Refreshing Revision

Number Sequences 1

What is the 11th:
a) Odd number; 21
b) Square number; 121
c) Prime number. 31

Factors

Find all the factors of:

27

1, 3, 9, 27.

Multiples

Subtract the 4th from the 9th multiples of:

3

15

Polygons

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

Heptagon, Octagon and Nonagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 95.01; 95.0
b) 503613; 504000
c) 94; 94.0
d) 0.009495; 0.00950

Area of a Triangle

Find the area of a triangle that has a base of 7cm and a height of 12cm.

42cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 9cm, a height of 7cm and a top (parallel to base) of 3cm. 42cm²

Fractions (Adding)

Evaluate:

$ \frac{2}{3} + \frac{5}{7}$ $= 1\frac{8}{21}$

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

$ \frac{3}{4} ÷ \frac{7}{5}$ $= \frac{15}{28}$

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{3}{6}$ $= 50$%

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 9cm. Give your answer to three significant figures.

56.5cm

Decimals (Adding)

Calculate the value of:

8.6 + 2.8

= 11.4

Decimals (Subtracting)

Calculate the value of:

5.4 − 3.6

= 1.8

Decimals (Multiplying)

Calculate the value of:

9.4 × 9.2

= 86.48

Decimals (Dividing)

Calculate the value of:

32.2 ÷ 14

= 2.3

Indices (Simple)

What is the value of:

1²

= 1

Indices (Advanced)

What is the value of:

$2^{-1}$

$= \frac{1}{2}$

Basic Addition

Calculate the value of:

69 + 58

= 127

Basic Subtraction

Calculate the value of:

51 − 29

= 22

Basic Multiplication

Calculate the value of:

97 × 37

= 3589

Basic Division 2

Calculate the value of:

1131 ÷ 13

= 87

Percentage (Of)

Find the value of:

95% of 80

= 76

Standard Form 1

Find the value of:

8.38 × 10⁴

= 83800

Highest Common Factor

Find the highest common factor of forty five and fifteen.

= 15

Times Tables (2-5)

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

Times Tables (2-12)

6 × 10 = 60	9 × 11 = 99
3 × 8 = 24	4 × 7 = 28
8 × 2 = 16	5 × 12 = 60
7 × 3 = 21	2 × 8 = 16

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

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

Fractions (Mixed)

Evaluate:

$ 2\frac{2}{3} − \frac{4}{5}$ $= 1\frac{13}{15}$

Pythagoras

Find BC if AB = 4.1m and AC = 5.2m. 6.62m

Trigonometry (Angle)

Find angle BCA if AC = 4.4m and BC = 5.7m. 39.5^o

Trigonometry (Side)

Find AB if angle ABC = 40^o and BC = 4.4m. 3.37m

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{4}{5}$ $= 0.8$

Decimal to Fraction

Convert this decimal to a fraction.

$0.6$ = $ \frac{3}{5}$

Percentage (Increase)

Increase £60 by 40%

£84

Lowest Common Multiple

What is the lowest common multiple of twelve and twenty.

= 60

Sequence (Arithmetic)

6,15,24,33,42...

Find the:
a) next term; 51
b) n^th term; 9n - 3
c) term number 34; 303

Sequence (Geometric)

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

Find the:
a) next term; 1458
b) n^th term; 6 × 3^n-1
c) term number 8; 13122

Interest (Simple)

If £180 is invested for 5 years with a simple interest rate of 5%, find the amount of interest earned. £45.00

Interest (Compound)

If £100 is invested with an interest rate of 1% compounded annually, find the value of the investment after 7 years. £107.21

Currency Exchange

If £1 is worth $1.21, convert:

a) £120 to dollars; $145.20

b) $160 to pounds; £132.23

Coordinates (Midpoint)

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

$(3,-7) \text{ and } (15,1)$

(9,-3)

Gradient

What is the gradient of the line joining:

$(8,5) \text{ and } (11,9)$

$\frac{4}{3}$

Coordinates (Square)

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

$(1,5),(7,9),(-3,11)$

(3,15)

Negative Numbers

a) 11 − 22 = -11
b) 11 × (-10) = -110
c) (6−17)(6−15) = 99
d) 110 ÷ (-10) = -11
e) (-6)² = 36

Substitution

If p = 6, q = 27 and
r = -8 evaluate:

a) 2q − p = 48
b) pq + r = 154
c) p² − 5q - r = -91

Equations (Type 1)

