Refreshing Revision

Number Sequences 1

What is the 6th:
a) Odd number; 11
b) Square number; 36
c) Prime number. 13

Factors

Find all the factors of:

29

1, 29.

Multiples

Subtract the 4th from the 7th multiples of:

8

24

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) 85.95; 86.0
b) 154180; 154000
c) 84; 84.0
d) 0.008495; 0.00850

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{1}{2} + \frac{5}{7}$ $= 1\frac{3}{14}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{3} × \frac{5}{7}$ $= \frac{5}{21}$

Fractions (Dividing)

Evaluate:

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

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 6cm. Give your answer to three significant figures.

113cm²

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:

6.8 + 6.9

= 13.7

Decimals (Subtracting)

Calculate the value of:

9.1 − 2.9

= 6.2

Decimals (Multiplying)

Calculate the value of:

6.7 × 9.4

= 62.98

Decimals (Dividing)

Calculate the value of:

141.1 ÷ 17

= 8.3

Indices (Simple)

What is the value of:

2³

= 8

Indices (Advanced)

What is the value of:

$25^{\frac{1}{2}}$

$= 5$

Basic Addition

Calculate the value of:

98 + 64

= 162

Basic Subtraction

Calculate the value of:

52 − 26

= 26

Basic Multiplication

Calculate the value of:

94 × 67

= 6298

Basic Division 2

Calculate the value of:

1134 ÷ 27

= 42

Percentage (Of)

Find the value of:

50% of 260

= 130

Standard Form 1

Find the value of:

1.87 × 10³

= 1870

Highest Common Factor

Find the highest common factor of sixteen and four.

= 4

Times Tables (2-5)

3 × 3 = 9	8 × 4 = 32
9 × 5 = 45	4 × 5 = 20
6 × 2 = 12	5 × 3 = 15
7 × 2 = 14	2 × 5 = 10

Times Tables (2-12)

9 × 5 = 45	5 × 2 = 10
3 × 2 = 6	6 × 12 = 72
4 × 5 = 20	7 × 12 = 84
8 × 6 = 48	2 × 11 = 22

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{10}{20}$ $= \frac{1}{2}$

Fractions (Mixed)

Evaluate:

$ 2\frac{1}{2} − \frac{4}{5}$ $= 1\frac{7}{10}$

Pythagoras

Find AB if AC = 4.2m and BC = 5.3m. 3.23m

Trigonometry (Angle)

Find angle ABC if AC = 3.6m and AB = 5m. 35.8^o

Trigonometry (Side)

Find AC if angle ABC = 29^o and BC = 5.3m. 2.57m

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.

$0.1$ = $ \frac{1}{10}$

Percentage (Increase)

Increase £40 by 30%

£52

Lowest Common Multiple

What is the lowest common multiple of six and twenty one.

= 42

Sequence (Arithmetic)

5,15,25,35,45...

Find the:
a) next term; 55
b) n^th term; 10n - 5
c) term number 45; 445

Sequence (Geometric)

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

Find the:
a) next term; 160
b) n^th term; 5 × 2^n-1
c) term number 11; 5120

Interest (Simple)

If £120 is invested for 6 years with a simple interest rate of 6%, find the amount of interest earned. £43.20

Interest (Compound)

If £240 is invested with an interest rate of 1% compounded annually, find the value of the investment after 9 years. £262.48

Currency Exchange

If £1 is worth $1.34, convert:

a) £120 to dollars; $160.80

b) $200 to pounds; £149.25

Coordinates (Midpoint)

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

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

(-3,5)

Gradient

What is the gradient of the line joining:

$(-5,3) \text{ and } (0,8)$

1

Coordinates (Square)

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

$(2,3),(8,8),(-3,9)$

(3,14)

Negative Numbers

a) 6 − 12 = -6
b) 6 × (-8) = -48
c) (10−21)(11−16) = 55
d) 48 ÷ (-8) = -6
e) (-9)² = 81

Substitution

If p = 5, q = 17 and
r = -10 evaluate:

a) 2q − p = 29
b) pq + r = 75
c) p² − 5q - r = -50

Equations (Type 1)

