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:

38

1, 2, 19, 38.

Multiples

Subtract the 6th from the 10th multiples of:

11

44

Polygons

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

Square, Pentagon and Hexagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 40.86; 40.9
b) 678065; 678000
c) 84; 84.0
d) 0.008495; 0.00850

Area of a Triangle

Find the area of a triangle that has a base of 7cm and a height of 10cm.

35cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 12cm and a top (parallel to base) of 5cm. 96cm²

Fractions (Adding)

Evaluate:

$ \frac{1}{3} + \frac{6}{7}$ $= 1\frac{4}{21}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{2} × \frac{3}{5}$ $= \frac{3}{10}$

Fractions (Dividing)

Evaluate:

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

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{1}{4}$ $= 25$%

Circle Area

Find the area of a circle that has a radius of 2cm. Give your answer to three significant figures.

12.6cm²

Circle Circumference

Find the circumference of a circle that has a radius of 8cm. Give your answer to three significant figures.

50.3cm

Decimals (Adding)

Calculate the value of:

4.6 + 9.9

= 14.5

Decimals (Subtracting)

Calculate the value of:

6.2 − 1.7

= 4.5

Decimals (Multiplying)

Calculate the value of:

7.7 × 9.4

= 72.38

Decimals (Dividing)

Calculate the value of:

139.2 ÷ 16

= 8.7

Indices (Simple)

What is the value of:

5³

= 125

Indices (Advanced)

What is the value of:

$1^{0}$

$= 1$

Basic Addition

Calculate the value of:

97 + 77

= 174

Basic Subtraction

Calculate the value of:

54 − 28

= 26

Basic Multiplication

Calculate the value of:

52 × 99

= 5148

Basic Division 2

Calculate the value of:

792 ÷ 12

= 66

Percentage (Of)

Find the value of:

45% of 180

= 81

Standard Form 1

Find the value of:

8.11 × 10⁶

= 8110000

Highest Common Factor

Find the highest common factor of forty and twenty five.

= 5

Times Tables (2-5)

5 × 5 = 25	8 × 3 = 24
4 × 4 = 16	3 × 4 = 12
7 × 2 = 14	6 × 5 = 30
9 × 5 = 45	2 × 2 = 4

Times Tables (2-12)

5 × 2 = 10	8 × 2 = 16
6 × 7 = 42	4 × 8 = 32
9 × 4 = 36	7 × 2 = 14
3 × 12 = 36	2 × 8 = 16

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{16}{40}$ $= \frac{2}{5}$

Fractions (Mixed)

Evaluate:

$ 1\frac{3}{4} − \frac{5}{6}$ $= \frac{11}{12}$

Pythagoras

Find BC if AB = 4.1m and AC = 5.3m. 6.70m

Trigonometry (Angle)

Find angle BCA if AB = 4.8m and AC = 6.3m. 37.3^o

Trigonometry (Side)

Find BC if angle BCA = 22^o and AB = 5.9m. 15.7m

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{5}{7}$ $= 0.714$

Decimal to Fraction

Convert this decimal to a fraction.

$0.88$ = $ \frac{22}{25}$

Percentage (Increase)

Increase £160 by 40%

£224

Lowest Common Multiple

What is the lowest common multiple of sixteen and twenty four.

= 48

Sequence (Arithmetic)

3,13,23,33,43...

Find the:
a) next term; 53
b) n^th term; 10n - 7
c) term number 31; 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 11; 354294

Interest (Simple)

If £140 is invested for 5 years with a simple interest rate of 1%, find the amount of interest earned. £7.00

Interest (Compound)

If £100 is invested with an interest rate of 4% compounded annually, find the value of the investment after 7 years. £131.59

Currency Exchange

If £1 is worth $1.27, convert:

a) £160 to dollars; $203.20

b) $100 to pounds; £78.74

Coordinates (Midpoint)

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

$(1,2) \text{ and } (9,14)$

(5,8)

Gradient

What is the gradient of the line joining:

$(-1,6) \text{ and } (2,11)$

$\frac{5}{3}$

Coordinates (Square)

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

$(2,4),(5,8),(-2,7)$

(1,11)

Negative Numbers

a) 7 − 18 = -11
b) 7 × (-11) = -77
c) (7−15)(8−19) = 88
d) 77 ÷ (-11) = -7
e) (-6)² = 36

