Refreshing Revision

Number Sequences 1

What is the 10th:
a) Odd number; 19
b) Square number; 100
c) Prime number. 29

Factors

Find all the factors of:

22

1, 2, 11, 22.

Multiples

Subtract the 4th from the 8th multiples of:

8

32

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) 88.58; 88.6
b) 802658; 803000
c) 50; 50.0
d) 0.005095; 0.00510

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 15cm, a height of 9cm and a top (parallel to base) of 5cm. 90cm²

Fractions (Adding)

Evaluate:

$ \frac{1}{3} + \frac{4}{7}$ $= \frac{19}{21}$

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

$ \frac{1}{2} ÷ \frac{5}{4}$ $= \frac{2}{5}$

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 12cm. Give your answer to three significant figures.

452cm²

Circle Circumference

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

6.28cm

Decimals (Adding)

Calculate the value of:

6.8 + 5.9

= 12.7

Decimals (Subtracting)

Calculate the value of:

9.1 − 3.8

= 5.3

Decimals (Multiplying)

Calculate the value of:

5.5 × 4.7

= 25.85

Decimals (Dividing)

Calculate the value of:

134.4 ÷ 16

= 8.4

Indices (Simple)

What is the value of:

5²

= 25

Indices (Advanced)

What is the value of:

$3^{-3}$

$= \frac{1}{27}$

Basic Addition

Calculate the value of:

95 + 27

= 122

Basic Subtraction

Calculate the value of:

53 − 27

= 26

Basic Multiplication

Calculate the value of:

72 × 77

= 5544

Basic Division 2

Calculate the value of:

2112 ÷ 22

= 96

Percentage (Of)

Find the value of:

55% of 380

= 209

Standard Form 1

Find the value of:

8.04 × 10²

= 804

Highest Common Factor

Find the highest common factor of twenty four and fifteen.

= 3

Times Tables (2-5)

3 × 3 = 9	5 × 4 = 20
7 × 4 = 28	9 × 3 = 27
4 × 5 = 20	6 × 4 = 24
8 × 2 = 16	2 × 5 = 10

Times Tables (2-12)

7 × 5 = 35	6 × 9 = 54
5 × 7 = 35	8 × 4 = 32
9 × 4 = 36	3 × 11 = 33
4 × 10 = 40	2 × 5 = 10

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{12}{24}$ $= \frac{1}{2}$

Fractions (Mixed)

Evaluate:

$ 1\frac{2}{3} − \frac{5}{6}$ $= \frac{5}{6}$

Pythagoras

Find BC if AB = 3.6m and AC = 4.6m. 5.84m

Trigonometry (Angle)

Find angle BCA if AB = 5.1m and AC = 6.2m. 39.4^o

Trigonometry (Side)

Find BC if angle BCA = 30^o and AC = 5.1m. 5.89m

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{4}{6}$ $= 0.667$

Decimal to Fraction

Convert this decimal to a fraction.

$0.71$ = $ \frac{71}{100}$

Percentage (Increase)

Increase £60 by 5%

£63

Lowest Common Multiple

What is the lowest common multiple of six and fourteen.

= 42

Sequence (Arithmetic)

3,9,15,21,27...

Find the:
a) next term; 33
b) n^th term; 6n - 3
c) term number 51; 303

Sequence (Geometric)

4,8,16,32,64...

Find the:
a) next term; 128
b) n^th term; 4 × 2^n-1
c) term number 11; 4096

Interest (Simple)

If £160 is invested for 7 years with a simple interest rate of 5%, find the amount of interest earned. £56.00

Interest (Compound)

If £140 is invested with an interest rate of 5% compounded annually, find the value of the investment after 4 years. £170.17

Currency Exchange

If £1 is worth $1.33, convert:

a) £240 to dollars; $319.20

b) $180 to pounds; £135.34

Coordinates (Midpoint)

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

$(-1,-5) \text{ and } (5,3)$

(2,-1)

Gradient

What is the gradient of the line joining:

$(-3,9) \text{ and } (3,12)$

$\frac{1}{2}$

Coordinates (Square)

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

$(4,2),(7,6),(0,5)$

(3,9)

