Refreshing Revision

Number Sequences 1

What is the 8th:
a) Odd number; 15
b) Square number; 64
c) Prime number. 19

Factors

Find all the factors of:

40

1, 2, 4, 5, 8, 10, 20, 40.

Multiples

Subtract the 4th from the 7th multiples of:

8

24

Polygons

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

Pentagon, Hexagon and Heptagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 25.15; 25.2
b) 907652; 908000
c) 36; 36.0
d) 0.003695; 0.00370

Area of a Triangle

Find the area of a triangle that has a base of 7cm and a height of 11cm.

38.5cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 8cm and a top (parallel to base) of 3cm. 56cm²

Fractions (Adding)

Evaluate:

$ \frac{2}{4} + \frac{6}{8}$ $= 1\frac{1}{4}$

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

$ \frac{2}{3} ÷ \frac{6}{4}$ $= \frac{4}{9}$

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{2}{7}$ $= 28.6$%

Circle Area

Find the area of a circle that has a radius of 4cm. Give your answer to three significant figures.

50.3cm²

Circle Circumference

Find the circumference of a circle that has a radius of 12cm. Give your answer to three significant figures.

75.4cm

Decimals (Adding)

Calculate the value of:

2.6 + 9.7

= 12.3

Decimals (Subtracting)

Calculate the value of:

7.3 − 2.5

= 4.8

Decimals (Multiplying)

Calculate the value of:

3.8 × 5.8

= 22.04

Decimals (Dividing)

Calculate the value of:

95.4 ÷ 18

= 5.3

Indices (Simple)

What is the value of:

5²

= 25

Indices (Advanced)

What is the value of:

$4^{-1}$

$= \frac{1}{4}$

Basic Addition

Calculate the value of:

97 + 35

= 132

Basic Subtraction

Calculate the value of:

72 − 25

= 47

Basic Multiplication

Calculate the value of:

73 × 89

= 6497

Basic Division 2

Calculate the value of:

1274 ÷ 26

= 49

Percentage (Of)

Find the value of:

80% of 280

= 224

Standard Form 1

Find the value of:

9.4 × 10⁵

= 940000

Highest Common Factor

Find the highest common factor of twenty four and twelve.

= 12

Times Tables (2-5)

3 × 4 = 12	8 × 2 = 16
4 × 2 = 8	6 × 5 = 30
9 × 4 = 36	7 × 3 = 21
5 × 4 = 20	2 × 5 = 10

Times Tables (2-12)

4 × 9 = 36	6 × 11 = 66
5 × 8 = 40	7 × 5 = 35
9 × 5 = 45	8 × 2 = 16
3 × 12 = 36	2 × 2 = 4

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

5 × 12 = 60	3 × 12 = 36
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{3}{9}$ $= \frac{1}{3}$

Fractions (Mixed)

Evaluate:

$ 1\frac{2}{3} − \frac{6}{7}$ $= \frac{17}{21}$

Pythagoras

Find AC if AB = 3.5m and BC = 5.3m. 3.98m

Trigonometry (Angle)

Find angle BCA if AB = 4.7m and AC = 6.1m. 37.6^o

Trigonometry (Side)

Find AC if angle ABC = 45^o and BC = 4.9m. 3.46m

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.

$0.27$ = $ \frac{27}{100}$

Percentage (Increase)

Increase £140 by 10%

£154

Lowest Common Multiple

What is the lowest common multiple of twelve and twenty.

= 60

Sequence (Arithmetic)

6,14,22,30,38...

Find the:
a) next term; 46
b) n^th term; 8n - 2
c) term number 53; 422

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 £180 is invested for 7 years with a simple interest rate of 6%, find the amount of interest earned. £75.60

Interest (Compound)

If £100 is invested with an interest rate of 3% compounded annually, find the value of the investment after 7 years. £122.99

Currency Exchange

If £1 is worth $1.29, convert:

a) £100 to dollars; $129.00

b) $120 to pounds; £93.02

Coordinates (Midpoint)

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

$(-1,-1) \text{ and } (5,7)$

(2,3)

Gradient

What is the gradient of the line joining:

$(-5,6) \text{ and } (-1,11)$

$\frac{5}{4}$

Coordinates (Square)

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

$(5,5),(10,10),(0,10)$

(5,15)

Negative Numbers

a) 6 − 18 = -12
b) 6 × (-6) = -36
c) (8−16)(11−22) = 88
d) 36 ÷ (-6) = -6
e) (-5)² = 25