Solve:

$3x = 21$

$x = 7$

Equations (Type 2)

Solve:

$4x +8= 24$

$x = 4$

Equations (Type 3)

Solve:

$4x +6= 2x + 18$

$x = 6$

Equations (Type 4)

Solve:

$5(4x +6)-6= 184$

$x = 8$

Equations (Type 5)

Solve:

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

$x = 0.357 \text{(to 3 sf)}$

Equations (Simultaneous 1)

Solve:

$5x-2y = 10$
$3x-2y = 2$

$x = 4, y = 5$

Equations (Simultaneous 2)

Solve:

$4x+2y = 16$
$5x-8y = -22$

$x = 2, y = 4$

Equations (Simultaneous 3)

Solve:

$5x+3y = -14.5$
$3x-2y = -3$

$x = -2, y = -1.5$

Sets (Union)

Find the union of:

{5,6,7,8,9,10} and
{2,6,12}

{2,5,6,7,8,9,10,12}

Sets (Intersection)

Find the intersection of:

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

{7,9}

Bearings

A plane flies from point A to point B on a bearing of 031^o. What bearing would it return on from B to A? 211^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:

8 ÷ 4 × 28 ÷ 4

14

Simplify

Simplify the following by collecting like terms:

$3x+5x^2-8x+x^2$

$6x^2-5x$

Ratio

Divide 25 in the ratio

4:1

20 and 5

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:

6

2 x 3

Percentage (Reverse)

In a sale an item costs £14 after a 30% reduction. What was the original price?

£20

Averages

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

5,8,8,6,7,8

Mean = 7, mode = 8,
median = 7.5 and range = 3

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.

0.181818... $\frac{2}{11}$

Percentage (Decrease)

Decrease £180 by 5%

£171

Brackets (Linear)

Expand:

$3(3x-3)$

$9x-9$

Brackets (Quadratic)

Expand:

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

$6x^2-6$

Factorise (Linear)

Factorise:

$4x-18$

$2(2x-9)$

Factorise (Quadratic 1)

Factorise:

$x^2-16$

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

Factorise (Quadratic 2)

Factorise:

$15x^2+2x-1$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

3.49 × 10^-2

= 0.0349

Standard Form 3

Write in standard form:

8910

= 8.91 × 10³

Standard Form 4

Write in standard form:

0.00643

= 6.43 × 10^-3

Sequence (Quadratic)

Find the n^th term:

$8, 16, 28, 44, 64, $

$2n^2+2n+4$

Standard Form 5

Multiply 4 × 10²
by 5 × 10⁴ and give the answer in standard form.

= 2 × 10⁷

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:

$3x^2-5x+1 = 0$

$x = 1.43$ and $0.232$

Polygon Angles

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

135°

Change The Subject

Make $k$ the subject of the formula
$$c=\frac{a(2+k)}{b}$$

$$k=\frac{bc}{a}-2$$

Basic Division 1

Calculate the value of:

1635 ÷ 3

= 545

Number Sequences 2

What is the 11th:
a) Cube number; 1331
b) Triangular number; 66
c) Fibonacci number. 89

Square Numbers

What is the difference between the 9th and the 10th square numbers?

19

Prime Numbers

What is the difference between the 4th and the 5th prime numbers?

11 - 7 = 4

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

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram c = 81

Angles with Parallels 2

Angle diagram j = 58

Rounding (1sf)

Round to one significant figure:
a) 46.95; 50
b) 262842; 300000
c) 20; 20
d) 0.00947; 0.009

Estimation

Round each value to one significant figure to make an estimate:$$91 + 9.9 \times 31$$$90 + 10 \times 30 = 390$

Pie Charts (1)

A pie chart shows the colours of 12 books. What sector angle represents the
9 red books?
270°

Graph Linear (2)

What is the equation?

$y=2x+2$

Pie Charts (2)

A pie chart shows the colours of 72 hats. How many green hats are represented
by a sector
angle of 330°?
66

Surds (1)

Simplify:
$$\sqrt{20}$$
$2\sqrt{5}$

Surds (2)

Simplify:
$$\dfrac{7}{\sqrt{5}}$$$\frac{7\sqrt{5}}{5}$

Surds (3)

Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$$\frac{30 - 6\sqrt{2}}{23}$