Refreshing Revision

Number Sequences 1

What is the 11th:
a) Odd number; 21
b) Square number; 121
c) Prime number. 31

Factors

Find all the factors of:

30

1, 2, 3, 5, 6, 10, 15, 30.

Multiples

Subtract the 7th from the 12th multiples of:

4

20

Polygons

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

Pentagon, Hexagon and Heptagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 64.72; 64.7
b) 443717; 444000
c) 24; 24.0
d) 0.002495; 0.00250

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 14cm, a height of 6cm and a top (parallel to base) of 6cm. 60cm²

Fractions (Adding)

Evaluate:

$ \frac{4}{5} + \frac{8}{10}$ $= 1\frac{3}{5}$

Fractions (Multiplying)

Evaluate:

$ \frac{3}{5} × \frac{7}{8}$ $= \frac{21}{40}$

Fractions (Dividing)

Evaluate:

$ \frac{2}{3} ÷ \frac{7}{5}$ $= \frac{10}{21}$

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

Circle Area

Find the area of a circle that has a radius of 1cm. Give your answer to three significant figures.

3.14cm²

Circle Circumference

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

25.1cm

Decimals (Adding)

Calculate the value of:

3.6 + 3.5

= 7.1

Decimals (Subtracting)

Calculate the value of:

7.3 − 1.8

= 5.5

Decimals (Multiplying)

Calculate the value of:

3.7 × 7.8

= 28.86

Decimals (Dividing)

Calculate the value of:

98.4 ÷ 12

= 8.2

Indices (Simple)

What is the value of:

1²

= 1

Indices (Advanced)

What is the value of:

$1^{1}$

$= 1$

Basic Addition

Calculate the value of:

59 + 37

= 96

Basic Subtraction

Calculate the value of:

84 − 29

= 55

Basic Multiplication

Calculate the value of:

32 × 96

= 3072

Basic Division 2

Calculate the value of:

2117 ÷ 29

= 73

Percentage (Of)

Find the value of:

40% of 360

= 144

Standard Form 1

Find the value of:

5.56 × 10³

= 5560

Highest Common Factor

Find the highest common factor of thirty and twenty five.

= 5

Times Tables (2-5)

4 × 5 = 20	3 × 5 = 15
9 × 4 = 36	6 × 4 = 24
5 × 4 = 20	7 × 5 = 35
8 × 4 = 32	2 × 3 = 6

Times Tables (2-12)

8 × 9 = 72	7 × 3 = 21
9 × 10 = 90	3 × 2 = 6
4 × 6 = 24	5 × 12 = 60
6 × 3 = 18	2 × 10 = 20

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{8}{20}$ $= \frac{2}{5}$

Fractions (Mixed)

Evaluate:

$ 3\frac{3}{4} − \frac{6}{7}$ $= 2\frac{25}{28}$

Pythagoras

Find AC if AB = 5.4m and BC = 7.2m. 4.76m

Trigonometry (Angle)

Find angle ABC if AC = 5.5m and BC = 6.7m. 55.2^o

Trigonometry (Side)

Find AC if angle ABC = 35^o and AB = 4.5m. 3.15m

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.

$ \frac{2}{4}$ $= 0.5$

Decimal to Fraction

Convert this decimal to a fraction.

$0.22$ = $ \frac{11}{50}$

Percentage (Increase)

Increase £160 by 5%

£168

Lowest Common Multiple

What is the lowest common multiple of fifteen and thirty.

= 30

Sequence (Arithmetic)

7,20,33,46,59...

Find the:
a) next term; 72
b) n^th term; 13n - 6
c) term number 32; 410

Sequence (Geometric)

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

Find the:
a) next term; 1215
b) n^th term; 5 × 3^n-1
c) term number 9; 32805

Interest (Simple)

If £140 is invested for 4 years with a simple interest rate of 3%, find the amount of interest earned. £16.80

Interest (Compound)

If £180 is invested with an interest rate of 3% compounded annually, find the value of the investment after 7 years. £221.38

Currency Exchange

If £1 is worth $1.23, convert:

a) £220 to dollars; $270.60

b) $140 to pounds; £113.82

Coordinates (Midpoint)

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

$(-8,8) \text{ and } (2,16)$

(-3,12)

Gradient

What is the gradient of the line joining:

$(5,-4) \text{ and } (10,2)$

$\frac{6}{5}$

Coordinates (Square)

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

$(1,5),(7,9),(-3,11)$

(3,15)

Negative Numbers

a) 10 − 22 = -12
b) 10 × (-12) = -120
c) (7−14)(8−20) = 84
d) 120 ÷ (-12) = -10
e) (-6)² = 36

Substitution

If p = 6, q = 27 and
r = -9 evaluate:

a) 2q − p = 48
b) pq + r = 153
c) p² − 5q - r = -90

Equations (Type 1)