Solve:

$5x = 15$

$x = 3$

Equations (Type 2)

Solve:

$2x -3= 5$

$x = 4$

Equations (Type 3)

Solve:

$6x -4= 4x + 14$

$x = 9$

Equations (Type 4)

Solve:

$2(4x +6)-10= 58$

$x = 7$

Equations (Type 5)

Solve:

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

$x = -6$

Equations (Simultaneous 1)

Solve:

$3x+2y = 18$
$2x+2y = 14$

$x = 4, y = 3$

Equations (Simultaneous 2)

Solve:

$4x-2y = 20$
$7x+4y = 65$

$x = 7, y = 4$

Equations (Simultaneous 3)

Solve:

$3x-3y = -28.5$
$7x-2y = -29$

$x = -2, y = 7.5$

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

{6,7,8,9,10} and
{1,3,6,10,15}

{6,10}

Bearings

A plane flies from point A to point B on a bearing of 131^o. What bearing would it return on from B to A? 311^o

Probability

A number is picked at random from the set

{6,7,8,9,10}

what is the probability it is even? $\frac35$

BIDMAS

Evaluate:

8² − 5 × 7 + 8

37

Simplify

Simplify the following by collecting like terms:

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

$6x^2-5x$

Ratio

Divide 120 in the ratio

6:9

48 and 72

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=x-2$

Gradient 1
y intercept -2

Prime Factors

Express the following number as the product of prime numbers:

90

2 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £17 after a 15% reduction. What was the original price?

£20

Averages

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

1,3,5,7,9

Mean = 5, no mode,
median = 5 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.

0.666666... $\frac{2}{3}$

Percentage (Decrease)

Decrease £140 by 30%

£98

Brackets (Linear)

Expand:

$4(4x-3)$

$16x-12$

Brackets (Quadratic)

Expand:

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

$4x^2-2x-12$

Factorise (Linear)

Factorise:

$28x-35$

$7(4x-5)$

Factorise (Quadratic 1)

Factorise:

$x^2+3x-4$

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

Factorise (Quadratic 2)

Factorise:

$x^2-16$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

3.31 × 10^-3

= 0.00331

Standard Form 3

Write in standard form:

3170000

= 3.17 × 10⁶

Standard Form 4

Write in standard form:

0.000613

= 6.13 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$10, 22, 38, 58, 82, $

$2n^2+6n+2$

Standard Form 5

Multiply 4 × 10⁴
by 4 × 10³ and give the answer in standard form.

= 1.6 × 10⁸

Equations (Quadratic 1)

Solve:

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

$x = 2$ and $-5$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

$2x^2-4x+1 = 0$

$x = 1.71$ and $0.293$

Polygon Angles

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

60°

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:

5544 ÷ 8

= 693

Number Sequences 2

What is the 10th:
a) Cube number; 1000
b) Triangular number; 55
c) Fibonacci number. 55

Square Numbers

What are the next three square numbers after
100

121, 144, 169

Prime Numbers

What is the difference between the 8th and the 9th prime numbers?

23 - 19 = 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: 0.7, 7.77, 7, 7.7, 0.77, 7.07, 0.07, in ascending order.
0.07, 0.7, 0.77, 7, 7.07, 7.7, 7.77,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram f = 132

Angles with Parallels 2

Angle diagram h = 75

Rounding (1sf)

Round to one significant figure:
a) 35.85; 40
b) 509881; 500000
c) 32; 30
d) 0.00555; 0.006

Estimation

Round each value to one significant figure to make an estimate:$$81 + 9.9 \times 64$$$80 + 10 \times 60 = 680$

Pie Charts (1)

A pie chart shows the colours of 10 books. What sector angle represents the
8 red books?
288°

Graph Linear (2)

What is the equation?

$y=x-2$

Pie Charts (2)

A pie chart shows the colours of 24 hats. How many green hats are represented
by a sector
angle of 225°?
15

Surds (1)

Simplify:
$$\sqrt{45}$$
$3\sqrt{5}$

Surds (2)

Simplify:
$$\dfrac{2}{\sqrt{10}}$$$\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}$

Surds (3)

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