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:

47

1, 47.

Multiples

Subtract the 6th from the 9th multiples of:

7

21

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) 83.11; 83.1
b) 233119; 233000
c) 55; 55.0
d) 0.005595; 0.00560

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 12cm, a height of 8cm and a top (parallel to base) of 4cm. 64cm²

Fractions (Adding)

Evaluate:

$ \frac{1}{2} + \frac{4}{5}$ $= 1\frac{3}{10}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{2} × \frac{3}{4}$ $= \frac{3}{8}$

Fractions (Dividing)

Evaluate:

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

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 8cm. Give your answer to three significant figures.

201cm²

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:

6.7 + 8.4

= 15.1

Decimals (Subtracting)

Calculate the value of:

9.1 − 2.6

= 6.5

Decimals (Multiplying)

Calculate the value of:

3.4 × 7.3

= 24.82

Decimals (Dividing)

Calculate the value of:

124.6 ÷ 14

= 8.9

Indices (Simple)

What is the value of:

5²

= 25

Indices (Advanced)

What is the value of:

$5^{1}$

$= 5$

Basic Addition

Calculate the value of:

49 + 78

= 127

Basic Subtraction

Calculate the value of:

91 − 25

= 66

Basic Multiplication

Calculate the value of:

99 × 44

= 4356

Basic Division 2

Calculate the value of:

2444 ÷ 26

= 94

Percentage (Of)

Find the value of:

90% of 360

= 324

Standard Form 1

Find the value of:

9.74 × 10⁴

= 97400

Highest Common Factor

Find the highest common factor of eighteen and twelve.

= 6

Times Tables (2-5)

6 × 5 = 30	7 × 4 = 28
3 × 5 = 15	9 × 2 = 18
8 × 4 = 32	5 × 5 = 25
4 × 2 = 8	2 × 5 = 10

Times Tables (2-12)

9 × 7 = 63	8 × 9 = 72
5 × 9 = 45	7 × 10 = 70
6 × 12 = 72	4 × 6 = 24
3 × 7 = 21	2 × 3 = 6

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{9}{27}$ $= \frac{1}{3}$

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find BC if AB = 5.7m and AC = 7.6m. 9.50m

Trigonometry (Angle)

Find angle BCA if AB = 3.3m and BC = 5.3m. 38.5^o

Trigonometry (Side)

Find AC if angle ABC = 41^o and AB = 5.2m. 4.52m

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{5}{10}$ $= 0.5$

Decimal to Fraction

Convert this decimal to a fraction.

$0.64$ = $ \frac{16}{25}$

Percentage (Increase)

Increase £180 by 35%

£243

Lowest Common Multiple

What is the lowest common multiple of four and twelve.

= 12

Sequence (Arithmetic)

5,15,25,35,45...

Find the:
a) next term; 55
b) n^th term; 10n - 5
c) term number 32; 315

Sequence (Geometric)

5,10,20,40,80...

Find the:
a) next term; 160
b) n^th term; 5 × 2^n-1
c) term number 11; 5120

Interest (Simple)

If £100 is invested for 9 years with a simple interest rate of 1%, find the amount of interest earned. £9.00

Interest (Compound)

If £100 is invested with an interest rate of 5% compounded annually, find the value of the investment after 6 years. £134.01

Currency Exchange

If £1 is worth $1.34, convert:

a) £200 to dollars; $268.00

b) $160 to pounds; £119.40

Coordinates (Midpoint)

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

$(9,-8) \text{ and } (21,0)$

(15,-4)

Gradient

What is the gradient of the line joining:

$(-8,-1) \text{ and } (-2,5)$

1

Coordinates (Square)

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

$(1,1),(6,5),(-3,6)$

(2,10)

Negative Numbers

a) 12 − 23 = -11
b) 12 × (-12) = -144
c) (11−18)(8−16) = 56
d) 144 ÷ (-12) = -12
e) (-12)² = 144

Substitution

If p = 6, q = 29 and
r = -10 evaluate:

a) 2q − p = 52
b) pq + r = 164
c) p² − 5q - r = -99

Equations (Type 1)

