Refreshing Revision

Number Sequences 1

What is the 8th:
a) Odd number; 15
b) Square number; 64
c) Prime number. 19

Factors

Find all the factors of:

22

1, 2, 11, 22.

Multiples

Subtract the 7th from the 10th multiples of:

3

9

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) 66.69; 66.7
b) 554910; 555000
c) 43; 43.0
d) 0.004395; 0.00440

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 14cm, a height of 10cm and a top (parallel to base) of 6cm. 100cm²

Fractions (Adding)

Evaluate:

$ \frac{1}{3} + \frac{6}{7}$ $= 1\frac{4}{21}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{3} × \frac{5}{6}$ $= \frac{5}{18}$

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 to 3 significant figures.

$ \frac{1}{6}$ $= 16.7$%

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 2cm. Give your answer to three significant figures.

12.6cm

Decimals (Adding)

Calculate the value of:

3.7 + 6.8

= 10.5

Decimals (Subtracting)

Calculate the value of:

9.2 − 1.7

= 7.5

Decimals (Multiplying)

Calculate the value of:

4.5 × 8.3

= 37.35

Decimals (Dividing)

Calculate the value of:

91.8 ÷ 17

= 5.4

Indices (Simple)

What is the value of:

2³

= 8

Indices (Advanced)

What is the value of:

$3^{0}$

$= 1$

Basic Addition

Calculate the value of:

89 + 26

= 115

Basic Subtraction

Calculate the value of:

51 − 26

= 25

Basic Multiplication

Calculate the value of:

68 × 34

= 2312

Basic Division 2

Calculate the value of:

2117 ÷ 29

= 73

Percentage (Of)

Find the value of:

90% of 100

= 90

Standard Form 1

Find the value of:

1.6 × 10³

= 1600

Highest Common Factor

Find the highest common factor of twenty seven and six.

= 3

Times Tables (2-5)

9 × 5 = 45	8 × 5 = 40
7 × 3 = 21	5 × 3 = 15
4 × 3 = 12	3 × 4 = 12
6 × 4 = 24	2 × 4 = 8

Times Tables (2-12)

6 × 12 = 72	3 × 3 = 9
4 × 8 = 32	7 × 2 = 14
8 × 11 = 88	9 × 8 = 72
5 × 8 = 40	2 × 4 = 8

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{20}{32}$ $= \frac{5}{8}$

Fractions (Mixed)

Evaluate:

$ 2\frac{4}{5} − \frac{7}{8}$ $= 1\frac{37}{40}$

Pythagoras

Find BC if AB = 4.3m and AC = 6m. 7.38m

Trigonometry (Angle)

Find angle BCA if AC = 4.3m and BC = 5.9m. 43.2^o

Trigonometry (Side)

Find BC if angle BCA = 60^o and AB = 3.7m. 4.27m

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{1}{4}$ $= 0.25$

Decimal to Fraction

Convert this decimal to a fraction.

$0.37$ = $ \frac{37}{100}$

Percentage (Increase)

Increase £80 by 5%

£84

Lowest Common Multiple

What is the lowest common multiple of eight and twenty eight.

= 56

Sequence (Arithmetic)

7,20,33,46,59...

Find the:
a) next term; 72
b) n^th term; 13n - 6
c) term number 51; 657

Sequence (Geometric)

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

Find the:
a) next term; 160
b) n^th term; 5 × 2^n-1
c) term number 12; 10240

Interest (Simple)

If £240 is invested for 9 years with a simple interest rate of 4%, find the amount of interest earned. £86.40

Interest (Compound)

If £180 is invested with an interest rate of 2% compounded annually, find the value of the investment after 6 years. £202.71

Currency Exchange

If £1 is worth $1.36, convert:

a) £120 to dollars; $163.20

b) $160 to pounds; £117.65

Coordinates (Midpoint)

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

$(9,8) \text{ and } (19,14)$

(14,11)

Gradient

What is the gradient of the line joining:

$(4,2) \text{ and } (10,8)$

1

Coordinates (Square)

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

$(5,1),(9,4),(2,5)$

(6,8)

Negative Numbers

a) 11 − 16 = -5
b) 11 × (-12) = -132
c) (8−14)(11−22) = 66
d) 132 ÷ (-12) = -11
e) (-11)² = 121

