Refreshing Revision

Number Sequences 1

What is the 12th:
a) Odd number; 23
b) Square number; 144
c) Prime number. 37

Factors

Find all the factors of:

49

1, 7, 49.

Multiples

Subtract the 5th from the 10th multiples of:

12

60

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) 56.78; 56.8
b) 695114; 695000
c) 69; 69.0
d) 0.006995; 0.00700

Area of a Triangle

Find the area of a triangle that has a base of 6cm and a height of 11cm.

33cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 12cm, a height of 7cm and a top (parallel to base) of 6cm. 63cm²

Fractions (Adding)

Evaluate:

$ \frac{1}{4} + \frac{7}{8}$ $= 1\frac{1}{8}$

Fractions (Multiplying)

Evaluate:

$ \frac{3}{4} × \frac{6}{8}$ $= \frac{9}{16}$

Fractions (Dividing)

Evaluate:

$ \frac{1}{3} ÷ \frac{5}{4}$ $= \frac{4}{15}$

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}{4}$ $= 75$%

Circle Area

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

154cm²

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:

2.8 + 9.4

= 12.2

Decimals (Subtracting)

Calculate the value of:

8.3 − 4.9

= 3.4

Decimals (Multiplying)

Calculate the value of:

8.3 × 5.4

= 44.82

Decimals (Dividing)

Calculate the value of:

59.8 ÷ 13

= 4.6

Indices (Simple)

What is the value of:

5³

= 125

Indices (Advanced)

What is the value of:

$5^{1}$

$= 5$

Basic Addition

Calculate the value of:

87 + 46

= 133

Basic Subtraction

Calculate the value of:

52 − 28

= 24

Basic Multiplication

Calculate the value of:

97 × 37

= 3589

Basic Division 2

Calculate the value of:

2375 ÷ 25

= 95

Percentage (Of)

Find the value of:

75% of 140

= 105

Standard Form 1

Find the value of:

8.46 × 10⁵

= 846000

Highest Common Factor

Find the highest common factor of forty and twenty five.

= 5

Times Tables (2-5)

7 × 4 = 28	6 × 4 = 24
5 × 4 = 20	9 × 2 = 18
3 × 4 = 12	4 × 4 = 16
8 × 5 = 40	2 × 3 = 6

Times Tables (2-12)

8 × 4 = 32	5 × 10 = 50
7 × 3 = 21	9 × 7 = 63
3 × 5 = 15	4 × 2 = 8
6 × 2 = 12	2 × 4 = 8

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{6}{18}$ $= \frac{1}{3}$

Fractions (Mixed)

Evaluate:

$ 2\frac{3}{4} − \frac{7}{8}$ $= 1\frac{7}{8}$

Pythagoras

Find AB if AC = 4.1m and BC = 5.9m. 4.24m

Trigonometry (Angle)

Find angle BCA if AC = 5.8m and BC = 7.1m. 35.2^o

Trigonometry (Side)

Find AC if angle ABC = 48^o and BC = 3.4m. 2.53m

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}{7}$ $= 0.571$

Decimal to Fraction

Convert this decimal to a fraction.

$0.65$ = $ \frac{13}{20}$

Percentage (Increase)

Increase £100 by 35%

£135

Lowest Common Multiple

What is the lowest common multiple of six and fifteen.

= 30

Sequence (Arithmetic)

5,17,29,41,53...

Find the:
a) next term; 65
b) n^th term; 12n - 7
c) term number 56; 665

Sequence (Geometric)

6,18,54,162,486...

Find the:
a) next term; 1458
b) n^th term; 6 × 3^n-1
c) term number 9; 39366

Interest (Simple)

If £180 is invested for 7 years with a simple interest rate of 6%, find the amount of interest earned. £75.60

Interest (Compound)

If £160 is invested with an interest rate of 5% compounded annually, find the value of the investment after 6 years. £214.42

Currency Exchange

If £1 is worth $1.38, convert:

a) £140 to dollars; $193.20

b) $140 to pounds; £101.45

Coordinates (Midpoint)

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

$(8,1) \text{ and } (16,13)$

(12,7)

Gradient

What is the gradient of the line joining:

$(-1,-7) \text{ and } (2,-3)$

$\frac{4}{3}$

Coordinates (Square)

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

$(1,5),(4,8),(-2,8)$

(1,11)

Negative Numbers

a) 6 − 11 = -5
b) 6 × (-8) = -48
c) (11−20)(12−17) = 45
d) 48 ÷ (-8) = -6
e) (-6)² = 36

