Refreshing Revision

Number Sequences 1

What is the 6th:
a) Odd number; 11
b) Square number; 36
c) Prime number. 13

Factors

Find all the factors of:

29

1, 29.

Multiples

Subtract the 5th from the 8th multiples of:

10

30

Polygons

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

Octagon, Nonagon and Decagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 82.82; 82.8
b) 177387; 177000
c) 32; 32.0
d) 0.003295; 0.00330

Area of a Triangle

Find the area of a triangle that has a base of 5cm and a height of 10cm.

25cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 9cm, a height of 7cm and a top (parallel to base) of 3cm. 42cm²

Fractions (Adding)

Evaluate:

$ \frac{4}{7} + \frac{10}{12}$ $= 1\frac{17}{42}$

Fractions (Multiplying)

Evaluate:

$ \frac{2}{4} × \frac{6}{8}$ $= \frac{3}{8}$

Fractions (Dividing)

Evaluate:

$ \frac{1}{3} ÷ \frac{6}{4}$ $= \frac{2}{9}$

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{5}{10}$ $= 50$%

Circle Area

Find the area of a circle that has a radius of 2cm. Give your answer to three significant figures.

12.6cm²

Circle Circumference

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

44.0cm

Decimals (Adding)

Calculate the value of:

2.8 + 6.7

= 9.5

Decimals (Subtracting)

Calculate the value of:

6.2 − 1.6

= 4.6

Decimals (Multiplying)

Calculate the value of:

8.7 × 3.9

= 33.93

Decimals (Dividing)

Calculate the value of:

76.5 ÷ 17

= 4.5

Indices (Simple)

What is the value of:

2²

= 4

Indices (Advanced)

What is the value of:

$2^{-3}$

$= \frac{1}{8}$

Basic Addition

Calculate the value of:

68 + 29

= 97

Basic Subtraction

Calculate the value of:

83 − 26

= 57

Basic Multiplication

Calculate the value of:

45 × 97

= 4365

Basic Division 2

Calculate the value of:

2052 ÷ 27

= 76

Percentage (Of)

Find the value of:

80% of 120

= 96

Standard Form 1

Find the value of:

3.87 × 10²

= 387

Highest Common Factor

Find the highest common factor of fourteen and four.

= 2

Times Tables (2-5)

6 × 4 = 24	3 × 4 = 12
8 × 3 = 24	7 × 2 = 14
9 × 3 = 27	5 × 5 = 25
4 × 3 = 12	2 × 3 = 6

Times Tables (2-12)

6 × 2 = 12	3 × 9 = 27
8 × 10 = 80	4 × 12 = 48
5 × 12 = 60	9 × 8 = 72
7 × 10 = 70	2 × 7 = 14

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{24}{30}$ $= \frac{4}{5}$

Fractions (Mixed)

Evaluate:

$ 3\frac{2}{3} − \frac{5}{6}$ $= 2\frac{5}{6}$

Pythagoras

Find AC if AB = 3.2m and BC = 4.6m. 3.30m

Trigonometry (Angle)

Find angle ABC if AC = 3.9m and BC = 5.1m. 49.9^o

Trigonometry (Side)

Find AB if angle ABC = 30^o and BC = 5m. 4.33m

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{2}{6}$ $= 0.333$

Decimal to Fraction

Convert this decimal to a fraction.

$0.69$ = $ \frac{69}{100}$

Percentage (Increase)

Increase £100 by 25%

£125

Lowest Common Multiple

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

= 84

Sequence (Arithmetic)

6,18,30,42,54...

Find the:
a) next term; 66
b) n^th term; 12n - 6
c) term number 44; 522

Sequence (Geometric)

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

Find the:
a) next term; 128
b) n^th term; 4 × 2^n-1
c) term number 9; 1024

Interest (Simple)

If £100 is invested for 7 years with a simple interest rate of 3%, find the amount of interest earned. £21.00

Interest (Compound)

If £180 is invested with an interest rate of 2% compounded annually, find the value of the investment after 4 years. £194.84

Currency Exchange

If £1 is worth $1.36, convert:

a) £160 to dollars; $217.60

b) $240 to pounds; £176.47

Coordinates (Midpoint)

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

$(-6,8) \text{ and } (2,16)$

(-2,12)

Gradient

What is the gradient of the line joining:

$(4,8) \text{ and } (8,12)$

1

Coordinates (Square)

