Number Sequences 1

What is the 5th:
a) Odd number; 9
b) Square number; 25
c) Prime number. 11

Factors

Find all the factors of:

22

1, 2, 11, 22.

Multiples

Subtract the 5th from the 9th multiples of:

10

40

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) 42.56; 42.6
b) 578822; 579000
c) 0.006295; 0.00630

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 8cm.

16cm2

Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 8cm and a top (parallel to base) of 7cm. 80cm2

Evaluate:

$$\frac{1}{4} + \frac{6}{9}$$ $$= \frac{11}{12}$$

Fractions (Multiplying)

Evaluate:

$$\frac{2}{3} × \frac{5}{6}$$ $$= \frac{5}{9}$$

Fractions (Dividing)

Evaluate:

$$\frac{2}{3} ÷ \frac{5}{4}$$ $$= \frac{8}{15}$$

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 to 3 significant figures.

$$\frac{1}{6}$$ $$= 16.7$$%

Circle Area

Find the area of a circle that has a radius of 10cm. Give your answer to three significant figures.

314cm2

Circle Circumference

Find the circumference of a circle that has a radius of 10cm. Give your answer to three significant figures.

62.8cm2

Calculate the value of:

3.5 + 7.9

= 11.4

Decimals (Subtracting)

Calculate the value of:

6.2 − 2.5

= 3.7

Decimals (Multiplying)

Calculate the value of:

7.2 × 2.6

= 18.72

Decimals (Dividing)

Calculate the value of:

118.4 ÷ 16

= 7.4

Indices (Simple)

What is the value of:

23

= 8

What is the value of:

5-1

= 0.2

Calculate the value of:

58 + 66

= 124

Basic Subtraction

Calculate the value of:

62 − 25

= 37

Basic Multiplication

Calculate the value of:

28 × 26

= 728

Basic Division 2

Calculate the value of:

1140 ÷ 15

= 76

Percentage (Of)

Find the value of:

30% of 60

= 18

Standard Form 1

Find the value of:

7.09 × 105

= 709000

Highest Common Factor

Find the highest common factor of eighteen and six.

= 6

Times Tables (2-5)

 5 × 3 = 15 6 × 2 = 12 7 × 4 = 28 8 × 5 = 40 3 × 3 = 9 9 × 2 = 18 4 × 4 = 16 2 × 5 = 10

Times Tables (2-12)

 6 × 5 = 30 5 × 6 = 30 3 × 8 = 24 7 × 3 = 21 9 × 3 = 27 4 × 3 = 12 8 × 8 = 64 2 × 3 = 6

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

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

Fractions (Mixed)

Evaluate:

$$2\frac{4}{5} − \frac{8}{9}$$ $$= 1\frac{41}{45}$$

Pythagoras

Find AB if AC = 3.1m and BC = 4.8m. 3.66m

Trigonometry (Angle)

Find angle ABC if AC = 4.5m and BC = 5.5m. 54.9o

Trigonometry (Side)

Find AC if angle ABC = 40o and AB = 3.4m. 2.85m

2

2

2

Fraction to Decimal

Convert this fraction to a decimal to 3 significant figures.

$$\frac{4}{6}$$ $$= 0.667$$

Decimal to Fraction

Convert this decimal to a fraction.

$$0.52$$ = $$\frac{13}{25}$$

Percentage (Increase)

Increase £80 by 15%

£92

Lowest Common Multiple

What is the lowest common multiple of six and ten.

= 30

Sequence (Arithmetic)

3,12,21,30,39...

Find the:
a) next term; 48
b) nth term; 9n - 6
c) term number 52; 462

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 £180 is invested for 8 years with a simple interest rate of 4%, find the amount of interest earned. £57.60

Interest (Compound)

If £140 is invested with an interest rate of 4% compounded annually, find the value of the investment after 6 years. £177.14

Currency Exchange

If £1 is worth $1.4, convert: a) £100 to dollars;$140.00

b) \$160 to pounds; £114.29

Coordinates (Midpoint)

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

$$(6,8) \text{ and } (14,20)$$

(10,14)

What is the gradient of the line joining:

$$(-2,-3) \text{ and } (4,0)$$

$$\frac{1}{2}$$

Coordinates (Square)