Solve:

$4x = 24$

$x = 6$

Equations (Type 2)

Solve:

$4x -9= -1$

$x = 2$

Equations (Type 3)

Solve:

$6x +4= 4x + 10$

$x = 3$

Equations (Type 4)

Solve:

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

$x = 3$

Equations (Type 5)

Solve:

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

$x = 0.375$

Equations (Simultaneous 1)

Solve:

$4x+4y = 44$
$3x+4y = 40$

$x = 4, y = 7$

Equations (Simultaneous 2)

Solve:

$3x-2y = 9$
$7x-4y = 25$

$x = 7, y = 6$

Equations (Simultaneous 3)

Solve:

$3x-2y = -3.5$
$5x+7y = -88.5$

$x = -6.5, y = -8$

Sets (Union)

Find the union of:

{1,2,3,4,5} and
{1,3,6,10,15}

{1,2,3,4,5,6,10,15}

Sets (Intersection)

Find the intersection of:

{2,4,6,8,10} and
{6,7,8,9,10}

{6,8,10}

Bearings

A plane flies from point A to point B on a bearing of 210^o. What bearing would it return on from B to A? 030^o

Probability

A number is picked at random from the set

{2,3,5,7,11,13}

what is the probability it is even? $\frac16$

BIDMAS

Evaluate:

35 ÷ 5 × 14 ÷ 2

49

Simplify

Simplify the following by collecting like terms:

$6m+7+5m+8$

$11m+15$

Ratio

Divide 100 in the ratio

9:1

90 and 10

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 £105 after a 25% reduction. What was the original price?

£140

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.

0.757575... $\frac{25}{33}$

Percentage (Decrease)

Decrease £140 by 25%

£105

Brackets (Linear)

Expand:

$2(4x-4)$

$8x-8$

Brackets (Quadratic)

Expand:

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

$6x^2-x-1$

Factorise (Linear)

Factorise:

$4x-12$

$4(x-3)$

Factorise (Quadratic 1)

Factorise:

$x^2-16$

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

Factorise (Quadratic 2)

Factorise:

$8x^2-10x-3$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

1.61 × 10^-3

= 0.00161

Standard Form 3

Write in standard form:

8930000

= 8.93 × 10⁶

Standard Form 4

Write in standard form:

0.000792

= 7.92 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$8, 17, 30, 47, 68, $

$2n^2+3n+3$

Standard Form 5

Multiply 5 × 10⁵
by 8 × 10⁴ and give the answer in standard form.

= 4 × 10¹⁰

Equations (Quadratic 1)

Solve:

$x^2-x-6= 0$

$x = 3$ and $-2$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

$3x^2+2x-3 = 0$

$x = 0.721$ and $-1.39$

Polygon Angles

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

144°

Change The Subject

Make $j$ the subject of the formula
$$b=\frac{3(j-4)}{c}$$

$$j=\frac{bc}{3}+4$$

Basic Division 1

Calculate the value of:

2343 ÷ 3

= 781

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
36

49, 64, 81

Prime Numbers

What is the difference between the 6th and the 7th prime numbers?

17 - 13 = 4

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

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram h = 75

Angles with Parallels 2

Angle diagram i = 97

Rounding (1sf)

Round to one significant figure:
a) 55.04; 60
b) 877550; 900000
c) 11; 10
d) 0.00784; 0.008

Estimation

Round each value to one significant figure to make an estimate:$$7.6 \times 63 - 163$$$8 \times 60 - 200 = 280$

Pie Charts (1)

A pie chart shows the colours of 72 books. What sector angle represents the
29 red books?
145°

Graph Linear (2)

What is the equation?

$y=3-x$

Pie Charts (2)

A pie chart shows the colours of 72 hats. How many green hats are represented
by a sector
angle of 145°?
29

Surds (1)

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

Surds (2)

Simplify:
$$\dfrac{7}{\sqrt{5}}$$$\frac{7\sqrt{5}}{5}$

Surds (3)

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