Substitution

If p = 5, q = 24 and
r = -6 evaluate:

a) 2q − p = 43
b) pq + r = 114
c) p² − 5q - r = -89

Equations (Type 1)

Solve:

$5x = 40$

$x = 8$

Equations (Type 2)

Solve:

$2x +6= 22$

$x = 8$

Equations (Type 3)

Solve:

$6x -5= 2x + 31$

$x = 9$

Equations (Type 4)

Solve:

$3(2x -5)-7= 8$

$x = 5$

Equations (Type 5)

Solve:

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

$x = 2.5$

Equations (Simultaneous 1)

Solve:

$2x+3y = 18$
$3x-3y = 12$

$x = 6, y = 2$

Equations (Simultaneous 2)

Solve:

$3x+4y = 26$
$7x-8y = -26$

$x = 2, y = 5$

Equations (Simultaneous 3)

Solve:

$3x-3y = -6$
$7x+2y = -72.5$

$x = -8.5, y = -6.5$

Sets (Union)

Find the union of:

{1,2,3,4,5} and
{6,7,8,9,10}

{1,2,3,4,5,6,7,8,9,10}

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 083^o. What bearing would it return on from B to A? 263^o

Probability

A number is picked at random from the set

{2,6,12}

what is the probability it is even? 1

BIDMAS

Evaluate:

9 + (9 × 7² − 2)

448

Simplify

Simplify the following by collecting like terms:

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

$11b+9c$

Ratio

Divide 170 in the ratio

9:8

90 and 80

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:

90

2 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £104 after a 35% reduction. What was the original price?

£160

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.

0.151515... $\frac{5}{33}$

Percentage (Decrease)

Decrease £40 by 20%

£32

Brackets (Linear)

Expand:

$3(2x-5)$

$6x-15$

Brackets (Quadratic)

Expand:

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

$6x^2+2x-8$

Factorise (Linear)

Factorise:

$36x-42$

$6(6x-7)$

Factorise (Quadratic 1)

Factorise:

$x^2-2x-8$

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

Factorise (Quadratic 2)

Factorise:

$2x^2+3x-2$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

1.52 × 10^-4

= 0.000152

Standard Form 3

Write in standard form:

620000

= 6.2 × 10⁵

Standard Form 4

Write in standard form:

0.0141

= 1.41 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$2, 8, 16, 26, 38, $

$n^2+3n-2$

Standard Form 5

Multiply 8 × 10³
by 6 × 10⁴ and give the answer in standard form.

= 4.8 × 10⁸

Equations (Quadratic 1)

Solve:

$x^2-x-6= 0$

$x = 3$ and $-2$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = -0.232$ and $-1.43$

Polygon Angles

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

128.6°

Change The Subject

Make $d$ the subject of the formula
$$e=\frac{2d-1}{3}$$

$$d=\frac{3e+1}{2}$$

Basic Division 1

Calculate the value of:

633 ÷ 3

= 211

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

144

12

Prime Numbers

What are the three largest prime numbers less than
29

23, 19, 17

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: 9.99, 0.99, 0.9, 9.9, 9.09, 9, 0.09, in ascending order.
0.09, 0.9, 0.99, 9, 9.09, 9.9, 9.99,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram d = 99

Angles with Parallels 2

Angle diagram b = 48

Rounding (1sf)

Round to one significant figure:
a) 45.32; 50
b) 387390; 400000
c) 81; 80
d) 0.00480; 0.005

Estimation

Round each value to one significant figure to make an estimate:$$(164 + 9.6) \div 17$$$(200 + 10) \div 20 = 10.5$

Pie Charts (1)

A pie chart shows the colours of 45 books. What sector angle represents the
39 red books?
312°

Graph Linear (2)

What is the equation?

$y=0.5x+3$

Pie Charts (2)

A pie chart shows the colours of 90 hats. How many green hats are represented
by a sector
angle of 52°?
13

Surds (1)

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

Surds (2)

Simplify:
$$\dfrac{9}{\sqrt{6}}$$$\frac{9\sqrt{6}}{6} = \frac{3\sqrt{6}}{2}$

Surds (3)

Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$$\frac{21 + 3\sqrt{2}}{47}$