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:

31

1, 31.

Multiples

Subtract the 7th from the 12th multiples of:

5

25

Polygons

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

Hexagon, Heptagon and Octagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 60.79; 60.8
b) 218470; 218000
c) 70; 70.0
d) 0.007095; 0.00710

Area of a Triangle

Find the area of a triangle that has a base of 5cm and a height of 8cm.

20cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 6cm and a top (parallel to base) of 5cm. 48cm²

Fractions (Adding)

Evaluate:

$ \frac{4}{5} + \frac{8}{9}$ $= 1\frac{31}{45}$

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

$ \frac{1}{3} ÷ \frac{5}{4}$ $= \frac{4}{15}$

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 11cm. Give your answer to three significant figures.

69.1cm

Decimals (Adding)

Calculate the value of:

8.7 + 4.6

= 13.3

Decimals (Subtracting)

Calculate the value of:

8.3 − 3.6

= 4.7

Decimals (Multiplying)

Calculate the value of:

3.2 × 7.2

= 23.04

Decimals (Dividing)

Calculate the value of:

37.8 ÷ 14

= 2.7

Indices (Simple)

What is the value of:

3²

= 9

Indices (Advanced)

What is the value of:

$4^{1}$

$= 4$

Basic Addition

Calculate the value of:

97 + 95

= 192

Basic Subtraction

Calculate the value of:

62 − 28

= 34

Basic Multiplication

Calculate the value of:

33 × 38

= 1254

Basic Division 2

Calculate the value of:

1425 ÷ 15

= 95

Percentage (Of)

Find the value of:

10% of 220

= 22

Standard Form 1

Find the value of:

6.54 × 10⁵

= 654000

Highest Common Factor

Find the highest common factor of twenty one and twelve.

= 3

Times Tables (2-5)

7 × 4 = 28	8 × 5 = 40
9 × 3 = 27	4 × 5 = 20
6 × 2 = 12	3 × 2 = 6
5 × 3 = 15	2 × 2 = 4

Times Tables (2-12)

9 × 6 = 54	5 × 7 = 35
3 × 4 = 12	4 × 9 = 36
8 × 3 = 24	7 × 5 = 35
6 × 10 = 60	2 × 2 = 4

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{3}{12}$ $= \frac{1}{4}$

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find BC if AB = 5.2m and AC = 7.2m. 8.88m

Trigonometry (Angle)

Find angle BCA if AB = 5.1m and AC = 7m. 36.1^o

Trigonometry (Side)

Find AB if angle ABC = 39^o and BC = 5.9m. 4.59m

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}{5}$ $= 0.2$

Decimal to Fraction

Convert this decimal to a fraction.

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

Percentage (Increase)

Increase £100 by 25%

£125

Lowest Common Multiple

What is the lowest common multiple of eight and twelve.

= 24

Sequence (Arithmetic)

4,13,22,31,40...

Find the:
a) next term; 49
b) n^th term; 9n - 5
c) term number 30; 265

Sequence (Geometric)

5,20,80,320,1280...

Find the:
a) next term; 5120
b) n^th term; 5 × 4^n-1
c) term number 11; 5242880

Interest (Simple)

If £240 is invested for 4 years with a simple interest rate of 5%, find the amount of interest earned. £48.00

Interest (Compound)

If £160 is invested with an interest rate of 6% compounded annually, find the value of the investment after 6 years. £226.96

Currency Exchange

If £1 is worth $1.37, convert:

a) £220 to dollars; $301.40

b) $220 to pounds; £160.58

Coordinates (Midpoint)

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

$(9,4) \text{ and } (21,14)$

(15,9)

Gradient

What is the gradient of the line joining:

$(-3,-5) \text{ and } (2,-2)$

$\frac{3}{5}$

Coordinates (Square)

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

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

(1,10)

Negative Numbers

a) 5 − 10 = -5
b) 5 × (-5) = -25
c) (12−24)(6−12) = 72
d) 25 ÷ (-5) = -5
e) (-6)² = 36

Substitution

If p = 5, q = 16 and
r = -11 evaluate:

a) 2q − p = 27
b) pq + r = 69
c) p² − 5q - r = -44

Equations (Type 1)

Solve:

$5x = 40$

$x = 8$

Equations (Type 2)

