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:

37

1, 37.

Multiples

Subtract the 6th from the 11th multiples of:

5

25

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) 67.67; 67.7
b) 510625; 511000
c) 33; 33.0
d) 0.003395; 0.00340

Area of a Triangle

Find the area of a triangle that has a base of 3cm and a height of 7cm.

10.5cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 10cm, a height of 9cm and a top (parallel to base) of 4cm. 63cm²

Fractions (Adding)

Evaluate:

$ \frac{3}{6} + \frac{8}{10}$ $= 1\frac{3}{10}$

Fractions (Multiplying)

Evaluate:

$ \frac{3}{5} × \frac{7}{9}$ $= \frac{7}{15}$

Fractions (Dividing)

Evaluate:

$ \frac{3}{4} ÷ \frac{7}{6}$ $= \frac{9}{14}$

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 to 3 significant figures.

$ \frac{5}{6}$ $= 83.3$%

Circle Area

Find the area of a circle that has a radius of 3cm. Give your answer to three significant figures.

28.3cm²

Circle Circumference

Find the circumference of a circle that has a radius of 6cm. Give your answer to three significant figures.

37.7cm

Decimals (Adding)

Calculate the value of:

3.5 + 7.7

= 11.2

Decimals (Subtracting)

Calculate the value of:

7.3 − 4.9

= 2.4

Decimals (Multiplying)

Calculate the value of:

3.9 × 8.8

= 34.32

Decimals (Dividing)

Calculate the value of:

51.3 ÷ 19

= 2.7

Indices (Simple)

What is the value of:

5²

= 25

Indices (Advanced)

What is the value of:

$3^{0}$

$= 1$

Basic Addition

Calculate the value of:

88 + 84

= 172

Basic Subtraction

Calculate the value of:

93 − 29

= 64

Basic Multiplication

Calculate the value of:

83 × 28

= 2324

Basic Division 2

Calculate the value of:

884 ÷ 13

= 68

Percentage (Of)

Find the value of:

10% of 220

= 22

Standard Form 1

Find the value of:

5.71 × 10⁵

= 571000

Highest Common Factor

Find the highest common factor of twelve and six.

= 6

Times Tables (2-5)

3 × 5 = 15	8 × 3 = 24
9 × 2 = 18	4 × 5 = 20
7 × 2 = 14	6 × 3 = 18
5 × 5 = 25	2 × 5 = 10

Times Tables (2-12)

9 × 11 = 99	7 × 7 = 49
8 × 4 = 32	6 × 6 = 36
3 × 8 = 24	5 × 4 = 20
4 × 3 = 12	2 × 9 = 18

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{35}{56}$ $= \frac{5}{8}$

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find BC if AB = 5.9m and AC = 7.5m. 9.54m

Trigonometry (Angle)

Find angle BCA if AB = 3.5m and BC = 5.2m. 42.3^o

Trigonometry (Side)

Find AC if angle BCA = 36^o and AB = 4.2m. 5.78m

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.

$0.45$ = $ \frac{9}{20}$

Percentage (Increase)

Increase £120 by 35%

£162

Lowest Common Multiple

What is the lowest common multiple of six and ten.

= 30

Sequence (Arithmetic)

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

Find the:
a) next term; 71
b) n^th term; 13n - 7
c) term number 35; 448

Sequence (Geometric)

5,10,20,40,80...

Find the:
a) next term; 160
b) n^th term; 5 × 2^n-1
c) term number 9; 1280

Interest (Simple)

If £120 is invested for 4 years with a simple interest rate of 6%, find the amount of interest earned. £28.80

Interest (Compound)

If £200 is invested with an interest rate of 1% compounded annually, find the value of the investment after 9 years. £218.74

Currency Exchange

If £1 is worth $1.35, convert:

a) £200 to dollars; $270.00

b) $160 to pounds; £118.52

Coordinates (Midpoint)

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

$(-2,3) \text{ and } (4,13)$

(1,8)

Gradient

What is the gradient of the line joining:

$(-3,0) \text{ and } (3,4)$

$\frac{2}{3}$

Coordinates (Square)

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

$(3,2),(6,5),(0,5)$

(3,8)