Substitution

If p = 6, q = 16 and
r = -7 evaluate:

a) 2q − p = 26
b) pq + r = 89
c) p² − 5q - r = -37

Equations (Type 1)

Solve:

$5x = 30$

$x = 6$

Equations (Type 2)

Solve:

$5x -5= 15$

$x = 4$

Equations (Type 3)

Solve:

$10x -4= 6x + 28$

$x = 8$

Equations (Type 4)

Solve:

$3(5x +3)+11= 80$

$x = 4$

Equations (Type 5)

Solve:

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

$x = -2.5$

Equations (Simultaneous 1)

Solve:

$4x+4y = 28$
$3x+4y = 26$

$x = 2, y = 5$

Equations (Simultaneous 2)

Solve:

$2x+4y = 28$
$6x-16y = -84$

$x = 2, y = 6$

Equations (Simultaneous 3)

Solve:

$2x-2y = -28$
$3x-5y = -56$

$x = -7, y = 7$

Sets (Union)

Find the union of:

{1,3,5,7,9} and
{1,3,6,10,15}

{1,3,5,6,7,9,10,15}

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 279^o. What bearing would it return on from B to A? 099^o

Probability

A number is picked at random from the set

{3,4,5,6,7,8}

what is the probability it is even? $\frac12$

BIDMAS

Evaluate:

5 + 4 × 6 − 3

26

Simplify

Simplify the following by collecting like terms:

$6m+7+5m+8$

$11m+15$

Ratio

Divide 36 in the ratio

4:2

24 and 12

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=-2x+1$

Gradient -2
y intercept 1

Prime Factors

Express the following number as the product of prime numbers:

1080

2 x 2 x 2 x 3 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £39 after a 35% reduction. What was the original price?

£60

Averages

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

2,6,12,6,14

Mean = 8, mode = 6,
median = 6 and range = 12

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.

0.959595... $\frac{95}{99}$

Percentage (Decrease)

Decrease £120 by 5%

£114

Brackets (Linear)

Expand:

$7(8x-9)$

$56x-63$

Brackets (Quadratic)

Expand:

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

$12x^2+5x-2$

Factorise (Linear)

Factorise:

$16x-8$

$8(2x-1)$

Factorise (Quadratic 1)

Factorise:

$x^2+2x-3$

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

Factorise (Quadratic 2)

Factorise:

$3x^2+11x-4$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

7.57 × 10^-3

= 0.00757

Standard Form 3

Write in standard form:

200

= 2 × 10²

Standard Form 4

Write in standard form:

0.0000504

= 5.04 × 10^-5

Sequence (Quadratic)

Find the n^th term:

$13, 27, 47, 73, 105, $

$3n^2+5n+5$

Standard Form 5

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

= 8.1 × 10¹³

Equations (Quadratic 1)

Solve:

$x^2+x-12= 0$

$x = 3$ and $-4$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

$2x^2+5x-1 = 0$

$x = 0.186$ and $-2.69$

Polygon Angles

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

40°

Change The Subject

Make $a$ the subject of the formula
$$b=2a-3$$

$$a=\frac{b+3}{2}$$

Basic Division 1

Calculate the value of:

3458 ÷ 7

= 494

Number Sequences 2

What is the 11th:
a) Cube number; 1331
b) Triangular number; 66
c) Fibonacci number. 89

Square Numbers

What is the difference between the 7th and the 8th square numbers?

15

Prime Numbers

What is the 5th prime number?

11

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: 5.55, 5.5, 5.05, 0.5, 0.55, 5, 0.05, in ascending order.
0.05, 0.5, 0.55, 5, 5.05, 5.5, 5.55,

Lengths (Ordering)

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

Capacities (Ordering)

Write down these capacities: 173ml, 21cl, 17cl, 200ml, 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) 55.67; 60
b) 338274; 300000
c) 92; 90
d) 0.00573; 0.006

Estimation

Round each value to one significant figure to make an estimate:$$7.8 \times 62 - 153$$$8 \times 60 - 200 = 280$

Pie Charts (1)

A pie chart shows the colours of 15 books. What sector angle represents the
12 red books?
288°

Graph Linear (2)

What is the equation?

$y=2x+2$

Pie Charts (2)

A pie chart shows the colours of 30 hats. How many green hats are represented
by a sector
angle of 24°?
2

Surds (1)

Simplify:
$$\sqrt{27}$$
$3\sqrt{3}$

Surds (2)

Simplify:
$$\dfrac{6}{\sqrt{11}}$$$\frac{6\sqrt{11}}{11}$

Surds (3)

Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$$\frac{21 + 3\sqrt{2}}{47}$