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:

47

1, 47.

Multiples

Subtract the 7th from the 11th multiples of:

8

32

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) 77.28; 77.3
b) 817863; 818000
c) 24; 24.0
d) 0.002495; 0.00250

Area of a Triangle

Find the area of a triangle that has a base of 5cm and a height of 9cm.

22.5cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 10cm and a top (parallel to base) of 3cm. 80cm²

Fractions (Adding)

Evaluate:

$ \frac{3}{4} + \frac{7}{8}$ $= 1\frac{5}{8}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{2} × \frac{4}{6}$ $= \frac{1}{3}$

Fractions (Dividing)

Evaluate:

$ \frac{1}{2} ÷ \frac{4}{3}$ $= \frac{3}{8}$

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{4}{7}$ $= 57.1$%

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 5cm. Give your answer to three significant figures.

31.4cm

Decimals (Adding)

Calculate the value of:

8.9 + 6.5

= 15.4

Decimals (Subtracting)

Calculate the value of:

9.2 − 4.9

= 4.3

Decimals (Multiplying)

Calculate the value of:

8.8 × 2.3

= 20.24

Decimals (Dividing)

Calculate the value of:

46.8 ÷ 12

= 3.9

Indices (Simple)

What is the value of:

4²

= 16

Indices (Advanced)

What is the value of:

$1^{\frac{1}{2}}$

$= 1$

Basic Addition

Calculate the value of:

99 + 39

= 138

Basic Subtraction

Calculate the value of:

83 − 25

= 58

Basic Multiplication

Calculate the value of:

65 × 92

= 5980

Basic Division 2

Calculate the value of:

1170 ÷ 18

= 65

Percentage (Of)

Find the value of:

40% of 80

= 32

Standard Form 1

Find the value of:

4.75 × 10⁶

= 4750000

Highest Common Factor

Find the highest common factor of twenty four and sixteen.

= 8

Times Tables (2-5)

9 × 4 = 36	6 × 3 = 18
4 × 2 = 8	5 × 2 = 10
3 × 4 = 12	7 × 2 = 14
8 × 2 = 16	2 × 2 = 4

Times Tables (2-12)

3 × 5 = 15	5 × 6 = 30
6 × 3 = 18	9 × 8 = 72
8 × 2 = 16	4 × 3 = 12
7 × 12 = 84	2 × 11 = 22

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

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

Fractions (Mixed)

Evaluate:

$ 1\frac{3}{4} − \frac{6}{7}$ $= \frac{25}{28}$

Pythagoras

Find BC if AB = 4m and AC = 5.7m. 6.96m

Trigonometry (Angle)

Find angle BCA if AC = 3.2m and BC = 4.3m. 41.9^o

Trigonometry (Side)

Find AC if angle ABC = 68^o and AB = 3.8m. 9.41m

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{3}{7}$ $= 0.429$

Decimal to Fraction

Convert this decimal to a fraction.

$0.54$ = $ \frac{27}{50}$

Percentage (Increase)

Increase £60 by 10%

£66

Lowest Common Multiple

What is the lowest common multiple of four and ten.

= 20

Sequence (Arithmetic)

6,16,26,36,46...

Find the:
a) next term; 56
b) n^th term; 10n - 4
c) term number 29; 286

Sequence (Geometric)

6,18,54,162,486...

Find the:
a) next term; 1458
b) n^th term; 6 × 3^n-1
c) term number 12; 1062882

Interest (Simple)

If £220 is invested for 7 years with a simple interest rate of 5%, find the amount of interest earned. £77.00

Interest (Compound)

If £200 is invested with an interest rate of 5% compounded annually, find the value of the investment after 7 years. £281.42

Currency Exchange

If £1 is worth $1.36, convert:

a) £240 to dollars; $326.40

b) $200 to pounds; £147.06

Coordinates (Midpoint)

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

$(-8,7) \text{ and } (-2,19)$

(-5,13)

Gradient

What is the gradient of the line joining:

$(0,-5) \text{ and } (3,-2)$

1

Coordinates (Square)

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

$(5,4),(8,9),(0,7)$

(3,12)

Negative Numbers

a) 10 − 21 = -11
b) 10 × (-9) = -90
c) (11−23)(9−18) = 108
d) 90 ÷ (-9) = -10
e) (-11)² = 121

