Refreshing Revision

Number Sequences 1

What is the 8th:
a) Odd number; 15
b) Square number; 64
c) Prime number. 19

Factors

Find all the factors of:

40

1, 2, 4, 5, 8, 10, 20, 40.

Multiples

Subtract the 7th from the 11th multiples of:

12

48

Polygons

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

Hexagon, Heptagon and Octagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 66.73; 66.7
b) 428594; 429000
c) 14; 14.0
d) 0.001495; 0.00150

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 17cm, a height of 7cm and a top (parallel to base) of 7cm. 84cm²

Fractions (Adding)

Evaluate:

$ \frac{4}{6} + \frac{8}{11}$ $= 1\frac{13}{33}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{2} × \frac{4}{6}$ $= \frac{1}{3}$

Fractions (Dividing)

Evaluate:

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

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.

$ \frac{2}{5}$ $= 40$%

Circle Area

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

452cm²

Circle Circumference

Find the circumference of a circle that has a radius of 8cm. Give your answer to three significant figures.

50.3cm

Decimals (Adding)

Calculate the value of:

4.6 + 8.6

= 13.2

Decimals (Subtracting)

Calculate the value of:

6.1 − 1.5

= 4.6

Decimals (Multiplying)

Calculate the value of:

4.8 × 5.5

= 26.4

Decimals (Dividing)

Calculate the value of:

105.6 ÷ 16

= 6.6

Indices (Simple)

What is the value of:

3²

= 9

Indices (Advanced)

What is the value of:

$5^{-3}$

$= \frac{1}{125}$

Basic Addition

Calculate the value of:

77 + 86

= 163

Basic Subtraction

Calculate the value of:

72 − 29

= 43

Basic Multiplication

Calculate the value of:

58 × 84

= 4872

Basic Division 2

Calculate the value of:

2522 ÷ 26

= 97

Percentage (Of)

Find the value of:

95% of 180

= 171

Standard Form 1

Find the value of:

3.78 × 10⁵

= 378000

Highest Common Factor

Find the highest common factor of fourteen and eight.

= 2

Times Tables (2-5)

5 × 2 = 10	9 × 2 = 18
7 × 2 = 14	6 × 3 = 18
4 × 2 = 8	3 × 5 = 15
8 × 5 = 40	2 × 3 = 6

Times Tables (2-12)

6 × 6 = 36	5 × 5 = 25
9 × 5 = 45	7 × 8 = 56
4 × 6 = 24	3 × 4 = 12
8 × 9 = 72	2 × 7 = 14

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{8}{16}$ $= \frac{1}{2}$

Fractions (Mixed)

Evaluate:

$ 2\frac{1}{2} − \frac{3}{4}$ $= 1\frac{3}{4}$

Pythagoras

Find AC if AB = 5m and BC = 7m. 4.90m

Trigonometry (Angle)

Find angle ABC if AB = 4.2m and BC = 5.7m. 42.5^o

Trigonometry (Side)

Find BC if angle BCA = 67^o and AB = 3.1m. 3.37m

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{4}{9}$ $= 0.444$

Decimal to Fraction

Convert this decimal to a fraction.

$0.9$ = $ \frac{9}{10}$

Percentage (Increase)

Increase £120 by 40%

£168

Lowest Common Multiple

What is the lowest common multiple of six and twenty one.

= 42

Sequence (Arithmetic)

6,16,26,36,46...

Find the:
a) next term; 56
b) n^th term; 10n - 4
c) term number 55; 546

Sequence (Geometric)

5,15,45,135,405...

Find the:
a) next term; 1215
b) n^th term; 5 × 3^n-1
c) term number 10; 98415

Interest (Simple)

If £240 is invested for 6 years with a simple interest rate of 2%, find the amount of interest earned. £28.80

Interest (Compound)

If £100 is invested with an interest rate of 4% compounded annually, find the value of the investment after 9 years. £142.33

Currency Exchange

If £1 is worth $1.22, convert:

a) £180 to dollars; $219.60

b) $120 to pounds; £98.36

Coordinates (Midpoint)

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

$(4,-6) \text{ and } (10,4)$

(7,-1)

Gradient

What is the gradient of the line joining:

$(8,-5) \text{ and } (11,1)$

2

Coordinates (Square)

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

$(1,3),(7,8),(-4,9)$

(2,14)