Negative Numbers

a) 8 − 17 = -9
b) 8 × (-11) = -88
c) (7−18)(9−15) = 66
d) 88 ÷ (-11) = -8
e) (-9)² = 81

Substitution

If p = 6, q = 22 and
r = -7 evaluate:

a) 2q − p = 38
b) pq + r = 125
c) p² − 5q - r = -67

Equations (Type 1)

Solve:

$3x = 18$

$x = 6$

Equations (Type 2)

Solve:

$3x -2= 25$

$x = 9$

Equations (Type 3)

Solve:

$4x -2= 2x + 16$

$x = 9$

Equations (Type 4)

Solve:

$5(4x -4)-7= 13$

$x = 2$

Equations (Type 5)

Solve:

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

$x = -0.4$

Equations (Simultaneous 1)

Solve:

$4x+4y = 40$
$2x+4y = 30$

$x = 5, y = 5$

Equations (Simultaneous 2)

Solve:

$3x+4y = 21$
$5x-12y = -21$

$x = 3, y = 3$

Equations (Simultaneous 3)

Solve:

$3x-7y = 34$
$5x-2y = -25.5$

$x = -8.5, y = -8.5$

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 315^o. What bearing would it return on from B to A? 135^o

Probability

A number is picked at random from the set

{2,4,6,8,10}

what is the probability it is even? 1

BIDMAS

Evaluate:

5 + 9 × 5 − 8

42

Simplify

Simplify the following by collecting like terms:

$5a−5−4a−5$

$a-10$

Ratio

Divide 210 in the ratio

6:9

84 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:

120

2 x 2 x 2 x 3 x 5

Percentage (Reverse)

In a sale an item costs £39 after a 35% reduction. What was the original price?

£60

Averages

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

5,6,7,8,9,10

Mean = 7.5, no mode,
median = 7.5 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.

0.595959... $\frac{59}{99}$

Percentage (Decrease)

Decrease £120 by 20%

£96

Brackets (Linear)

Expand:

$7(4x-6)$

$28x-42$

Brackets (Quadratic)

Expand:

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

$3x^2+7x-6$

Factorise (Linear)

Factorise:

$25x-20$

$5(5x-4)$

Factorise (Quadratic 1)

Factorise:

$x^2-4$

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

Factorise (Quadratic 2)

Factorise:

$2x^2+5x-12$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

5.33 × 10^-2

= 0.0533

Standard Form 3

Write in standard form:

7740

= 7.74 × 10³

Standard Form 4

Write in standard form:

0.00473

= 4.73 × 10^-3

Sequence (Quadratic)

Find the n^th term:

$4, 19, 40, 67, 100, $

$3n^2+6n-5$

Standard Form 5

Multiply 9 × 10⁶
by 5 × 10⁶ and give the answer in standard form.

= 4.5 × 10¹³

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:

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

$x = 0.744$ and $-1.34$

Polygon Angles

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

51.4°

Change The Subject

Make $h$ the subject of the formula
$$e=\frac{h}{4}-5$$

$$h=4(e+5)$$

Basic Division 1

Calculate the value of:

1396 ÷ 2

= 698

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
4

9, 16, 25

Prime Numbers

What is the 4th prime number?

7

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: 4.44, 4, 0.44, 4.4, 0.4, 4.04, 0.04, in ascending order.
0.04, 0.4, 0.44, 4, 4.04, 4.4, 4.44,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram e = 69

Angles with Parallels 2

Angle diagram c = 78

Rounding (1sf)

Round to one significant figure:
a) 30.92; 30
b) 701871; 700000
c) 56; 60
d) 0.00921; 0.009

Estimation

Round each value to one significant figure to make an estimate:$$71 + 9.6 \times 24$$$70 + 10 \times 20 = 270$

Pie Charts (1)

A pie chart shows the colours of 20 books. What sector angle represents the
3 red books?
54°

Graph Linear (2)

What is the equation?

$y=2x-4$

Pie Charts (2)

A pie chart shows the colours of 72 hats. How many green hats are represented
by a sector
angle of 50°?
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:
$$\dfrac{8}{3 + \sqrt{6}}$$$\frac{24 - 8\sqrt{6}}{3}$