### Number Sequences 1

What is the 9th:
a) Odd number; 17
b) Square number; 81
c) Prime number. 23

### Factors

Find all the factors of:

24

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

### Multiples

Subtract the 7th from the 10th multiples of:

4

12

### Polygons

What are the names of regular polygons with:
a) four sides;
b) five sides;
c) six sides.

Square, Pentagon and Hexagon (all regular)

### Rounding

Round the following numbers to three significant figures:
a) 31.75; 31.8
b) 332538; 333000
c) 0.002895; 0.00290

### Area of a Triangle

Find the area of a triangle that has a base of 3cm and a height of 6cm.

9cm2

### Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 7cm and a top (parallel to base) of 3cm. 56cm2

Evaluate:

$$\frac{4}{5} + \frac{6}{9}$$ $$= 1\frac{7}{15}$$

### Fractions (Multiplying)

Evaluate:

$$\frac{3}{4} × \frac{6}{7}$$ $$= \frac{9}{14}$$

### Fractions (Dividing)

Evaluate:

$$\frac{1}{3} ÷ \frac{5}{4}$$ $$= \frac{4}{15}$$

### 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.

$$\frac{4}{5}$$ $$= 80$$%

### Circle Area

Find the area of a circle that has a radius of 7cm. Give your answer to three significant figures.

154cm2

### Circle Circumference

Find the circumference of a circle that has a radius of 4cm. Give your answer to three significant figures.

25.1cm2

Calculate the value of:

8.8 + 7.9

= 16.7

### Decimals (Subtracting)

Calculate the value of:

5.4 − 2.5

= 2.9

### Decimals (Multiplying)

Calculate the value of:

3.7 × 4.7

= 17.39

### Decimals (Dividing)

Calculate the value of:

32.4 ÷ 12

= 2.7

### Indices (Simple)

What is the value of:

33

= 27

What is the value of:

3-3

= 0.037037037037037

Calculate the value of:

28 + 49

= 77

### Basic Subtraction

Calculate the value of:

61 − 28

= 33

### Basic Multiplication

Calculate the value of:

45 × 66

= 2970

### Basic Division 2

Calculate the value of:

954 ÷ 18

= 53

### Percentage (Of)

Find the value of:

60% of 220

= 132

### Standard Form 1

Find the value of:

7.19 × 104

= 71900

### Highest Common Factor

Find the highest common factor of twenty eight and eight.

= 4

### Times Tables (2-5)

 8 × 4 = 32 4 × 3 = 12 5 × 2 = 10 6 × 2 = 12 3 × 5 = 15 7 × 2 = 14 9 × 5 = 45 2 × 4 = 8

### Times Tables (2-12)

 5 × 12 = 60 6 × 10 = 60 3 × 3 = 9 4 × 2 = 8 9 × 3 = 27 8 × 8 = 64 7 × 4 = 28 2 × 4 = 8

### Times Tables (2)

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

### Times Tables (3)

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

### Times Tables (4)

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

### Times Tables (5)

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

### Times Tables (6)

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

### Times Tables (7)

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

### Times Tables (8)

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

### Times Tables (9)

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

### Times Tables (12)

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

### Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{36}{63}$$ $$= \frac{4}{7}$$

### Fractions (Mixed)

Evaluate:

$$3\frac{3}{4} − \frac{5}{6}$$ $$= 2\frac{11}{12}$$

### Pythagoras

Find AC if AB = 3.5m and BC = 4.9m. 3.43m

### Trigonometry (Angle)

Find angle BCA if AB = 3.6m and BC = 5.2m. 43.8o

### Trigonometry (Side)

Find AC if angle ABC = 55o and BC = 5.3m. 4.34m

2

2

2

### Fraction to Decimal

Convert this fraction to a decimal to 3 significant figures.

$$\frac{4}{7}$$ $$= 0.571$$

### Decimal to Fraction

Convert this decimal to a fraction.

$$0.65$$ = $$\frac{13}{20}$$

### Percentage (Increase)

Increase £20 by 20%

£24

### Lowest Common Multiple

What is the lowest common multiple of eight and twenty.

= 40

### Sequence (Arithmetic)

5,17,29,41,53...

Find the:
a) next term; 65
b) nth term; 12n - 7
c) term number 47; 557

### Sequence (Geometric)

4,8,16,32,64...