Substitution

If p = 5, q = 22 and
r = -8 evaluate:

a) 2q − p = 39
b) pq + r = 102
c) p² − 5q - r = -77

Equations (Type 1)

Solve:

$3x = 24$

$x = 8$

Equations (Type 2)

Solve:

$3x -1= 14$

$x = 5$

Equations (Type 3)

Solve:

$9x -2= 6x + 19$

$x = 7$

Equations (Type 4)

Solve:

$5(5x +3)-8= 207$

$x = 8$

Equations (Type 5)

Solve:

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

$x = -0.75$

Equations (Simultaneous 1)

Solve:

$2x+2y = 20$
$4x-2y = 22$

$x = 7, y = 3$

Equations (Simultaneous 2)

Solve:

$4x+4y = 44$
$6x+12y = 90$

$x = 7, y = 4$

Equations (Simultaneous 3)

Solve:

$2x+2y = -27$
$3x+5y = -49.5$

$x = -9, y = -4.5$

Sets (Union)

Find the union of:

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

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

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 104^o. What bearing would it return on from B to A? 284^o

Probability

A number is picked at random from the set

{1,3,5,7,9}

what is the probability it is even? 0

BIDMAS

Evaluate:

21 ÷ 3 × 18 ÷ 2

63

Simplify

Simplify the following by collecting like terms:

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

$11b+9c$

Ratio

Divide 55 in the ratio

8:3

40 and 15

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=-x-1$

Gradient -1
y intercept -1

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 £102 after a 15% reduction. What was the original price?

£120

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.

0.494949... $\frac{49}{99}$

Percentage (Decrease)

Decrease £180 by 20%

£144

Brackets (Linear)

Expand:

$2(2x-4)$

$4x-8$

Brackets (Quadratic)

Expand:

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

$9x^2-6x-3$

Factorise (Linear)

Factorise:

$4x-4$

$4(x-1)$

Factorise (Quadratic 1)

Factorise:

$x^2-16$

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

Factorise (Quadratic 2)

Factorise:

$2x^2+5x-3$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

2.5 × 10^-3

= 0.0025

Standard Form 3

Write in standard form:

837

= 8.37 × 10²

Standard Form 4

Write in standard form:

0.000054

= 5.4 × 10^-5

Sequence (Quadratic)

Find the n^th term:

$1, 11, 25, 43, 65, $

$2n^2+4n-5$

Standard Form 5

Multiply 6 × 10⁶
by 8 × 10³ and give the answer in standard form.

= 4.8 × 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:

$3x^2+5x-1 = 0$

$x = 0.180$ and $-1.85$

Polygon Angles

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

144°

Change The Subject

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

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

Basic Division 1

Calculate the value of:

6128 ÷ 8

= 766

Number Sequences 2

What is the 10th:
a) Cube number; 1000
b) Triangular number; 55
c) Fibonacci number. 55

Square Numbers

What is the square of

9

81

Prime Numbers

What is the difference between the 5th and the 6th prime numbers?

13 - 11 = 2

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: 0.2, 2.22, 0.22, 2.02, 2.2, 2, 0.02, in ascending order.
0.02, 0.2, 0.22, 2, 2.02, 2.2, 2.22,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram b = 52

Angles with Parallels 2

Angle diagram j = 58

Rounding (1sf)

Round to one significant figure:
a) 88.38; 90
b) 240736; 200000
c) 81; 80
d) 0.00525; 0.005

Estimation

Round each value to one significant figure to make an estimate:$$(182 + 6.5) \div 18$$$(200 + 7) \div 20 = 10.35$

Pie Charts (1)

A pie chart shows the colours of 180 books. What sector angle represents the
169 red books?
338°

Graph Linear (2)

What is the equation?

$y=x-4$

Pie Charts (2)

A pie chart shows the colours of 9 hats. How many green hats are represented
by a sector
angle of 160°?
4

Surds (1)

Simplify:
$$\sqrt{18}$$
$3\sqrt{2}$

Surds (2)

Simplify:
$$\dfrac{3}{4\sqrt{2}}$$$\frac{3\sqrt{2}}{8}$

Surds (3)

Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$$\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}$