Negative Numbers

a) 5 − 14 = -9
b) 5 × (-10) = -50
c) (11−22)(12−24) = 132
d) 50 ÷ (-10) = -5
e) (-11)² = 121

Substitution

If p = 5, q = 20 and
r = -7 evaluate:

a) 2q − p = 35
b) pq + r = 93
c) p² − 5q - r = -68

Equations (Type 1)

Solve:

$4x = 20$

$x = 5$

Equations (Type 2)

Solve:

$2x -8= 4$

$x = 6$

Equations (Type 3)

Solve:

$6x -5= 5x + 0$

$x = 5$

Equations (Type 4)

Solve:

$5(4x -6)+11= 101$

$x = 6$

Equations (Type 5)

Solve:

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

$x = -0.75$

Equations (Simultaneous 1)

Solve:

$2x-3y = 3$
$3x-3y = 9$

$x = 6, y = 3$

Equations (Simultaneous 2)

Solve:

$3x+2y = 25$
$6x+8y = 70$

$x = 5, y = 5$

Equations (Simultaneous 3)

Solve:

$3x-2y = -1$
$5x+7y = -43$

$x = -3, y = -4$

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

{5,6,7,8,9,10} and
{3,6,9,12,15}

{6,9}

Bearings

A plane flies from point A to point B on a bearing of 310^o. What bearing would it return on from B to A? 130^o

Probability

A number is picked at random from the set

{2,3,5,7,11,13}

what is the probability it is even? $\frac16$

BIDMAS

Evaluate:

7 + (2 × 6² − 6)

73

Simplify

Simplify the following by collecting like terms:

$3y+2w+7y$

$10y+2w$

Ratio

Divide 150 in the ratio

1:9

15 and 135

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=-2x+1$

Gradient -2
y intercept 1

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 £13 after a 35% reduction. What was the original price?

£20

Averages

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

2,6,12,6,14

Mean = 8, mode = 6,
median = 6 and range = 12

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.

0.444444... $\frac{4}{9}$

Percentage (Decrease)

Decrease £20 by 45%

£11

Brackets (Linear)

Expand:

$8(9x-7)$

$72x-56$

Brackets (Quadratic)

Expand:

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

$3x^2+3x-6$

Factorise (Linear)

Factorise:

$8x-20$

$4(2x-5)$

Factorise (Quadratic 1)

Factorise:

$x^2+x-6$

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

Factorise (Quadratic 2)

Factorise:

$2x^2+3x-2$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

2.39 × 10^-3

= 0.00239

Standard Form 3

Write in standard form:

597000

= 5.97 × 10⁵

Standard Form 4

Write in standard form:

0.0689

= 6.89 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$-3, 7, 21, 39, 61, $

$2n^2+4n-9$

Standard Form 5

Multiply 6 × 10⁵
by 5 × 10⁵ and give the answer in standard form.

= 3 × 10¹¹

Equations (Quadratic 1)

Solve:

$x^2+2x-8= 0$

$x = 2$ and $-4$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.472$ and $-1.27$

Polygon Angles

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

135°

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:

1072 ÷ 2

= 536

Number Sequences 2

What is the 9th:
a) Cube number; 729
b) Triangular number; 45
c) Fibonacci number. 34

Square Numbers

What are the next three square numbers after
1

4, 9, 16

Prime Numbers

What is the difference between the 11th and the 12th prime numbers?

37 - 31 = 6

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: 6, 0.66, 6.6, 0.6, 6.66, 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: 18mm, 1.08m, 107cm, 17cm, 1.8m, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

Write down these capacities: 18cl, 21cl, 17cl, 173ml, 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) 69.39; 70
b) 850242; 900000
c) 52; 50
d) 0.00924; 0.009

Estimation

Round each value to one significant figure to make an estimate:$$6.7 \times 93 - 153$$$7 \times 90 - 200 = 430$

Pie Charts (1)

A pie chart shows the colours of 10 books. What sector angle represents the
6 red books?
216°

Graph Linear (2)

What is the equation?

$x=5$

Pie Charts (2)

A pie chart shows the colours of 180 hats. How many green hats are represented
by a sector
angle of 114°?
57