Substitution

If p = 6, q = 27 and
r = -12 evaluate:

a) 2q − p = 48
b) pq + r = 150
c) p² − 5q - r = -87

Equations (Type 1)

Solve:

$2x = 18$

$x = 9$

Equations (Type 2)

Solve:

$3x -9= 3$

$x = 4$

Equations (Type 3)

Solve:

$6x +2= 3x + 14$

$x = 4$

Equations (Type 4)

Solve:

$3(5x -2)+11= 110$

$x = 7$

Equations (Type 5)

Solve:

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

$x = 5$

Equations (Simultaneous 1)

Solve:

$5x+2y = 14$
$4x+2y = 12$

$x = 2, y = 2$

Equations (Simultaneous 2)

Solve:

$3x-4y = -7$
$7x-12y = -27$

$x = 3, y = 4$

Equations (Simultaneous 3)

Solve:

$3x+7y = 46.5$
$5x+2y = 48.5$

$x = 8.5, y = 3$

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

{1,3,5,7,9} and
{2,6,12}

∅

Bearings

A plane flies from point A to point B on a bearing of 201^o. What bearing would it return on from B to A? 021^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:

(18 − 6)² + 2 × 2

148

Simplify

Simplify the following by collecting like terms:

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

$11b+9c$

Ratio

Divide 75 in the ratio

8:7

40 and 35

Graph Linear (1)

Draw a rough sketch of the graph of:

$2y=x+4$

Gradient 0.5
y intercept 2

Prime Factors

Express the following number as the product of prime numbers:

60

2 x 2 x 3 x 5

Percentage (Reverse)

In a sale an item costs £85 after a 15% reduction. What was the original price?

£100

Averages

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

5,3,7,5,10

Mean = 6, mode = 5,
median = 5 and range = 7

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.

0.979797... $\frac{97}{99}$

Percentage (Decrease)

Decrease £80 by 20%

£64

Brackets (Linear)

Expand:

$9(9x-3)$

$81x-27$

Brackets (Quadratic)

Expand:

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

$4x^2-4$

Factorise (Linear)

Factorise:

$20x-45$

$5(4x-9)$

Factorise (Quadratic 1)

Factorise:

$x^2-x-12$

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

Factorise (Quadratic 2)

Factorise:

$3x^2-11x-4$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

1.37 × 10^-2

= 0.0137

Standard Form 3

Write in standard form:

90100

= 9.01 × 10⁴

Standard Form 4

Write in standard form:

0.0201

= 2.01 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$0, 11, 28, 51, 80, $

$3n^2+2n-5$

Standard Form 5

Multiply 4 × 10³
by 6 × 10⁵ and give the answer in standard form.

= 2.4 × 10⁹

Equations (Quadratic 1)

Solve:

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

$x = 5$ and $-2$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 2.35$ and $-0.851$

Polygon Angles

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

120°

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:

1858 ÷ 2

= 929

Number Sequences 2

What is the 12th:
a) Cube number; 1728
b) Triangular number; 78
c) Fibonacci number. 144

Square Numbers

What is the square of

12

144

Prime Numbers

What is the 8th prime number?

19

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: 0.55, 5.5, 5.55, 5, 5.05, 0.5, 0.05, in ascending order.
0.05, 0.5, 0.55, 5, 5.05, 5.5, 5.55,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram b = 52

Angles with Parallels 2

Angle diagram a = 132

Rounding (1sf)

Round to one significant figure:
a) 97.89; 100
b) 417922; 400000
c) 65; 60
d) 0.00283; 0.003

Estimation

Round each value to one significant figure to make an estimate:$$(161 + 2.6) \div 18$$$(200 + 3) \div 20 = 10.15$

Pie Charts (1)

A pie chart shows the colours of 24 books. What sector angle represents the
10 red books?
150°

Graph Linear (2)

What is the equation?

$y=4-0.5x$

Pie Charts (2)

A pie chart shows the colours of 90 hats. How many green hats are represented
by a sector
angle of 112°?
28

Surds (1)

Simplify:
$$\sqrt{75}$$
$5\sqrt{3}$

Surds (2)

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

Surds (3)

Simplify:
$$\dfrac{3}{4 + \sqrt{2}}$$$\frac{12 - 3\sqrt{2}}{14} = \frac{6 - \sqrt{2}}{7}$