Refreshing Revision

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:

38

1, 2, 19, 38.

Multiples

Subtract the 6th from the 11th multiples of:

8

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 (3sf)

Round to three significant figures:
a) 99.26; 99.3
b) 687709; 688000
c) 69; 69.0
d) 0.006995; 0.00700

Area of a Triangle

Find the area of a triangle that has a base of 7cm and a height of 10cm.

35cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 11cm and a top (parallel to base) of 5cm. 99cm²

Fractions (Adding)

Evaluate:

$ \frac{4}{5} + \frac{7}{8}$ $= 1\frac{27}{40}$

Fractions (Multiplying)

Evaluate:

$ \frac{3}{5} × \frac{7}{9}$ $= \frac{7}{15}$

Fractions (Dividing)

Evaluate:

$ \frac{2}{3} ÷ \frac{6}{4}$ $= \frac{4}{9}$

Circle (Vocabulary)

Name the red part.

Venn Diagrams

Describe the red region.

Shape Formulas

What is the formula?

Formulas (Advanced)

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 9cm. Give your answer to three significant figures.

254cm²

Circle Circumference

Find the circumference of a circle that has a radius of 11cm. Give your answer to three significant figures.

69.1cm

Decimals (Adding)

Calculate the value of:

9.9 + 5.6

= 15.5

Decimals (Subtracting)

Calculate the value of:

9.2 − 3.6

= 5.6

Decimals (Multiplying)

Calculate the value of:

4.6 × 9.6

= 44.16

Decimals (Dividing)

Calculate the value of:

107.9 ÷ 13

= 8.3

Indices (Simple)

What is the value of:

5³

= 125

Indices (Advanced)

What is the value of:

$1^{\frac{1}{3}}$

$= 1$

Basic Addition

Calculate the value of:

59 + 38

= 97

Basic Subtraction

Calculate the value of:

93 − 29

= 64

Basic Multiplication

Calculate the value of:

47 × 58

= 2726

Basic Division 2

Calculate the value of:

1080 ÷ 15

= 72

Percentage (Of)

Find the value of:

45% of 200

= 90

Standard Form 1

Find the value of:

7.48 × 10²

= 748

Highest Common Factor

Find the highest common factor of thirty and twenty five.

= 5

Times Tables (2-5)

7 × 5 = 35	3 × 3 = 9
5 × 5 = 25	4 × 5 = 20
9 × 2 = 18	8 × 5 = 40
6 × 3 = 18	2 × 4 = 8

Times Tables (2-12)

4 × 8 = 32	7 × 5 = 35
8 × 9 = 72	5 × 3 = 15
6 × 7 = 42	9 × 7 = 63
3 × 5 = 15	2 × 5 = 10

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{16}{32}$ $= \frac{1}{2}$

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find AB if AC = 5.4m and BC = 6.4m. 3.44m

Trigonometry (Angle)

Find angle ABC if AC = 3.6m and AB = 5.2m. 34.7^o

Trigonometry (Side)

Find BC if angle BCA = 54^o and AB = 4.9m. 6.06m

Roman Numerals (1-12)

Give your answer in Roman numerals.

²

Roman Numerals (60-100)

Give your answer in Roman numerals.

²

Roman Numerals (Large)

Give your answer in Roman numerals.

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.

$0.75$ = $ \frac{3}{4}$

Percentage (Increase)

Increase £80 by 40%

£112

Lowest Common Multiple

What is the lowest common multiple of fifteen and twenty five.

= 75

Sequence (Arithmetic)

6,19,32,45,58...

Find the:
a) next term; 71
b) n^th term; 13n - 7
c) term number 54; 695

Sequence (Geometric)

5,10,20,40,80...

Find the:
a) next term; 160
b) n^th term; 5 × 2^n-1
c) term number 12; 10240

Interest (Simple)

If £180 is invested for 6 years with a simple interest rate of 6%, find the amount of interest earned. £64.80

Interest (Compound)

If £200 is invested with an interest rate of 1% compounded annually, find the value of the investment after 8 years. £216.57

Currency Exchange

If £1 is worth $1.33, convert:

a) £120 to dollars; $159.60

b) $240 to pounds; £180.45

Coordinates (Midpoint)

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

$(-7,0) \text{ and } (3,8)$

(-2,4)

Gradient

What is the gradient of the line joining:

$(-5,6) \text{ and } (1,12)$

1

Coordinates (Square)

