Refreshing Revision

Number Sequences 1

What is the 10th:
a) Odd number; 19
b) Square number; 100
c) Prime number. 29

Factors

Find all the factors of:

22

1, 2, 11, 22.

Multiples

Subtract the 4th from the 9th multiples of:

9

45

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) 14.87; 14.9
b) 976500; 976000
c) 43; 43.0
d) 0.004395; 0.00440

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 11cm, a height of 7cm and a top (parallel to base) of 5cm. 56cm²

Fractions (Adding)

Evaluate:

$ \frac{3}{4} + \frac{7}{10}$ $= 1\frac{9}{20}$

Fractions (Multiplying)

Evaluate:

$ \frac{2}{4} × \frac{6}{7}$ $= \frac{3}{7}$

Fractions (Dividing)

Evaluate:

$ \frac{3}{4} ÷ \frac{7}{6}$ $= \frac{9}{14}$

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}{3}$ $= 33.3$%

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 10cm. Give your answer to three significant figures.

62.8cm

Decimals (Adding)

Calculate the value of:

4.9 + 2.5

= 7.4

Decimals (Subtracting)

Calculate the value of:

7.4 − 3.6

= 3.8

Decimals (Multiplying)

Calculate the value of:

6.3 × 6.6

= 41.58

Decimals (Dividing)

Calculate the value of:

150.4 ÷ 16

= 9.4

Indices (Simple)

What is the value of:

4³

= 64

Indices (Advanced)

What is the value of:

$27^{\frac{1}{3}}$

$= 3$

Basic Addition

Calculate the value of:

47 + 24

= 71

Basic Subtraction

Calculate the value of:

51 − 28

= 23

Basic Multiplication

Calculate the value of:

87 × 25

= 2175

Basic Division 2

Calculate the value of:

1701 ÷ 27

= 63

Percentage (Of)

Find the value of:

15% of 260

= 39

Standard Form 1

Find the value of:

5.78 × 10³

= 5780

Highest Common Factor

Find the highest common factor of fourteen and eight.

= 2

Times Tables (2-5)

6 × 5 = 30	9 × 4 = 36
7 × 3 = 21	5 × 3 = 15
3 × 3 = 9	8 × 5 = 40
4 × 5 = 20	2 × 3 = 6

Times Tables (2-12)

7 × 2 = 14	4 × 11 = 44
6 × 7 = 42	9 × 3 = 27
5 × 2 = 10	8 × 11 = 88
3 × 7 = 21	2 × 4 = 8

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{7}{21}$ $= \frac{1}{3}$

Fractions (Mixed)

Evaluate:

$ 3\frac{1}{2} − \frac{5}{6}$ $= 2\frac{2}{3}$

Pythagoras

Find AB if AC = 3.7m and BC = 5.4m. 3.93m

Trigonometry (Angle)

Find angle BCA if AB = 5.5m and AC = 7.1m. 37.8^o

Trigonometry (Side)

Find AC if angle ABC = 48^o and BC = 3.9m. 2.90m

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{3}{7}$ $= 0.429$

Decimal to Fraction

Convert this decimal to a fraction.

$0.55$ = $ \frac{11}{20}$

Percentage (Increase)

Increase £160 by 40%

£224

Lowest Common Multiple

What is the lowest common multiple of six and fourteen.

= 42

Sequence (Arithmetic)

3,10,17,24,31...

Find the:
a) next term; 38
b) n^th term; 7n - 4
c) term number 53; 367

Sequence (Geometric)

5,20,80,320,1280...

Find the:
a) next term; 5120
b) n^th term; 5 × 4^n-1
c) term number 10; 1310720

Interest (Simple)

If £240 is invested for 7 years with a simple interest rate of 1%, find the amount of interest earned. £16.80

Interest (Compound)

If £160 is invested with an interest rate of 2% compounded annually, find the value of the investment after 9 years. £191.21

Currency Exchange

If £1 is worth $1.24, convert:

a) £140 to dollars; $173.60

b) $160 to pounds; £129.03

Coordinates (Midpoint)

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

$(-5,-6) \text{ and } (7,2)$

(1,-2)

Gradient

What is the gradient of the line joining:

