Refreshing Revision

Number Sequences 1

What is the 12th:
a) Odd number; 23
b) Square number; 144
c) Prime number. 37

Factors

Find all the factors of:

24

1, 2, 3, 4, 6, 8, 12, 24.

Multiples

Subtract the 7th from the 10th multiples of:

7

21

Polygons

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

Pentagon, Hexagon and Heptagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 26.85; 26.8
b) 808409; 808000
c) 15; 15.0
d) 0.001595; 0.00160

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 13cm, a height of 12cm and a top (parallel to base) of 5cm. 108cm²

Fractions (Adding)

Evaluate:

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

Fractions (Multiplying)

Evaluate:

$ \frac{3}{5} × \frac{6}{7}$ $= \frac{18}{35}$

Fractions (Dividing)

Evaluate:

$ \frac{3}{5} ÷ \frac{8}{7}$ $= \frac{21}{40}$

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{2}{4}$ $= 50$%

Circle Area

Find the area of a circle that has a radius of 1cm. Give your answer to three significant figures.

3.14cm²

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:

9.9 + 6.8

= 16.7

Decimals (Subtracting)

Calculate the value of:

7.3 − 3.8

= 3.5

Decimals (Multiplying)

Calculate the value of:

3.3 × 6.9

= 22.77

Decimals (Dividing)

Calculate the value of:

104.4 ÷ 18

= 5.8

Indices (Simple)

What is the value of:

2²

= 4

Indices (Advanced)

What is the value of:

$3^{0}$

$= 1$

Basic Addition

Calculate the value of:

69 + 24

= 93

Basic Subtraction

Calculate the value of:

73 − 26

= 47

Basic Multiplication

Calculate the value of:

39 × 97

= 3783

Basic Division 2

Calculate the value of:

1121 ÷ 19

= 59

Percentage (Of)

Find the value of:

60% of 160

= 96

Standard Form 1

Find the value of:

8.37 × 10⁴

= 83700

Highest Common Factor

Find the highest common factor of fourteen and ten.

= 2

Times Tables (2-5)

9 × 2 = 18	6 × 5 = 30
7 × 2 = 14	5 × 5 = 25
8 × 5 = 40	4 × 4 = 16
3 × 2 = 6	2 × 3 = 6

Times Tables (2-12)

4 × 11 = 44	3 × 3 = 9
7 × 9 = 63	8 × 11 = 88
5 × 4 = 20	9 × 3 = 27
6 × 9 = 54	2 × 8 = 16

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{16}{20}$ $= \frac{4}{5}$

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find BC if AB = 5.7m and AC = 6.9m. 8.95m

Trigonometry (Angle)

Find angle BCA if AB = 4.4m and BC = 6.4m. 43.4^o

Trigonometry (Side)

Find AC if angle ABC = 63^o and AB = 5.6m. 11.0m

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{3}{4}$ $= 0.75$

Decimal to Fraction

Convert this decimal to a fraction.

$0.9$ = $ \frac{9}{10}$

Percentage (Increase)

Increase £60 by 30%

£78

Lowest Common Multiple

What is the lowest common multiple of eight and sixteen.

= 16

Sequence (Arithmetic)

6,19,32,45,58...

Find the:
a) next term; 71
b) n^th term; 13n - 7
c) term number 47; 604

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 £220 is invested for 4 years with a simple interest rate of 3%, find the amount of interest earned. £26.40

Interest (Compound)

If £140 is invested with an interest rate of 2% compounded annually, find the value of the investment after 6 years. £157.66

Currency Exchange

If £1 is worth $1.21, convert:

a) £200 to dollars; $242.00

b) $180 to pounds; £148.76

Coordinates (Midpoint)

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

$(6,-4) \text{ and } (16,8)$

(11,2)

Gradient

What is the gradient of the line joining:

$(-7,5) \text{ and } (-4,10)$

$\frac{5}{3}$

Coordinates (Square)

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

$(2,1),(7,7),(-4,6)$

(1,12)

