Number Sequences 1

What is the 7th:
a) Odd number; 13
b) Square number; 49
c) Prime number. 17

Factors

Find all the factors of:

24

1, 2, 3, 4, 6, 8, 12, 24.

Multiples

Subtract the 7th from the 12th multiples of:

4

20

Polygons

What are the names of regular polygons with:
a) eight sides;
b) nine sides;
c) ten sides.

Octagon, Nonagon and Decagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 12.08; 12.1
b) 641335; 641000
c) 67; 67.0
d) 0.006795; 0.00680

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 9cm.

18cm2

Area of a Trapezium

Find the area of a trapezium that has a base of 15cm, a height of 8cm and a top (parallel to base) of 7cm. 88cm2

Evaluate:

$$\frac{4}{7} + \frac{8}{10}$$ $$= 1\frac{13}{35}$$

Fractions (Multiplying)

Evaluate:

$$\frac{3}{4} × \frac{6}{8}$$ $$= \frac{9}{16}$$

Fractions (Dividing)

Evaluate:

$$\frac{1}{3} ÷ \frac{7}{5}$$ $$= \frac{5}{21}$$

Circle (Vocabulary)

Name the red part.

Venn Diagrams

Describe the red region.

Shape Formulas

What is the formula?

What is it?

Fraction to Percentage

Convert this fraction to a percentage.

$$\frac{3}{5}$$ $$= 60$$%

Circle Area

Find the area of a circle that has a radius of 5cm. Give your answer to three significant figures.

78.5cm2

Circle Circumference

Find the circumference of a circle that has a radius of 12cm. Give your answer to three significant figures.

75.4cm

Calculate the value of:

6.5 + 4.4

= 10.9

Decimals (Subtracting)

Calculate the value of:

5.1 − 2.9

= 2.2

Decimals (Multiplying)

Calculate the value of:

9.4 × 7.2

= 67.68

Decimals (Dividing)

Calculate the value of:

126.1 ÷ 13

= 9.7

Indices (Simple)

What is the value of:

52

= 25

What is the value of:

$$5^{-2}$$

$$= \frac{1}{25}$$

Calculate the value of:

88 + 24

= 112

Basic Subtraction

Calculate the value of:

71 − 28

= 43

Basic Multiplication

Calculate the value of:

46 × 88

= 4048

Basic Division 2

Calculate the value of:

1092 ÷ 13

= 84

Percentage (Of)

Find the value of:

5% of 380

= 19

Standard Form 1

Find the value of:

5.38 × 104

= 53800

Highest Common Factor

Find the highest common factor of forty and twenty.

= 20

Times Tables (2-5)

 5 × 4 = 20 7 × 3 = 21 8 × 2 = 16 6 × 3 = 18 4 × 4 = 16 3 × 3 = 9 9 × 2 = 18 2 × 4 = 8

Times Tables (2-12)

 4 × 6 = 24 6 × 2 = 12 9 × 10 = 90 5 × 3 = 15 7 × 4 = 28 3 × 12 = 36 8 × 6 = 48 2 × 9 = 18

Times Tables (2)

 3 × 2 = 6 7 × 2 = 14 5 × 2 = 10 8 × 2 = 16 4 × 2 = 8 6 × 2 = 12 9 × 2 = 18 2 × 2 = 4

Times Tables (3)

 4 × 3 = 12 6 × 3 = 18 8 × 3 = 24 9 × 3 = 27 5 × 3 = 15 3 × 3 = 9 7 × 3 = 21 2 × 3 = 6

Times Tables (4)

 4 × 4 = 16 3 × 4 = 12 9 × 4 = 36 5 × 4 = 20 6 × 4 = 24 8 × 4 = 32 7 × 4 = 28 2 × 4 = 8

Times Tables (5)

 8 × 5 = 40 5 × 5 = 25 3 × 5 = 15 9 × 5 = 45 6 × 5 = 30 4 × 5 = 20 7 × 5 = 35 2 × 5 = 10

Times Tables (6)

 3 × 6 = 18 4 × 6 = 24 9 × 6 = 54 5 × 6 = 30 7 × 6 = 42 6 × 6 = 36 8 × 6 = 48 2 × 6 = 12

Times Tables (7)

 5 × 7 = 35 9 × 7 = 63 3 × 7 = 21 7 × 7 = 49 4 × 7 = 28 8 × 7 = 56 6 × 7 = 42 2 × 7 = 14

Times Tables (8)

