Refreshing Revision

Number Sequences 1

What is the 5th:
a) Odd number; 9
b) Square number; 25
c) Prime number. 11

Factors

Find all the factors of:

29

1, 29.

Multiples

Subtract the 6th from the 9th multiples of:

9

27

Polygons

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

Heptagon, Octagon and Nonagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 76.68; 76.7
b) 763175; 763000
c) 41; 41.0
d) 0.004195; 0.00420

Area of a Triangle

Find the area of a triangle that has a base of 7cm and a height of 10cm.

35cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 11cm and a top (parallel to base) of 3cm. 77cm²

Fractions (Adding)

Evaluate:

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

Fractions (Multiplying)

Evaluate:

$ \frac{3}{4} × \frac{5}{7}$ $= \frac{15}{28}$

Fractions (Dividing)

Evaluate:

$ \frac{1}{3} ÷ \frac{7}{5}$ $= \frac{5}{21}$

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 to 3 significant figures.

$ \frac{2}{6}$ $= 33.3$%

Circle Area

Find the area of a circle that has a radius of 6cm. Give your answer to three significant figures.

113cm²

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:

6.8 + 4.9

= 11.7

Decimals (Subtracting)

Calculate the value of:

5.4 − 1.5

= 3.9

Decimals (Multiplying)

Calculate the value of:

6.5 × 3.2

= 20.8

Decimals (Dividing)

Calculate the value of:

106.8 ÷ 12

= 8.9

Indices (Simple)

What is the value of:

3³

= 27

Indices (Advanced)

What is the value of:

$4^{-2}$

$= \frac{1}{16}$

Basic Addition

Calculate the value of:

85 + 68

= 153

Basic Subtraction

Calculate the value of:

53 − 28

= 25

Basic Multiplication

Calculate the value of:

73 × 87

= 6351

Basic Division 2

Calculate the value of:

1445 ÷ 17

= 85

Percentage (Of)

Find the value of:

60% of 180

= 108

Standard Form 1

Find the value of:

6.43 × 10³

= 6430

Highest Common Factor

Find the highest common factor of twenty one and nine.

= 3

Times Tables (2-5)

3 × 2 = 6	9 × 2 = 18
8 × 3 = 24	4 × 2 = 8
6 × 4 = 24	7 × 2 = 14
5 × 2 = 10	2 × 2 = 4

Times Tables (2-12)

8 × 5 = 40	3 × 4 = 12
5 × 7 = 35	7 × 6 = 42
4 × 8 = 32	9 × 6 = 54
6 × 2 = 12	2 × 10 = 20

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{10}{25}$ $= \frac{2}{5}$

Fractions (Mixed)

Evaluate:

$ 1\frac{1}{2} − \frac{4}{5}$ $= \frac{7}{10}$

Pythagoras

Find BC if AB = 4.4m and AC = 5.6m. 7.12m

Trigonometry (Angle)

Find angle ABC if AB = 3.7m and BC = 5.4m. 46.7^o

Trigonometry (Side)

Find AB if angle ABC = 54^o and BC = 5.1m. 3.00m

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.

$0.84$ = $ \frac{21}{25}$

Percentage (Increase)

Increase £20 by 10%

£22

Lowest Common Multiple

What is the lowest common multiple of fifteen and forty.

= 120

Sequence (Arithmetic)

6,16,26,36,46...

Find the:
a) next term; 56
b) n^th term; 10n - 4
c) term number 53; 526

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 £140 is invested for 8 years with a simple interest rate of 3%, find the amount of interest earned. £33.60

Interest (Compound)

If £220 is invested with an interest rate of 1% compounded annually, find the value of the investment after 6 years. £233.53

Currency Exchange

If £1 is worth $1.21, convert:

a) £120 to dollars; $145.20

b) $220 to pounds; £181.82

Coordinates (Midpoint)

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

$(2,-5) \text{ and } (14,1)$

(8,-2)

Gradient

What is the gradient of the line joining:

$(1,-9) \text{ and } (6,-4)$

1

Coordinates (Square)

