \( ax^3 \pm bx^2 \pm cx \pm d \)
Inverse functions
Inverse functions (1) : \( x - a \)
Inverse functions (2) : \( x + a \)
Inverse functions (3) : \( a - x \)
Inverse functions (4) : \( ax \)
Inverse functions (5) : \( \frac{x}{a} \)
Inverse functions (6) : \( \frac{a}{x} \)
Inverse functions (7) : \( ax + b \)
Inverse functions (8) : \( b - ax \)
Inverse functions (9) : \(ax - b \)
Inverse functions (10) : \( \frac{x+b}{a} \)
Inverse functions (11) : \( \frac{x-b}{a} \)
Inverse functions (12) : \( \frac{b-x}{a} \)
Inverse functions (13) : \( \frac{a}{x + b} \)
Inverse functions (14) : \( \frac{a}{x - b} \)
Inverse functions (15) : \( \frac{x}{a} + b \)
Inverse functions (16) : \( \frac{x}{a} - b \)
Inverse functions (17) : \( \sqrt{x} \)
Inverse functions (18) : \( a \sqrt{x} \)
Inverse functions (19) : \( \sqrt{x + a } \)
Inverse functions (20) : \( \sqrt{x - a } \)
Inverse functions (21) : \( \sqrt{a - x} \)
Inverse functions (22) : \( \frac{ \sqrt{x}}{a} \)
Inverse functions (23) : \( \frac{a}{\sqrt{x}} \)
Inverse functions (24) : \( \sqrt{ \frac{a}{x} } \)
Inverse functions (25) : \( \sqrt{\frac{x}{a}} \)
Inverse functions (26) : \( \sqrt{x} + a \)
Inverse functions (27) : \( \sqrt{x} - a \)
Inverse functions (28) : \( a - \sqrt{x} \)
Inverse functions (29) : \( a \sqrt{x + b} \)
Inverse functions (30) : \( a \sqrt{x - b} \)
Inverse functions (31) : \( a + \sqrt{x - b} \)
Inverse functions (32) : \( a - \sqrt{x - b} \)
Inverse functions (33) : \( a - \sqrt{x + b} \)
Inverse functions (34) : \( \frac{\sqrt{x + b}}{a} \)
Inverse functions (35) : \( \sqrt{ \frac{x-b}{a}} \)
Inverse functions (36) : \( \sqrt{ \frac{x+b}{a}} \)
Inverse functions (37) : \( \frac{\sqrt{x}}{a}+b \)
Inverse functions (38) : \( \frac{\sqrt{x}}{a}-b \)
Inverse functions (39) : \( b - \frac{\sqrt{x}}{a} \)
Inverse functions (40) : \( \sqrt{ax + b} \)
Inverse functions (41) : \( \sqrt{ax - b} \)
Inverse functions (42) : \( \sqrt{b - ax} \)
Inverse functions (43) : \( \frac{ \sqrt{x}}{a} + b \)
Inverse functions mixture
Forming composite functions
(1) : \( fg(x) \\ f(x) = ax \pm b \\\ \\\ g(x) = cx \pm d \)
(2) : \( gf(x) \\\ f(x) = ax \pm b \\\ \\\ g(x) = cx \pm d \)
(3) : \( fg(x) \\\ f(x) = x^2 \\\ \\\ g(x) = ax \pm b \)
(4) : \( g(x) \\\ f(x) = x^2 \\\ \\\ g(x) = ax \pm b \)
(5) : \( fg(x) \\\ f(x) = ax^2 \\\ \\\ g(x) = bx \pm c \)
(6) : \( gf(x) \\\ f(x) = ax^2 \\\ \\\ g(x) = bx \pm c \)
(7) : \( fg(x) \\\ f(x) = x^2 \pm a \\\ \\\ g(x) = x \pm b \)
(8) : \( gf(x) \\\ f(x) = x^2 \pm a \\\ \\\ g(x) = x \pm b \)
(9) : \( fg(x) \\\ f(x) = a \pm bx \\\ \\\ g(x) = cx \pm d \)
(10): \( gf(x) \\\ f(x) = a \pm bx \\\ \\\ g(x) = cx \pm d \)
Composite functions - mixture
Trigonometry recap
Sine ratio - calculating angles/sides (mix)
Cosine ratio - calculating angles/sides (mix)
Tangent ratio - calculating angles and sides (mix)
Quadratic inequalitites
Solving (1) :\(x^2 - bx + c \ge 0 \)
Solving (2) :\(x^2 - bx + c \le 0 \)
Solving (3) :\(x^2 - bx - c \ge 0 \)
Solving (4) :\(x^2 - bx - c \le 0 \)
Solving (5) :\( x^2 + bx - c \ge 0 \)
Quadratic inequalitites
Solving (6) :\( x^2 + bx - c \le 0 \)
Solving (7) :\( x^2 + bx + c \ge 0\)
Solving (8) :\( x^2 + bx + c \le 0\)
Solving Mixture
Year 11 - Term 2
Scale factors - Length
Using scale factors - simple
Missing lengths - similar rectangles
Calculating missing sides in similar shapes
Enlargement - lengths mixture
Enlargement - finding the new length
Enlargement - finding the original length
Scale Factors - Area
Enlargement - area - mixture
Enlargement - finding the new area
Enlargement - finding the original area
Scale factors - Volume
Enlargement - finding the new volume
Enlargement - finding the original volume
Direct proportion problems
Solve problems involving scaling
Solve problems involving rates
Direct Proportion problems (£s)
Direct Proportion problems
Solving recipe problems
Solving best buy problems
UK currency for foreign currency
Foreign currency to UK currency
Exchange rates - comparing prices
Forming and using formulae
Direct proportion (1) : \( y \propto kx \)
Direct proportion (2) : \( y \propto kx^2 \)
Direct proportion (3) : \( y \propto k \sqrt[3]{x} \)
Direct proportion (4) : \( y \propto kx^3 \)
Direct proportion (5) : \( y \propto \ k \sqrt{x} \)
Direct proportion - formula - mixture
Mass Volume Density
Density mass volume (1) - density
Density mass volume (2) - mass