Negative Numbers

a) 7 − 18 = -11
b) 7 × (-10) = -70
c) (12−21)(8−20) = 108
d) 70 ÷ (-10) = -7
e) (-10)² = 100

Substitution

If p = 5, q = 23 and
r = -12 evaluate:

a) 2q − p = 41
b) pq + r = 103
c) p² − 5q - r = -78

Equations (Type 1)

Solve:

$3x = 6$

$x = 2$

Equations (Type 2)

Solve:

$3x +5= 29$

$x = 8$

Equations (Type 3)

Solve:

$7x +5= 4x + 11$

$x = 2$

Equations (Type 4)

Solve:

$5(5x +6)-12= 143$

$x = 5$

Equations (Type 5)

Solve:

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

$x = 0.4$

Equations (Simultaneous 1)

Solve:

$3x-2y = -2$
$4x+2y = 16$

$x = 2, y = 4$

Equations (Simultaneous 2)

Solve:

$4x-3y = -9$
$5x+12y = 99$

$x = 3, y = 7$

Equations (Simultaneous 3)

Solve:

$3x-3y = -13.5$
$7x+2y = -9$

$x = -2, y = 2.5$

Sets (Union)

Find the union of:

{1,2,3,4,5} and
{6,7,8,9,10}

{1,2,3,4,5,6,7,8,9,10}

Sets (Intersection)

Find the intersection of:

{6,7,8,9,10} and
{2,6,12}

{6}

Bearings

A plane flies from point A to point B on a bearing of 273^o. What bearing would it return on from B to A? 093^o

Probability

A number is picked at random from the set

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

what is the probability it is even? $\frac12$

BIDMAS

Evaluate:

6 + 6 × 4 − 4

26

Simplify

Simplify the following by collecting like terms:

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

$3y^2-3y$

Ratio

Divide 90 in the ratio

8:7

48 and 42

Graph (Linear)

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:

540

2 x 2 x 3 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £162 after a 10% reduction. What was the original price?

£180

Averages

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

1,2,3,4,5

Mean = 3, no mode,
median = 3 and range = 4

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.

0.131313... $\frac{13}{99}$

Percentage (Decrease)

Decrease £40 by 40%

£24

Brackets (Linear)

Expand:

$6(5x-6)$

$30x-36$

Brackets (Quadratic)

Expand:

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

$2x^2+4x-16$

Factorise (Linear)

Factorise:

$4x-14$

$2(2x-7)$

Factorise (Quadratic 1)

Factorise:

$x^2-16$

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

Factorise (Quadratic 2)

Factorise:

$20x^2+11x-3$

$(4x+3)(5x-1)$

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

6.74 × 10^-2

= 0.0674

Standard Form 3

Write in standard form:

4810000

= 4.81 × 10⁶

Standard Form 4

Write in standard form:

0.0726

= 7.26 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$10, 20, 36, 58, 86, $

$3n^2+n+6$

Standard Form 5

Multiply 9 × 10³
by 8 × 10⁴ and give the answer in standard form.

= 7.2 × 10⁸

Equations (Quadratic 1)

Solve:

$x^2+2x-15= 0$

$x = 3$ and $-5$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

$5x^2-3x-4 = 0$

$x = 1.24$ and $-0.643$

Polygon Angles

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

45°

Change The Subject

Make $d$ the subject of the formula
$$e=\frac{2d-1}{3}$$

$$d=\frac{3e+1}{2}$$

Basic Division 1

Calculate the value of:

2394 ÷ 9

= 266

Number Sequences 2

What is the 7th:
a) Cube number; 343
b) Triangular number; 28
c) Fibonacci number. 13

Square Numbers

What are the three largest square numbers less than
81

64, 49, 36

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: 1.11, 1.1, 0.11, 1, 0.1, 1.01, 0.01, in ascending order.
0.01, 0.1, 0.11, 1, 1.01, 1.1, 1.11,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram j = 97

Angles with Parallels 2

Angle diagram b = 48

Rounding (1sf)

Round to one significant figure:
a) 64.59; 60
b) 764717; 800000
c) 51; 50
d) 0.00378; 0.004