 4 × 8 = 32 3 × 8 = 24 7 × 8 = 56 6 × 8 = 48 5 × 8 = 40 8 × 8 = 64 9 × 8 = 72 2 × 8 = 16

Times Tables (9)

 9 × 9 = 81 3 × 9 = 27 5 × 9 = 45 8 × 9 = 72 7 × 9 = 63 6 × 9 = 54 4 × 9 = 36 2 × 9 = 18

Times Tables (12)

 7 × 12 = 84 4 × 12 = 48 3 × 12 = 36 8 × 12 = 96 6 × 12 = 72 5 × 12 = 60 9 × 12 = 108 2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{9}{27}$$ $$= \frac{1}{3}$$

Fractions (Mixed)

Evaluate:

$$1\frac{3}{4} − \frac{7}{8}$$ $$= \frac{7}{8}$$

Pythagoras

Find AC if AB = 4.4m and BC = 6.3m. 4.51m

Trigonometry (Angle)

Find angle ABC if AC = 3.1m and BC = 4.2m. 47.6o

Trigonometry (Side)

Find BC if angle BCA = 35o and AC = 5.6m. 6.84m

2

2

2

Fraction to Decimal

Convert this fraction to a decimal to 3 significant figures.

$$\frac{1}{6}$$ $$= 0.167$$

Decimal to Fraction

Convert this decimal to a fraction.

$$0.33$$ = $$\frac{33}{100}$$

Percentage (Increase)

Increase £40 by 45%

£58

Lowest Common Multiple

What is the lowest common multiple of twelve and twenty four.

= 24

Sequence (Arithmetic)

2,9,16,23,30...

Find the:
a) next term; 37
b) nth term; 7n - 5
c) term number 42; 289

Sequence (Geometric)

7,28,112,448,1792...

Find the:
a) next term; 7168
b) nth term; 7 × 4n-1
c) term number 10; 1835008

Interest (Simple)

If £220 is invested for 4 years with a simple interest rate of 4%, find the amount of interest earned. £35.20

Interest (Compound)

If £140 is invested with an interest rate of 6% compounded annually, find the value of the investment after 4 years. £176.75

Currency Exchange

If £1 is worth $1.25, convert: a) £180 to dollars;$225.00

b) \$200 to pounds; £160.00

Coordinates (Midpoint)

What are the coordinates of the midpoint of the line joining:

$$(9,-4) \text{ and } (19,8)$$

(14,2)

What is the gradient of the line joining:

$$(-9,9) \text{ and } (-3,14)$$

$$\frac{5}{6}$$

Coordinates (Square)

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?

$$(3,3),(6,9),(-3,6)$$

(0,12)

Negative Numbers

a) 11 − 16 = -5
b) 11 × (-5) = -55
c) (12−18)(12−20) = 48
d) 55 ÷ (-5) = -11
e) (-11)2 = 121

Substitution

If p = 6, q = 22 and
r = -12 evaluate:

a) 2q − p = 38
b) pq + r = 120
c) p2 − 5q - r = -62

Equations (Type 1)

Solve:

$$4x = 12$$

$$x = 3$$

Equations (Type 2)

Solve:

$$3x +3= 27$$

$$x = 8$$

Equations (Type 3)

Solve:

$$7x +4= 2x + 39$$

$$x = 7$$

Equations (Type 4)

Solve:

$$2(2x +5)+12= 34$$

$$x = 3$$

Equations (Type 5)

Solve:

$$4(2x + 2)= 5(3x + 4)$$

$$x = -1.71 \text{(to 3 sf)}$$

Equations (Simultaneous 1)

Solve:

$$2x+4y = 30$$
$$3x-4y = -15$$

$$x = 3, y = 6$$

Equations (Simultaneous 2)

Solve:

$$3x-2y = 7$$
$$6x+6y = 54$$

$$x = 5, y = 4$$

Equations (Simultaneous 3)

Solve:

$$2x+2y = -5$$
$$3x+5y = 0.5$$

$$x = -6.5, y = 4$$

Sets (Union)

Find the union of:

{1,3,5,7,9} and
{5,6,7,8,9,10}

{1,3,5,6,7,8,9,10}

Sets (Intersection)

Find the intersection of:

{1,3,5,7,9} and
{3,4,5,6,7,8}

{3,5,7}

Bearings

A plane flies from point A to point B on a bearing of 062o. What bearing would it return on from B to A? 242o

Probability

A number is picked at random from the set

{3,6,9,12,15}

what is the probability it is even? $$\frac25$$

Evaluate:

7 + (8 × 62 − 6)

289

Simplify

Simplify the following by collecting like terms:

$$3a+5b-3a+4b^2$$

$$5b+4b^2$$

Ratio

Divide 99 in the ratio

7:2

77 and 22

Graph (Linear)

Draw a rough sketch of the graph of:

$$2y=x+4$$

y intercept 2

Prime Factors

Express the following number as the product of prime numbers:

18

2 x 3 x 3

Percentage (Reverse)

In a sale an item costs £22 after a 45% reduction. What was the original price?