Density mass volume (3) - volume
Density mass volume - Mixture
Force Area Pressure
Pressure Force and Area (1) - pressure
Pressure , Force and Area (2) - force
Pressure , Force and Area (3) - area
Pressure , Force and Area - mixture
Inverse Proportion
Inverse proportion problems
Forming and using formulae
Inverse proportion (1) : \( y \propto \frac{k}{x} \)
Inverse proportion (2) : \( y \propto \frac{k}{x^2} \)
Inverse proportion (3) : \( y \propto \frac{k}{\sqrt{x}} \)
Ratio Problems
Dividing in a given ratio
Dividing in a given ratio - difference known
Dividing in a given ratio - one share known
Find the larger share - smaller known
Find the smaller share -larger known
Find the larger share - difference known
Find the smaller share - difference known
Percentage calculations- non calc
5% of a quantity
5% 10% and 15% of quantity
5% 10% and 20% of a quantity
15% of a quantity
Multiples of 5%
Percentages - missing values
Expressing as a percentage
Calculate a percentage increase
Calculate a percentage decrease
Calculate a percentage change
Fraction - calculations - non calc
Calculate a fraction of a quantity
Multiply - fraction by an integer
Find the product of a pair of proper fractions
Multiply - mixed number by an integer
Find the whole -given a fraction
Angles and Polygons
Angles and polygons
Calculate missing angles triangles
Calculate angles in a quadrilateral
Interior angles - polygons
Exterior angles - polygons
Angles and parallel lines
(1) Corresponding angles
(2) Allied/co-interior angles
(3) Alternate angles
Basic Mixtures (1-3)
Mixture (1)
Pythagoras
Calculating c in \( a^2 + b^2 =c^2 \)
Calculating a in \( a^2 + b^2 =c^2 \)
Calculating b in \( a^2 + b^2 =c^2 \)
Calculating the distance between 2 points
Calculating any side - calculator
Calculating any side - exact
Pythagoras - height of an equilateral triangle
Pythagoras - height of an isosceles triangle
Pythagoras - length of a diagonal
Pythagoras - compass directions and distance
Pythagoras - mixture
Trigonometry
Sine ratio - calculating the opposite
Sine ratio - calculating the hypotenuse
Sine ratio - calculating the angle
Sine ratio - calculating angles and sides
Cosine ratio - calculating the adjacent
Cosine ratio - calculating the hypotenuse
Cosine ratio - calculating the angle
Cosine ratio - calculating angles and sides
Tangent ratio - calculating the opposite
Tangent ratio - calculating the adjacent
Tangent ratio - calculating the angle
Tangent ratio - calculating angles and sides
Mixed ratios - calculating angles
Mixed ratios - calculating angles and sides
Trigonometry
Trigonometry in 3D - Cuboid Problems
Trigonometry in 3D - Pyramid Problems
Trigonometry in 3D - mixed Problems
Cosine rule - calculating angles and sides
Cosine rule - calculating an angle
Cosine rule - calculating sides
Sine rule - calculating angles and sides
Sine rule - calculating an angle
Sine rule - calculating sides
Sine and cosine rules calculating sides
Sine and cosine rules calculating an angle
Sine and cosine rules mixture
Simplifying Expressions
Multiplying terms \( ax^m \times b x^n \)
Dividing terms \( ax^n y^m \div cx \)
Simplifying \( (ax^n)^m \)
nth term - linear
Find the nth term linear - inc
Find the nth term linear - dec
Find the nth term linear - mixture
nth term quadratic
Find the nth term quadratic
Find the 10th term - quadratic
Find the nth term mixture - lin/quad
Fractions sequences - nth term
Other sequences
Continue a fibonacci sequence
Continue a geometric sequence
Find missing terms in a geometric sequence
Recognise a linear sequence
Fractions and sequences
Algebraic sequences
Simultaneous Equations
Find pairs of values
Solve problems with two unknowns
Simultaneous Eqns (1): \( x + y = r \\\ \\\ x - y = s \)
Simultaneous Eqns (2): \( ax + by = r \\\ \\\ ax - y = s \)
Simultaneous Eqns (3): \( ax + by = r \\\ \\\ ax + y = s \)
Simultaneous Eqns (4): \( ax - by = r \\\ \\\ ax - y = s \)
Simultaneous Eqns (5): \( ax + by = r \\\ \\\ x - by = s \)
Simultaneous Eqns (6): \( ax - by = r \\\ \\\ x - by = s \)
Simultaneous Eqns (7): \( ax + by = r \\\ \\\ x + by = s \)
Simultaneous Eqns (8): \( ax + by = r \\\ \\\ cx + dy = s \)
Simultaneous Eqns (9): \( ax - by = r \\\ \\\ cx - dy = s \)
Simultaneous Eqns (10): \( ax - by = r \\\ \\\ cx + dy = s \)
Quadratic/Linear :\(y= x^2 + bx + c \\\ \\\ y = dx + e \)
Random Order
Yes
No