Solve:

$4x = 16$

$x = 4$

Equations (Type 2)

Solve:

$3x +7= 31$

$x = 8$

Equations (Type 3)

Solve:

$5x -5= 2x + 4$

$x = 3$

Equations (Type 4)

Solve:

$5(5x -3)+7= 217$

$x = 9$

Equations (Type 5)

Solve:

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

$x = -4$

Equations (Simultaneous 1)

Solve:

$5x-2y = 0$
$2x+2y = 14$

$x = 2, y = 5$

Equations (Simultaneous 2)

Solve:

$3x-4y = -7$
$6x+16y = 154$

$x = 7, y = 7$

Equations (Simultaneous 3)

Solve:

$3x-3y = 49.5$
$7x-2y = 68$

$x = 7, y = -9.5$

Sets (Union)

Find the union of:

{1,3,5,7,9} and
{2,6,12}

{1,2,3,5,6,7,9,12}

Sets (Intersection)

Find the intersection of:

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

{6,7,8}

Bearings

A plane flies from point A to point B on a bearing of 293^o. What bearing would it return on from B to A? 113^o

Probability

A number is picked at random from the set

{3,6,9,12,15}

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

BIDMAS

Evaluate:

24 ÷ 3 × 20 ÷ 4

40

Simplify

Simplify the following by collecting like terms:

$2y+2y^2-5y+y^2$

$3y^2-3y$

Ratio

Divide 48 in the ratio

7:1

42 and 6

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=x$

Gradient 1
y intercept 0

Prime Factors

Express the following number as the product of prime numbers:

30

2 x 3 x 5

Percentage (Reverse)

In a sale an item costs £45 after a 25% reduction. What was the original price?

£60

Averages

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

1,2,3,4,5

Mean = 3, no mode,
median = 3 and range = 4

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.

0.838383... $\frac{83}{99}$

Percentage (Decrease)

Decrease £140 by 40%

£84

Brackets (Linear)

Expand:

$7(6x-9)$

$42x-63$

Brackets (Quadratic)

Expand:

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

$3x^2+2x-8$

Factorise (Linear)

Factorise:

$4x-8$

$4(x-2)$

Factorise (Quadratic 1)

Factorise:

$x^2-2x-3$

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

Factorise (Quadratic 2)

Factorise:

$9x^2-16$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

2.13 × 10^-4

= 0.000213

Standard Form 3

Write in standard form:

55400

= 5.54 × 10⁴

Standard Form 4

Write in standard form:

0.00027

= 2.7 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$12, 25, 44, 69, 100, $

$3n^2+4n+5$

Standard Form 5

Multiply 9 × 10⁵
by 6 × 10⁶ and give the answer in standard form.

= 5.4 × 10¹²

Equations (Quadratic 1)

Solve:

$x^2-x-12= 0$

$x = 4$ and $-3$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.540$ and $-0.740$

Polygon Angles

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

36°

Change The Subject

Make $d$ the subject of the formula
$$e=\frac{2d-1}{3}$$

$$d=\frac{3e+1}{2}$$

Basic Division 1

Calculate the value of:

2082 ÷ 3

= 694

Number Sequences 2

What is the 10th:
a) Cube number; 1000
b) Triangular number; 55
c) Fibonacci number. 55

Square Numbers

What are the three largest square numbers less than
100

81, 64, 49

Prime Numbers

What are the three largest prime numbers less than
41

37, 31, 29

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: 2.02, 0.2, 2.2, 2.22, 2, 0.22, 0.02, in ascending order.
0.02, 0.2, 0.22, 2, 2.02, 2.2, 2.22,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram f = 132

Angles with Parallels 2

Angle diagram a = 132

Rounding (1sf)

Round to one significant figure:
a) 90.93; 90
b) 300876; 300000
c) 44; 40
d) 0.00456; 0.005

Estimation

Round each value to one significant figure to make an estimate:$$4.6 \times 44 - 182$$$5 \times 40 - 200 = 0$

Pie Charts (1)

A pie chart shows the colours of 40 books. What sector angle represents the
9 red books?
81°

Graph Linear (2)

What is the equation?

$x=5$

Pie Charts (2)

A pie chart shows the colours of 10 hats. How many green hats are represented
by a sector
angle of 72°?
2

Surds (1)

Simplify:
$$\sqrt{45}$$
$3\sqrt{5}$

Surds (2)

Simplify:
$$\dfrac{5}{2\sqrt{3}}$$$\frac{5\sqrt{3}}{6}$

Surds (3)

Simplify:
$$\dfrac{3}{4 + \sqrt{2}}$$$\frac{12 - 3\sqrt{2}}{14} = \frac{6 - \sqrt{2}}{7}$