Refreshing Revision

Number Sequences 1

What is the 9th:
a) Odd number; 17
b) Square number; 81
c) Prime number. 23

Factors

Find all the factors of:

28

1, 2, 4, 7, 14, 28.

Multiples

Subtract the 5th from the 8th multiples of:

4

12

Polygons

What are the names of regular polygons with:
a) three sides;
b) four sides;
c) five sides.

Equilateral Triangle, Square and Pentagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 78.52; 78.5
b) 963438; 963000
c) 65; 65.0
d) 0.006595; 0.00660

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 9cm.

18cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 15cm, a height of 8cm and a top (parallel to base) of 5cm. 80cm²

Fractions (Adding)

Evaluate:

$ \frac{2}{5} + \frac{7}{8}$ $= 1\frac{11}{40}$

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

$ \frac{2}{4} ÷ \frac{7}{5}$ $= \frac{5}{14}$

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.

$ \frac{4}{5}$ $= 80$%

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:

7.9 + 2.5

= 10.4

Decimals (Subtracting)

Calculate the value of:

9.2 − 3.7

= 5.5

Decimals (Multiplying)

Calculate the value of:

8.9 × 9.9

= 88.11

Decimals (Dividing)

Calculate the value of:

32.4 ÷ 12

= 2.7

Indices (Simple)

What is the value of:

2²

= 4

Indices (Advanced)

What is the value of:

$4^{-1}$

$= \frac{1}{4}$

Basic Addition

Calculate the value of:

45 + 67

= 112

Basic Subtraction

Calculate the value of:

84 − 25

= 59

Basic Multiplication

Calculate the value of:

58 × 44

= 2552

Basic Division 2

Calculate the value of:

1298 ÷ 22

= 59

Percentage (Of)

Find the value of:

80% of 60

= 48

Standard Form 1

Find the value of:

5.97 × 10⁴

= 59700

Highest Common Factor

Find the highest common factor of twelve and eight.

= 4

Times Tables (2-5)

8 × 2 = 16	5 × 5 = 25
6 × 3 = 18	7 × 3 = 21
9 × 2 = 18	3 × 5 = 15
4 × 3 = 12	2 × 2 = 4

Times Tables (2-12)

3 × 11 = 33	8 × 6 = 48
6 × 5 = 30	5 × 2 = 10
9 × 7 = 63	4 × 11 = 44
7 × 5 = 35	2 × 4 = 8

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{21}{28}$ $= \frac{3}{4}$

Fractions (Mixed)

Evaluate:

$ 1\frac{4}{5} − \frac{8}{9}$ $= \frac{41}{45}$

Pythagoras

Find AC if AB = 6m and BC = 7.1m. 3.80m

Trigonometry (Angle)

Find angle ABC if AC = 4m and AB = 6m. 33.7^o

Trigonometry (Side)

Find AB if angle ABC = 34^o and BC = 5.4m. 4.48m

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{4}{8}$ $= 0.5$

Decimal to Fraction

Convert this decimal to a fraction.

$0.57$ = $ \frac{57}{100}$

Percentage (Increase)

Increase £100 by 25%

£125

Lowest Common Multiple

What is the lowest common multiple of six and ten.

= 30

Sequence (Arithmetic)

6,14,22,30,38...

Find the:
a) next term; 46
b) n^th term; 8n - 2
c) term number 33; 262

Sequence (Geometric)

3,6,12,24,48...

Find the:
a) next term; 96
b) n^th term; 3 × 2^n-1
c) term number 11; 3072

Interest (Simple)

If £120 is invested for 5 years with a simple interest rate of 6%, find the amount of interest earned. £36.00

Interest (Compound)

If £240 is invested with an interest rate of 6% compounded annually, find the value of the investment after 7 years. £360.87

Currency Exchange

If £1 is worth $1.36, convert:

a) £100 to dollars; $136.00

b) $240 to pounds; £176.47

Coordinates (Midpoint)

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

$(4,5) \text{ and } (14,13)$

(9,9)

Gradient

What is the gradient of the line joining:

$(-7,0) \text{ and } (-1,3)$

$\frac{1}{2}$

Coordinates (Square)

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

$(2,1),(5,6),(-3,4)$

(0,9)