Negative Numbers

a) 11 − 22 = -11
b) 11 × (-9) = -99
c) (11−19)(9−21) = 96
d) 99 ÷ (-9) = -11
e) (-8)² = 64

Substitution

If p = 6, q = 27 and
r = -6 evaluate:

a) 2q − p = 48
b) pq + r = 156
c) p² − 5q - r = -93

Equations (Type 1)

Solve:

$5x = 15$

$x = 3$

Equations (Type 2)

Solve:

$5x +2= 42$

$x = 8$

Equations (Type 3)

Solve:

$4x +5= 2x + 11$

$x = 3$

Equations (Type 4)

Solve:

$2(5x +4)+11= 79$

$x = 6$

Equations (Type 5)

Solve:

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

$x = -0.706 \text{(to 3 sf)}$

Equations (Simultaneous 1)

Solve:

$4x-5y = -1$
$3x-5y = -7$

$x = 6, y = 5$

Equations (Simultaneous 2)

Solve:

$3x-5y = -7$
$6x-20y = -64$

$x = 6, y = 5$

Equations (Simultaneous 3)

Solve:

$5x+5y = -2.5$
$3x+2y = 7.5$

$x = 8.5, y = -9$

Sets (Union)

Find the union of:

{6,7,8,9,10} and
{2,6,12}

{2,6,7,8,9,10,12}

Sets (Intersection)

Find the intersection of:

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

{6,10}

Bearings

A plane flies from point A to point B on a bearing of 349^o. What bearing would it return on from B to A? 169^o

Probability

A number is picked at random from the set

{2,4,6,8,10}

what is the probability it is even? 1

BIDMAS

Evaluate:

42 ÷ 6 × 42 ÷ 6

49

Simplify

Simplify the following by collecting like terms:

$7d−3e−5d+7e$

$4e+2d$

Ratio

Divide 40 in the ratio

1:4

8 and 32

Graph Linear (1)

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:

18

2 x 3 x 3

Percentage (Reverse)

In a sale an item costs £36 after a 10% reduction. What was the original price?

£40

Averages

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

7,7,2,7,7

Mean = 6, mode = 7,
median = 7 and range = 5

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.

0.393939... $\frac{13}{33}$

Percentage (Decrease)

Decrease £20 by 35%

£13

Brackets (Linear)

Expand:

$3(4x-2)$

$12x-6$

Brackets (Quadratic)

Expand:

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

$4x^2-4x-3$

Factorise (Linear)

Factorise:

$12x-9$

$3(4x-3)$

Factorise (Quadratic 1)

Factorise:

$x^2+3x-4$

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

Factorise (Quadratic 2)

Factorise:

$4x^2-4x-3$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

5.36 × 10^-5

= 0.0000536

Standard Form 3

Write in standard form:

598

= 5.98 × 10²

Standard Form 4

Write in standard form:

0.000701

= 7.01 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$-1, 10, 25, 44, 67, $

$2n^2+5n-8$

Standard Form 5

Multiply 7 × 10³
by 9 × 10³ and give the answer in standard form.

= 6.3 × 10⁷

Equations (Quadratic 1)

Solve:

$x^2-x-20= 0$

$x = 5$ and $-4$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.732$ and $-2.73$

Polygon Angles

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

128.6°

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:

1620 ÷ 4

= 405

Number Sequences 2

What is the 5th:
a) Cube number; 125
b) Triangular number; 15
c) Fibonacci number. 5

Square Numbers

What are the next three square numbers after
9

16, 25, 36

Prime Numbers

What is the difference between the 10th and the 11th prime numbers?

31 - 29 = 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: 3.3, 0.3, 0.33, 3.33, 3, 3.03, 0.03, in ascending order.
0.03, 0.3, 0.33, 3, 3.03, 3.3, 3.33,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram a = 48

Angles with Parallels 2

Angle diagram f = 65

Rounding (1sf)

Round to one significant figure:
a) 87.31; 90
b) 473323; 500000
c) 48; 50
d) 0.00466; 0.005

Estimation

Round each value to one significant figure to make an estimate:$$21 + 6.9 \times 64$$$20 + 7 \times 60 = 440$

Pie Charts (1)

A pie chart shows the colours of 40 books. What sector angle represents the
33 red books?
297°

Graph Linear (2)

What is the equation?

$y=8-2x$

Pie Charts (2)

A pie chart shows the colours of 9 hats. How many green hats are represented
by a sector
angle of 120°?
3