£40

Averages

Find the mean, mode, median and range of the following:

2,4,6,8,10

Mean = 6, no mode,
median = 6 and range = 8

Time (Analogue)

What time is this?

Time (Digital)

Sketch a clock face:

Decimals (Recurring)

Write the following recurring decimal as a fraction in its lowest terms.

0.131313... $$\frac{13}{99}$$

Percentage (Decrease)

Decrease £80 by 10%

£72

Brackets (Linear)

Expand:

$$3(2x-7)$$

$$6x-21$$

Expand:

$$(x+3)(4x-4)$$

$$4x^2+8x-12$$

Factorise (Linear)

Factorise:

$$35x-10$$

$$5(7x-2)$$

Factorise:

$$x^2+x-6$$

$$(x+3)(x-2)$$

Factorise:

$$x^2-x-6$$

$$(x+2)(x-3)$$

Which theorem?

Standard Form 2

Find the value of:

4.3 × 10-5

= 0.000043

Standard Form 3

Write in standard form:

3430

= 3.43 × 103

Standard Form 4

Write in standard form:

0.021

= 2.1 × 10-2

Find the nth term:

$$4, 15, 32, 55, 84,$$

$$3n^2+2n-1$$

Standard Form 5

Multiply 8 × 103
by 4 × 103 and give the answer in standard form.

= 3.2 × 107

Solve:

$$x^2+2x-8= 0$$

$$x = 2$$ and $$-4$$

Solve this equation giving the solutions to 3 significant figures:

$$3x^2+2x-2 = 0$$

$$x = 0.549$$ and $$-1.22$$

Polygon Angles

What is the size of each exterior angle of a regular pentagon?

72°

Change The Subject

Make $$g$$ the subject of the formula
$$e=\frac{g}{h}+d$$

$$g=h(e-d)$$

Basic Division 1

Calculate the value of:

924 ÷ 3

= 308

Number Sequences 2

What is the 12th:
a) Cube number; 1728
b) Triangular number; 78
c) Fibonacci number. 144

Square Numbers

What is the square of

7

49

Prime Numbers

What is the difference between the 7th and the 8th prime numbers?

19 - 17 = 2

Last Lesson

Write down something you learnt in the previous mathematics lesson.

Last Week

Write down something you learnt in one of the mathematics lessons last week.

Angles

Calculate $$x$$.

Decimals (Ordering)

Write down these numbers: 7.7, 7, 0.77, 7.77, 7.07, 0.7, 0.07, in ascending order.
0.07, 0.7, 0.77, 7, 7.07, 7.7, 7.77,

Lengths (Ordering)

Write down these lengths: 17cm, 1.8m, 18mm, 107cm, 1.08m, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

Write down these capacities: 18cl, 173ml, 200ml, 21cl, 17cl, 18ml, in order.
18ml, 17cl, 173ml, 18cl, 200ml, 21cl,

j = 97

a = 132

Rounding (1sf)

Round to one significant figure:
a) 30.35; 30
b) 926373; 900000
c) 26; 30
d) 0.00970; 0.01

Bringing Memories Back To Life

• Jan, South Canterbury
•
• Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you.
• Barbara Schindler, Newton Rigg College
•
• I use Refreshing Revision a lot but today all the brackets and fractions keep coming up 'jumbled' . There are curly brackets, part words / 's in odd places and it is impossible to make out the question. It is doing this on 2 computers I have tried. Can you help? thank you.

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• Lesley, UK
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• Mrs B, Stockport
•
• Refreshing Revision really useful resource, that I have actually used for Ks2 revision as some topics are appropriate. I'd love to see either ks2 version, with purely ks2 SATs level topics or adding them to the current version.

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• Mr Barton, Podcast #183
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• … very common practise in UK maths classrooms would be the first five minutes of the lesson the students would be presented with four questions on four topics they've encountered some time in the past. A classic structure for this is a question from last lesson a question from last week a question from last term and a question from last year which is quite nice for spacing and that for me seems very clear that's retrieval practise because the kids have been taught it and then having to try and remember things from long term memory.

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