Solve:

$2x -8= 4$

$x = 6$

Equations (Type 3)

Solve:

$6x -2= 2x + 34$

$x = 9$

Equations (Type 4)

Solve:

$2(2x +4)-12= 8$

$x = 3$

Equations (Type 5)

Solve:

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

$x = -1.83 \text{(to 3 sf)}$

Equations (Simultaneous 1)

Solve:

$4x-2y = 8$
$2x+2y = 10$

$x = 3, y = 2$

Equations (Simultaneous 2)

Solve:

$4x+4y = 56$
$6x-8y = -14$

$x = 7, y = 7$

Equations (Simultaneous 3)

Solve:

$3x+3y = -13.5$
$7x+2y = -51.5$

$x = -8.5, y = 4$

Sets (Union)

Find the union of:

{1,3,5,7,9} and
{1,3,6,10,15}

{1,3,5,6,7,9,10,15}

Sets (Intersection)

Find the intersection of:

{2,4,6,8,10} and
{1,3,6,10,15}

{6,10}

Bearings

A plane flies from point A to point B on a bearing of 217^o. What bearing would it return on from B to A? 037^o

Probability

A number is picked at random from the set

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

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

BIDMAS

Evaluate:

3² − 8 × 8 + 4

-51

Simplify

Simplify the following by collecting like terms:

$7d−3e−5d+7e$

$4e+2d$

Ratio

Divide 25 in the ratio

2:3

10 and 15

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 £96 after a 20% reduction. What was the original price?

£120

Averages

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

2,4,6,8,10

Mean = 6, no mode,
median = 6 and range = 8

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.

0.323232... $\frac{32}{99}$

Percentage (Decrease)

Decrease £80 by 25%

£60

Brackets (Linear)

Expand:

$4(2x-2)$

$8x-8$

Brackets (Quadratic)

Expand:

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

$4x^2-5x-6$

Factorise (Linear)

Factorise:

$15x-21$

$3(5x-7)$

Factorise (Quadratic 1)

Factorise:

$x^2+3x-4$

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

Factorise (Quadratic 2)

Factorise:

$3x^2-8x-16$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

9.44 × 10^-5

= 0.0000944

Standard Form 3

Write in standard form:

16300

= 1.63 × 10⁴

Standard Form 4

Write in standard form:

0.0667

= 6.67 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$11, 21, 35, 53, 75, $

$2n^2+4n+5$

Standard Form 5

Multiply 9 × 10²
by 9 × 10⁵ and give the answer in standard form.

= 8.1 × 10⁸

Equations (Quadratic 1)

Solve:

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

$x = 5$ and $-3$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.434$ and $-0.768$

Polygon Angles

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

72°

Change The Subject

Make $a$ the subject of the formula
$$b=2a-3$$

$$a=\frac{b+3}{2}$$

Basic Division 1

Calculate the value of:

2136 ÷ 3

= 712

Number Sequences 2

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

Square Numbers

What is the square of

4

16

Prime Numbers

What is the difference between the 10th and the 11th prime numbers?

31 - 29 = 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: 0.6, 6.6, 0.66, 6.66, 6, 6.06, 0.06, in ascending order.
0.06, 0.6, 0.66, 6, 6.06, 6.6, 6.66,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram c = 81

Angles with Parallels 2

Angle diagram f = 65

Rounding (1sf)

Round to one significant figure:
a) 64.22; 60
b) 279598; 300000
c) 13; 10
d) 0.00545; 0.005

Estimation

Round each value to one significant figure to make an estimate:$$6.6 \times 93 - 152$$$7 \times 90 - 200 = 430$

Pie Charts (1)

A pie chart shows the colours of 15 books. What sector angle represents the
13 red books?
312°

Graph Linear (2)

What is the equation?

$y=3-2x$

Pie Charts (2)

A pie chart shows the colours of 18 hats. How many green hats are represented
by a sector
angle of 200°?
10

Surds (1)

Simplify:
$$\sqrt{48}$$
$4\sqrt{3}$

Surds (2)

Simplify:
$$\dfrac{4}{5\sqrt{3}}$$$\frac{4\sqrt{3}}{15}$

Surds (3)

Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$$\frac{10 + 2\sqrt{7}}{18}$