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

$(3,5),(9,10),(-2,11)$

(4,16)

Negative Numbers

a) 7 − 17 = -10
b) 7 × (-6) = -42
c) (8−14)(9−15) = 36
d) 42 ÷ (-6) = -7
e) (-6)² = 36

Substitution

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

a) 2q − p = 38
b) pq + r = 126
c) p² − 5q - r = -68

Equations (Type 1)

Solve:

$4x = 32$

$x = 8$

Equations (Type 2)

Solve:

$4x -2= 6$

$x = 2$

Equations (Type 3)

Solve:

$8x -6= 6x + 4$

$x = 5$

Equations (Type 4)

Solve:

$5(2x -5)+8= 43$

$x = 6$

Equations (Type 5)

Solve:

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

$x = -2.2$

Equations (Simultaneous 1)

Solve:

$3x+3y = 27$
$2x-3y = 3$

$x = 6, y = 3$

Equations (Simultaneous 2)

Solve:

$2x-3y = -15$
$5x-12y = -69$

$x = 3, y = 7$

Equations (Simultaneous 3)

Solve:

$2x+5y = -23$
$3x+2y = -23.5$

$x = -6.5, y = -2$

Sets (Union)

Find the union of:

{6,7,8,9,10} and
{1,3,6,10,15}

{1,3,6,7,8,9,10,15}

Sets (Intersection)

Find the intersection of:

{1,2,3,4,5} and
{1,3,5,7,9}

{1,3,5}

Bearings

A plane flies from point A to point B on a bearing of 341^o. What bearing would it return on from B to A? 161^o

Probability

A number is picked at random from the set

{2,6,12}

what is the probability it is even? 1

BIDMAS

Evaluate:

5² − 6 × 8 + 7

-16

Simplify

Simplify the following by collecting like terms:

$3n+7−2n+8$

$n+15$

Ratio

Divide 66 in the ratio

5:6

30 and 36

Graph (Linear)

Draw a rough sketch of the graph of:

$2y=x$

Gradient 0.5
y intercept 0

Prime Factors

Express the following number as the product of prime numbers:

6

2 x 3

Percentage (Reverse)

In a sale an item costs £90 after a 25% reduction. What was the original price?

£120

Averages

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

1,3,5,7,9

Mean = 5, no mode,
median = 5 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.

0.444444... $\frac{4}{9}$

Percentage (Decrease)

Decrease £60 by 10%

£54

Brackets (Linear)

Expand:

$2(4x-6)$

$8x-12$

Brackets (Quadratic)

Expand:

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

$3x^2+10x-8$

Factorise (Linear)

Factorise:

$30x-35$

$5(6x-7)$

Factorise (Quadratic 1)

Factorise:

$x^2+2x-8$

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

Factorise (Quadratic 2)

Factorise:

$2x^2+7x-4$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

3.33 × 10^-5

= 0.0000333

Standard Form 3

Write in standard form:

5520000

= 5.52 × 10⁶

Standard Form 4

Write in standard form:

0.00283

= 2.83 × 10^-3

Sequence (Quadratic)

Find the n^th term:

$16, 25, 36, 49, 64, $

$n^2+6n+9$

Standard Form 5

Multiply 6 × 10⁴
by 9 × 10² and give the answer in standard form.

= 5.4 × 10⁷

Equations (Quadratic 1)

Solve:

$x^2-x-30= 0$

$x = 6$ and $-5$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 1.87$ and $-0.535$

Polygon Angles

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

36°

Change The Subject

Make $k$ the subject of the formula
$$c=\frac{a(2+k)}{b}$$

$$k=\frac{bc}{a}-2$$

Basic Division 1

Calculate the value of:

6759 ÷ 9

= 751

Number Sequences 2

What is the 9th:
a) Cube number; 729
b) Triangular number; 45
c) Fibonacci number. 34

Square Numbers

What is the square root of

64

8

Prime Numbers

What is the 4th prime number?

7

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: 0.33, 3.03, 3.3, 3, 3.33, 0.3, 0.03, in ascending order.
0.03, 0.3, 0.33, 3, 3.03, 3.3, 3.33,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram h = 75

Angles with Parallels 2

Angle diagram g = 122

Rounding (1sf)

Round to one significant figure:
a) 55.55; 60
b) 935469; 900000
c) 44; 40
d) 0.00780; 0.008