Negative Numbers

a) 11 − 23 = -12
b) 11 × (-5) = -55
c) (6−13)(9−21) = 84
d) 55 ÷ (-5) = -11
e) (-8)² = 64

Substitution

If p = 5, q = 28 and
r = -10 evaluate:

a) 2q − p = 51
b) pq + r = 130
c) p² − 5q - r = -105

Equations (Type 1)

Solve:

$2x = 18$

$x = 9$

Equations (Type 2)

Solve:

$3x -4= 14$

$x = 6$

Equations (Type 3)

Solve:

$9x +2= 4x + 22$

$x = 4$

Equations (Type 4)

Solve:

$3(5x +6)+6= 114$

$x = 6$

Equations (Type 5)

Solve:

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

$x = 0$

Equations (Simultaneous 1)

Solve:

$3x+3y = 24$
$4x-3y = 11$

$x = 5, y = 3$

Equations (Simultaneous 2)

Solve:

$4x-3y = 10$
$6x+12y = 114$

$x = 7, y = 6$

Equations (Simultaneous 3)

Solve:

$3x-5y = 22.5$
$5x+3y = -64.5$

$x = -7.5, y = -9$

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

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

{7,9}

Bearings

A plane flies from point A to point B on a bearing of 024^o. What bearing would it return on from B to A? 204^o

Probability

A number is picked at random from the set

{1,2,3,4,5}

what is the probability it is even? $\frac25$

BIDMAS

Evaluate:

8² − 7 × 9 + 3

4

Simplify

Simplify the following by collecting like terms:

$2y+2y^2-5y+y^2$

$3y^2-3y$

Ratio

Divide 182 in the ratio

4:9

56 and 126

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:

36

2 x 2 x 3 x 3

Percentage (Reverse)

In a sale an item costs £78 after a 35% reduction. What was the original price?

£120

Averages

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

1,3,1,10,5

Mean = 4, mode = 1,
median = 3 and range = 9

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.

0.282828... $\frac{28}{99}$

Percentage (Decrease)

Decrease £140 by 10%

£126

Brackets (Linear)

Expand:

$5(3x-8)$

$15x-40$

Brackets (Quadratic)

Expand:

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

$2x^2-2x-4$

Factorise (Linear)

Factorise:

$49x-63$

$7(7x-9)$

Factorise (Quadratic 1)

Factorise:

$x^2-4$

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

Factorise (Quadratic 2)

Factorise:

$2x^2-x-3$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

2.38 × 10^-2

= 0.0238

Standard Form 3

Write in standard form:

9470

= 9.47 × 10³

Standard Form 4

Write in standard form:

0.000863

= 8.63 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$-1, 7, 17, 29, 43, $

$n^2+5n-7$

Standard Form 5

Multiply 5 × 10²
by 6 × 10³ and give the answer in standard form.

= 3 × 10⁶

Equations (Quadratic 1)

Solve:

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

$x = 2$ and $-5$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.847$ and $-1.18$

Polygon Angles

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

45°

Change The Subject

Make $b$ the subject of the formula
$$c=3b-5$$

$$b=\frac{c+5}{3}$$

Basic Division 1

Calculate the value of:

2584 ÷ 8

= 323

Number Sequences 2

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

Square Numbers

What are the three largest square numbers less than
121

100, 81, 64

Prime Numbers

What are the next three prime numbers after
17

19, 23, 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: 0.66, 6, 6.66, 6.6, 6.06, 0.6, 0.06, in ascending order.
0.06, 0.6, 0.66, 6, 6.06, 6.6, 6.66,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram e = 69

Angles with Parallels 2

Angle diagram e = 63

Rounding (1sf)

Round to one significant figure:
a) 54.45; 50
b) 439111; 400000
c) 72; 70
d) 0.00962; 0.01

Estimation

Round each value to one significant figure to make an estimate:$$2.8 \times 74 - 163$$$3 \times 70 - 200 = 10$

Pie Charts (1)

A pie chart shows the colours of 120 books. What sector angle represents the
103 red books?
309°

Graph Linear (2)

What is the equation?

$y=x-1$

Pie Charts (2)

A pie chart shows the colours of 45 hats. How many green hats are represented
by a sector
angle of 320°?
40

Surds

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