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

$(5,2),(10,6),(1,7)$

(6,11)

Negative Numbers

a) 9 − 15 = -6
b) 9 × (-6) = -54
c) (5−10)(7−15) = 40
d) 54 ÷ (-6) = -9
e) (-12)² = 144

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:

$4x = 8$

$x = 2$

Equations (Type 2)

Solve:

$5x -5= 10$

$x = 3$

Equations (Type 3)

Solve:

$6x +5= 2x + 17$

$x = 3$

Equations (Type 4)

Solve:

$2(2x -4)+5= 25$

$x = 7$

Equations (Type 5)

Solve:

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

$x = -3.25$

Equations (Simultaneous 1)

Solve:

$5x+3y = 51$
$4x+3y = 45$

$x = 6, y = 7$

Equations (Simultaneous 2)

Solve:

$4x-2y = 24$
$6x+4y = 50$

$x = 7, y = 2$

Equations (Simultaneous 3)

Solve:

$3x+2y = -8.5$
$5x-7y = 84$

$x = 3.5, y = -9.5$

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

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

{6,8,10}

Bearings

A plane flies from point A to point B on a bearing of 227^o. What bearing would it return on from B to A? 047^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:

5² − 5 × 3 + 8

18

Simplify

Simplify the following by collecting like terms:

$3a+5b-3a+4b^2$

$5b+4b^2$

Ratio

Divide 63 in the ratio

2:7

14 and 49

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=2x+2$

Gradient 2
y intercept 2

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 £66 after a 45% reduction. What was the original price?

£120

Averages

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

5,8,8,6,7,8

Mean = 7, mode = 8,
median = 7.5 and range = 3

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.

0.686868... $\frac{68}{99}$

Percentage (Decrease)

Decrease £140 by 15%

£119

Brackets (Linear)

Expand:

$8(3x-5)$

$24x-40$

Brackets (Quadratic)

Expand:

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

$6x^2+3x-9$

Factorise (Linear)

Factorise:

$40x-32$

$8(5x-4)$

Factorise (Quadratic 1)

Factorise:

$x^2+x-6$

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

Factorise (Quadratic 2)

Factorise:

$8x^2+2x-1$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

6.31 × 10^-3

= 0.00631

Standard Form 3

Write in standard form:

90200

= 9.02 × 10⁴

Standard Form 4

Write in standard form:

0.0209

= 2.09 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$18, 33, 54, 81, 114, $

$3n^2+6n+9$

Standard Form 5

Multiply 9 × 10⁵
by 4 × 10⁴ and give the answer in standard form.

= 3.6 × 10¹⁰

Equations (Quadratic 1)

Solve:

$x^2-3x-10= 0$

$x = 5$ and $-2$

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 pentagon?

72°

Change The Subject

Make $c$ the subject of the formula
$$d=\frac{3c+1}{2}$$

$$c=\frac{2d-1}{3}$$

Basic Division 1

Calculate the value of:

2268 ÷ 9

= 252

Number Sequences 2

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

Square Numbers

What are the next three square numbers after
1

4, 9, 16

Prime Numbers

What are the next three prime numbers after
43

47, 53, 59

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: 0.88, 0.8, 8.88, 8.08, 8.8, 8, 0.08, in ascending order.
0.08, 0.8, 0.88, 8, 8.08, 8.8, 8.88,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram e = 69

Angles with Parallels 2

Angle diagram j = 58

Rounding (1sf)

Round to one significant figure:
a) 70.51; 70
b) 721408; 700000
c) 69; 70
d) 0.00490; 0.005

Estimation

Round each value to one significant figure to make an estimate:$$64 + 7.5 \times 31$$$60 + 8 \times 30 = 300$

Pie Charts (1)

A pie chart shows the colours of 30 books. What sector angle represents the
9 red books?
108°

Graph Linear (2)

What is the equation?

$y=3-x$

Pie Charts (2)

A pie chart shows the colours of 90 hats. How many green hats are represented
by a sector
angle of 264°?
66