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

$$(3,4),(9,8),(-1,10)$$

(5,14)

Negative Numbers

a) 9 − 17 = -8
b) 9 × (-10) = -90
c) (7−18)(9−14) = 55
d) 90 ÷ (-10) = -9
e) (-12)2 = 144

Substitution

If p = 6, q = 23 and
r = -9 evaluate:

a) 2q − p = 40
b) pq + r = 129
c) p2 − 5q - r = -70

Equations (Type 1)

Solve:

$$3x = 18$$

$$x = 6$$

Equations (Type 2)

Solve:

$$4x -2= 30$$

$$x = 8$$

Equations (Type 3)

Solve:

$$3x -6= 2x + -2$$

$$x = 4$$

Equations (Type 4)

Solve:

$$2(2x -2)-7= -3$$

$$x = 2$$

Equations (Type 5)

Solve:

$$6(4x + 3)= 5(3x + 2)$$

$$x = -0.889 \text{(to 3 sf)}$$

Equations (Simultaneous 1)

Solve:

$$2x-2y = 8$$
$$4x-2y = 20$$

$$x = 6, y = 2$$

Equations (Simultaneous 2)

Solve:

$$5x+3y = 30$$
$$5x-12y = -45$$

$$x = 3, y = 5$$

Equations (Simultaneous 3)

Solve:

$$4x-5y = -52.5$$
$$3x+4y = 26.5$$

$$x = -2.5, y = 8.5$$

Sets (Union)

Find the union of:

{1,2,3,4,5} and
{2,4,6,8,10}

{1,2,3,4,5,6,8,10}

Sets (Intersection)

Find the intersection of:

{1,2,3,4,5} and
{6,7,8,9,10}

Bearings

A plane flies from point A to point B on a bearing of 345o. What bearing would it return on from B to A? 165o

Probability

A number is picked at random from the set

{1,2,3,4,5}

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

Evaluate:

32 − 8 × 8 + 8

-47

Simplify

Simplify the following by collecting like terms:

$$6m+7+5m+8$$

$$11m+15$$

Ratio

Divide 36 in the ratio

5:1

30 and 6

Graph (Linear)

Draw a rough sketch of the graph of:

$$y=-x-1$$

y intercept -1

Prime Factors

Express the following number as the product of prime numbers:

216

2 x 2 x 2 x 3 x 3 x 3

Percentage (Reverse)

In a sale an item costs £11 after a 45% reduction. What was the original price?

£20

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.

0.666666... $$\frac{2}{3}$$

Percentage (Decrease)

Decrease £180 by 30%

£126

Brackets (Linear)

Expand:

$$8(5x-6)$$

$$40x-48$$

Expand:

$$(3x+1)(2x-2)$$

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

Factorise (Linear)

Factorise:

$$81x-18$$

$$9(9x-2)$$

Factorise:

$$x^2-2x-8$$

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

Factorise:

$$6x^2-5x-4$$

$$(2x+1)(3x-4)$$

Which theorem?

Standard Form 2

Find the value of:

6.97 × 10-5

= 0.0000697

Standard Form 3

Write in standard form:

3620

= 3.62 × 103

Standard Form 4

Write in standard form:

0.0745

= 7.45 × 10-2

Find the nth term:

$$-2, 5, 16, 31, 50,$$

$$2n^2+n-5$$

Standard Form 5

Multiply 5 × 102
by 6 × 102 and give the answer in standard form.

= 3 × 105

Solve:

$$x^2-x-6= 0$$

$$x = 3$$ and $$-2$$

Solve this equation giving the solutions to 3 significant figures:

$$3x^2+4x-5 = 0$$

$$x = 0.786$$ and $$-2.12$$

Polygon Angles

What is the size of each interior angle of a regular hexagon?

120°

Change The Subject

Make $$c$$ the subject of the formula
$$d=\frac{3c+1}{2}$$

$$c=\frac{2d-1}{3}$$

Basic Division 1

Calculate the value of:

3675 ÷ 5

= 735

Number Sequences 2

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

Square Numbers

What are the next three square numbers after
1

4, 9, 16

Prime Numbers

What is the difference between the 8th and the 9th prime numbers?

23 - 19 = 4

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.

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