$(7,7) \text{ and } (13,11)$

$\frac{2}{3}$

Coordinates (Square)

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

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

(-2,11)

Negative Numbers

a) 11 − 16 = -5
b) 11 × (-8) = -88
c) (6−16)(7−13) = 60
d) 88 ÷ (-8) = -11
e) (-8)² = 64

Substitution

If p = 6, q = 21 and
r = -9 evaluate:

a) 2q − p = 36
b) pq + r = 117
c) p² − 5q - r = -60

Equations (Type 1)

Solve:

$3x = 9$

$x = 3$

Equations (Type 2)

Solve:

$4x +8= 40$

$x = 8$

Equations (Type 3)

Solve:

$6x +3= 3x + 15$

$x = 4$

Equations (Type 4)

Solve:

$2(5x +6)+6= 48$

$x = 3$

Equations (Type 5)

Solve:

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

$x = -0.429 \text{(to 3 sf)}$

Equations (Simultaneous 1)

Solve:

$3x-3y = 0$
$2x-3y = -3$

$x = 3, y = 3$

Equations (Simultaneous 2)

Solve:

$4x+5y = 23$
$5x+15y = 55$

$x = 2, y = 3$

Equations (Simultaneous 3)

Solve:

$3x-3y = -33$
$7x-2y = -69.5$

$x = -9.5, y = 1.5$

Sets (Union)

Find the union of:

{5,6,7,8,9,10} and
{3,6,9,12,15}

{3,5,6,7,8,9,10,12,15}

Sets (Intersection)

Find the intersection of:

{5,6,7,8,9,10} and
{1,3,6,10,15}

{6,10}

Bearings

A plane flies from point A to point B on a bearing of 280^o. What bearing would it return on from B to A? 100^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:

28 ÷ 7 × 40 ÷ 8

20

Simplify

Simplify the following by collecting like terms:

$3y+2w+7y$

$10y+2w$

Ratio

Divide 144 in the ratio

7:9

63 and 81

Graph (Linear)

Draw a rough sketch of the graph of:

$y=-x+2$

Gradient -1
y intercept 2

Prime Factors

Express the following number as the product of prime numbers:

120

2 x 2 x 2 x 3 x 5

Percentage (Reverse)

In a sale an item costs £60 after a 25% reduction. What was the original price?

£80

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.

0.121212... $\frac{4}{33}$

Percentage (Decrease)

Decrease £40 by 5%

£38

Brackets (Linear)

Expand:

$4(5x-5)$

$20x-20$

Brackets (Quadratic)

Expand:

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

$4x^2-10x-6$

Factorise (Linear)

Factorise:

$42x-49$

$7(6x-7)$

Factorise (Quadratic 1)

Factorise:

$x^2-x-2$

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

Factorise (Quadratic 2)

Factorise:

$12x^2+x-1$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

8.88 × 10^-3

= 0.00888

Standard Form 3

Write in standard form:

990

= 9.9 × 10²

Standard Form 4

Write in standard form:

0.000559

= 5.59 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$15, 28, 47, 72, 103, $

$3n^2+4n+8$

Standard Form 5

Multiply 9 × 10⁵
by 4 × 10³ and give the answer in standard form.

= 3.6 × 10⁹

Equations (Quadratic 1)

Solve:

$x^2-2x-8= 0$

$x = 4$ and $-2$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.740$ and $-0.540$

Polygon Angles

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

135°

Change The Subject

Make $f$ the subject of the formula
$$h=g(e-f)$$

$$f=e-\frac{h}{g}$$

Basic Division 1

Calculate the value of:

642 ÷ 3

= 214

Number Sequences 2

What is the 8th:
a) Cube number; 512
b) Triangular number; 36
c) Fibonacci number. 21

Square Numbers

What is the square root of

1

1

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: 7, 7.77, 0.77, 0.7, 7.07, 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: 17cm, 107cm, 18mm, 1.08m, 1.8m, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram i = 54

Angles with Parallels 2

Angle diagram g = 122

Rounding (1sf)

Round to one significant figure:
a) 16.15; 20
b) 619962; 600000
c) 71; 70
d) 0.00767; 0.008