Find the:
a) next term; 128
b) nth term; 4 × 2n-1
c) term number 10; 2048

### Interest (Simple)

If £140 is invested for 5 years with a simple interest rate of 2%, find the amount of interest earned. £14.00

### Interest (Compound)

If £240 is invested with an interest rate of 2% compounded annually, find the value of the investment after 8 years. £281.20

### Currency Exchange

If £1 is worth $1.52, convert: a) £160 to dollars;$243.20

b) \$240 to pounds; £105.26

### Coordinates (Midpoint)

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

$$(-9,1) \text{ and } (1,9)$$

(-4,5)

What is the gradient of the line joining:

$$(7,4) \text{ and } (11,7)$$

$$\frac{3}{4}$$

### Coordinates (Square)

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

$$(2,2),(5,5),(-1,5)$$

(2,8)

### Negative Numbers

a) 9 − 14 = -5
b) 9 × (-7) = -63
c) (8−15)(5−14) = 63
d) 63 ÷ (-7) = -9
e) (-12)2 = 144

### Substitution

If p = 6, q = 19 and
r = -12 evaluate:

a) 2q − p = 32
b) pq + r = 102
c) p2 − 5q - r = -47

### Equations (Type 1)

Solve:

$$4x = 20$$

$$x = 5$$

### Equations (Type 2)

Solve:

$$4x +7= 19$$

$$x = 3$$

### Equations (Type 3)

Solve:

$$8x +6= 6x + 24$$

$$x = 9$$

### Equations (Type 4)

Solve:

$$2(2x +2)+8= 48$$

$$x = 9$$

### Equations (Type 5)

Solve:

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

$$x = -0.154 \text{(to 3 sf)}$$

### Equations (Simultaneous 1)

Solve:

$$4x-3y = -1$$
$$5x+3y = 19$$

$$x = 2, y = 3$$

### Equations (Simultaneous 2)

Solve:

$$3x+5y = 48$$
$$4x+20y = 144$$

$$x = 6, y = 6$$

### Equations (Simultaneous 3)

Solve:

$$4x-3y = -33.5$$
$$4x+2y = -11$$

$$x = -5, y = 4.5$$

### Sets (Union)

Find the union of:

{2,4,6,8,10} and
{5,6,7,8,9,10}

{2,4,5,6,7,8,9,10}

### Sets (Intersection)

Find the intersection of:

{1,3,5,7,9} and
{1,3,6,10,15}

{1,3}

### Bearings

A plane flies from point A to point B on a bearing of 209o. What bearing would it return on from B to A? 029o

### Probability

A number is picked at random from the set

{1,3,6,10,15}

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

Evaluate:

12 ÷ 4 × 8 ÷ 2

12

### Simplify

Simplify the following by collecting like terms:

$$5a−5−4a−5$$

$$a-10$$

### Ratio

Divide 96 in the ratio

7:9

42 and 54

### Graph (Linear)

Draw a rough sketch of the graph of:

$$y=x+2$$

y intercept 2

### Prime Factors

Express the following number as the product of prime numbers:

23

23

### Percentage (Reverse)

In a sale an item costs £48 after a 20% reduction. What was the original price?

£60

### Averages

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

2,6,12,6,14

Mean = 8, mode = 6,
median = 6 and range = 12

### 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.

0.656565... $$\frac{65}{99}$$

### Percentage (Decrease)

Decrease £160 by 40%

£96

### Brackets (Linear)

Expand:

$$3(3x-6)$$

$$9x-18$$

Expand:

$$(3x+4)(2x-4)$$

$$6x^2-4x-16$$

### Factorise (Linear)

Factorise:

$$24x-18$$

$$6(4x-3)$$

Factorise:

$$x^2+3x-4$$

$$(x+4)(x-1)$$

Factorise:

$$5x^2+18x-8$$

$$(x+4)(5x-2)$$

Which theorem?

### Standard Form 2

Find the value of:

1.63 × 10-2

= 0.0163

### Standard Form 3

Write in standard form:

299

= 2.99 × 102

### Standard Form 4

Write in standard form:

0.00619

= 6.19 × 10-3

Find the nth term:

$$13, 18, 25, 34, 45,$$

$$n^2+2n+10$$

### Standard Form 5

Multiply 6 × 105
by 6 × 103 and give the answer in standard form.

= 3.6 × 109

Solve:

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

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

Solve this equation giving the solutions to 3 significant figures:

$$4x^2+2x-4 = 0$$

$$x = 0.781$$ and $$-1.28$$

### Polygon Angles

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

36°

### Change The Subject

Make $$a$$ the subject of the formula
$$b=2a-3$$

$$a=\frac{b+3}{2}$$

### Basic Division 1

Calculate the value of:

1442 ÷ 7

= 206

### Number Sequences 2

What is the 7th:
a) Cube number; 343
b) Triangular number; 28
c) Fibonacci number. 13

## A Mathematics Lesson Starter Of The Day

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• 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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• Answers for the starter would be great so students can get immediate feedback and become independent learners.

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• Mrs B, Stockport
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• 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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• It would be great if these questions came with answers as well.

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