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

$(5,1),(11,6),(0,7)$

(6,12)

Negative Numbers

a) 12 − 22 = -10
b) 12 × (-9) = -108
c) (9−18)(6−14) = 72
d) 108 ÷ (-9) = -12
e) (-8)² = 64

Substitution

If p = 5, q = 27 and
r = -7 evaluate:

a) 2q − p = 49
b) pq + r = 128
c) p² − 5q - r = -103

Equations (Type 1)

Solve:

$3x = 6$

$x = 2$

Equations (Type 2)

Solve:

$2x +6= 12$

$x = 3$

Equations (Type 3)

Solve:

$6x +5= 3x + 26$

$x = 7$

Equations (Type 4)

Solve:

$2(4x +3)+9= 39$

$x = 3$

Equations (Type 5)

Solve:

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

$x = 0.105 \text{(to 3 sf)}$

Equations (Simultaneous 1)

Solve:

$5x+4y = 43$
$4x-4y = 20$

$x = 7, y = 2$

Equations (Simultaneous 2)

Solve:

$2x+4y = 34$
$5x-12y = -25$

$x = 7, y = 5$

Equations (Simultaneous 3)

Solve:

$3x-7y = 74.5$
$5x-2y = 56.5$

$x = 8.5, y = -7$

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

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

∅

Bearings

A plane flies from point A to point B on a bearing of 344^o. What bearing would it return on from B to A? 164^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:

12 ÷ 2 × 48 ÷ 6

48

Simplify

Simplify the following by collecting like terms:

$3b+5c+8b+4c$

$11b+9c$

Ratio

Divide 285 in the ratio

10:9

150 and 135

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=-2x$

Gradient -2
y intercept 0

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 £42 after a 30% reduction. What was the original price?

£60

Averages

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

1,3,1,10,5

Mean = 4, mode = 1,
median = 3 and range = 9

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.

0.737373... $\frac{73}{99}$

Percentage (Decrease)

Decrease £40 by 30%

£28

Brackets (Linear)

Expand:

$7(9x-6)$

$63x-42$

Brackets (Quadratic)

Expand:

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

$6x^2+8x-8$

Factorise (Linear)

Factorise:

$4x-10$

$2(2x-5)$

Factorise (Quadratic 1)

Factorise:

$x^2-x-2$

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

Factorise (Quadratic 2)

Factorise:

$12x^2-x-6$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

7.09 × 10^-4

= 0.000709

Standard Form 3

Write in standard form:

4640000

= 4.64 × 10⁶

Standard Form 4

Write in standard form:

0.00245

= 2.45 × 10^-3

Sequence (Quadratic)

Find the n^th term:

$2, 14, 30, 50, 74, $

$2n^2+6n-6$

Standard Form 5

Multiply 5 × 10⁴
by 6 × 10⁴ and give the answer in standard form.

= 3 × 10⁹

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:

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

$x = 1.48$ and $-0.677$

Polygon Angles

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

72°

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:

6792 ÷ 8

= 849

Number Sequences 2

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

Square Numbers

What is the square of

12

144

Prime Numbers

What are the next three prime numbers after
23

29, 31, 37

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: 7.77, 7.07, 0.77, 0.7, 7.7, 7, 0.07, in ascending order.
0.07, 0.7, 0.77, 7, 7.07, 7.7, 7.77,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram g = 122

Angles with Parallels 2

Angle diagram i = 97

Rounding (1sf)

Round to one significant figure:
a) 91.28; 90
b) 684672; 700000
c) 78; 80
d) 0.00656; 0.007

Estimation

Round each value to one significant figure to make an estimate:$$2.8 \times 63 - 162$$$3 \times 60 - 200 = -20$

Pie Charts (1)

A pie chart shows the colours of 15 books. What sector angle represents the
3 red books?
72°

Graph Linear (2)

What is the equation?

$y=2-x$

Pie Charts (2)

A pie chart shows the colours of 20 hats. How many green hats are represented
by a sector
angle of 234°?
13

Surds (1)

Simplify:
$$\sqrt{48}$$
$4\sqrt{3}$

Surds (2)

Simplify:
$$\dfrac{8}{3\sqrt{7}}$$$\frac{8\sqrt{7}}{21}$

Surds (3)

Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$$\frac{10 + 2\sqrt{7}}{18}$