Substitution

If p = 5, q = 24 and
r = -8 evaluate:

a) 2q − p = 43
b) pq + r = 112
c) p² − 5q - r = -87

Equations (Type 1)

Solve:

$4x = 24$

$x = 6$

Equations (Type 2)

Solve:

$2x +5= 9$

$x = 2$

Equations (Type 3)

Solve:

$6x -4= 4x + 14$

$x = 9$

Equations (Type 4)

Solve:

$2(2x +4)-8= 32$

$x = 8$

Equations (Type 5)

Solve:

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

$x = -0.667 \text{(to 3 sf)}$

Equations (Simultaneous 1)

Solve:

$4x+5y = 40$
$3x-5y = -5$

$x = 5, y = 4$

Equations (Simultaneous 2)

Solve:

$4x-3y = 6$
$7x-9y = -12$

$x = 6, y = 6$

Equations (Simultaneous 3)

Solve:

$3x+2y = 25$
$5x+7y = 54.5$

$x = 6, y = 3.5$

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:

{2,4,6,8,10} and
{5,6,7,8,9,10}

{6,8,10}

Bearings

A plane flies from point A to point B on a bearing of 313^o. What bearing would it return on from B to A? 133^o

Probability

A number is picked at random from the set

{3,6,9,12,15}

what is the probability it is even? $\frac25$

BIDMAS

Evaluate:

6 + 5 × 8 − 6

40

Simplify

Simplify the following by collecting like terms:

$3y+2w+7y$

$10y+2w$

Ratio

Divide 24 in the ratio

3:1

18 and 6

Graph Linear (1)

Draw a rough sketch of the graph of:

$y=-x-1$

Gradient -1
y intercept -1

Prime Factors

Express the following number as the product of prime numbers:

12

2 x 2 x 3

Percentage (Reverse)

In a sale an item costs £133 after a 5% reduction. What was the original price?

£140

Averages

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

2,4,6,8,10

Mean = 6, no mode,
median = 6 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.

0.969696... $\frac{32}{33}$

Percentage (Decrease)

Decrease £140 by 30%

£98

Brackets (Linear)

Expand:

$3(6x-3)$

$18x-9$

Brackets (Quadratic)

Expand:

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

$2x^2-4x-16$

Factorise (Linear)

Factorise:

$16x-20$

$4(4x-5)$

Factorise (Quadratic 1)

Factorise:

$x^2-2x-3$

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

Factorise (Quadratic 2)

Factorise:

$6x^2+x-1$

$(2x+1)(3x-1)$

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

8.35 × 10^-4

= 0.000835

Standard Form 3

Write in standard form:

404000

= 4.04 × 10⁵

Standard Form 4

Write in standard form:

0.0505

= 5.05 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$8, 13, 20, 29, 40, $

$n^2+2n+5$

Standard Form 5

Multiply 6 × 10³
by 9 × 10⁵ and give the answer in standard form.

= 5.4 × 10⁹

Equations (Quadratic 1)

Solve:

$x^2-x-12= 0$

$x = 4$ and $-3$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 0.554$ and $-1.80$

Polygon Angles

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

45°

Change The Subject

Make $c$ the subject of the formula
$$d=\frac{3c+1}{2}$$

$$c=\frac{2d-1}{3}$$

Basic Division 1

Calculate the value of:

4135 ÷ 5

= 827

Number Sequences 2

What is the 6th:
a) Cube number; 216
b) Triangular number; 21
c) Fibonacci number. 8

Square Numbers

What is the square root of

81

9

Prime Numbers

What is the 6th prime number?

13

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: 5.5, 0.55, 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: 18mm, 1.8m, 1.08m, 17cm, 107cm, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram b = 52

Angles with Parallels 2

Angle diagram i = 97

Rounding (1sf)

Round to one significant figure:
a) 94.55; 90
b) 457798; 500000
c) 47; 50
d) 0.00974; 0.01

Estimation

Round each value to one significant figure to make an estimate:$$(152 + 2.5) \div 17$$$(200 + 3) \div 20 = 10.15$

Pie Charts (1)

A pie chart shows the colours of 120 books. What sector angle represents the
35 red books?
105°

Graph Linear (2)

What is the equation?

$y=0.5x+1$

Pie Charts (2)

A pie chart shows the colours of 6 hats. How many green hats are represented
by a sector
angle of 240°?
4

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}$