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:

48

1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Multiples

Subtract the 7th from the 10th multiples of:

11

33

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) 17.75; 17.8
b) 848597; 849000
c) 95; 95.0
d) 0.009595; 0.00960

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 7cm.

14cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 9cm and a top (parallel to base) of 3cm. 63cm²

Fractions (Adding)

Evaluate:

$ \frac{3}{5} + \frac{7}{9}$ $= 1\frac{17}{45}$

Fractions (Multiplying)

Evaluate:

$ \frac{3}{5} × \frac{6}{7}$ $= \frac{18}{35}$

Fractions (Dividing)

Evaluate:

$ \frac{1}{3} ÷ \frac{5}{4}$ $= \frac{4}{15}$

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{4}{8}$ $= 50$%

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 11cm. Give your answer to three significant figures.

69.1cm

Decimals (Adding)

Calculate the value of:

5.8 + 8.5

= 14.3

Decimals (Subtracting)

Calculate the value of:

7.3 − 4.9

= 2.4

Decimals (Multiplying)

Calculate the value of:

4.8 × 6.5

= 31.2

Decimals (Dividing)

Calculate the value of:

46.8 ÷ 12

= 3.9

Indices (Simple)

What is the value of:

5³

= 125

Indices (Advanced)

What is the value of:

$3^{-2}$

$= \frac{1}{9}$

Basic Addition

Calculate the value of:

75 + 59

= 134

Basic Subtraction

Calculate the value of:

94 − 29

= 65

Basic Multiplication

Calculate the value of:

57 × 49

= 2793

Basic Division 2

Calculate the value of:

1134 ÷ 27

= 42

Percentage (Of)

Find the value of:

60% of 80

= 48

Standard Form 1

Find the value of:

4.57 × 10⁶

= 4570000

Highest Common Factor

Find the highest common factor of forty and twenty.

= 20

Times Tables (2-5)

8 × 3 = 24	6 × 4 = 24
7 × 5 = 35	3 × 3 = 9
9 × 4 = 36	5 × 2 = 10
4 × 2 = 8	2 × 4 = 8

Times Tables (2-12)

5 × 8 = 40	4 × 5 = 20
6 × 2 = 12	3 × 10 = 30
7 × 5 = 35	9 × 7 = 63
8 × 12 = 96	2 × 6 = 12

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

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

Fractions (Mixed)

Evaluate:

$ 2\frac{4}{5} − \frac{8}{9}$ $= 1\frac{41}{45}$

Pythagoras

Find BC if AB = 4.7m and AC = 6.5m. 8.02m

Trigonometry (Angle)

Find angle BCA if AB = 5.7m and AC = 6.7m. 40.4^o

Trigonometry (Side)

Find AB if angle ABC = 66^o and BC = 5.6m. 2.28m

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{1}{2}$ $= 0.5$

Decimal to Fraction

Convert this decimal to a fraction.

$0.33$ = $ \frac{33}{100}$

Percentage (Increase)

Increase £40 by 40%

£56

Lowest Common Multiple

What is the lowest common multiple of twenty and thirty.

= 60

Sequence (Arithmetic)

5,14,23,32,41...

Find the:
a) next term; 50
b) n^th term; 9n - 4
c) term number 47; 419

Sequence (Geometric)

6,24,96,384,1536...

Find the:
a) next term; 6144
b) n^th term; 6 × 4^n-1
c) term number 12; 25165824

Interest (Simple)

If £200 is invested for 6 years with a simple interest rate of 4%, find the amount of interest earned. £48.00

Interest (Compound)

If £220 is invested with an interest rate of 1% compounded annually, find the value of the investment after 8 years. £238.23

Currency Exchange

If £1 is worth $1.23, convert:

a) £240 to dollars; $295.20

b) $240 to pounds; £195.12

Coordinates (Midpoint)

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

$(-1,0) \text{ and } (9,12)$

(4,6)

Gradient

What is the gradient of the line joining:

$(-7,2) \text{ and } (-4,8)$

2

Coordinates (Square)

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

$(2,2),(5,5),(-1,5)$

(2,8)

Negative Numbers

a) 5 − 11 = -6
b) 5 × (-9) = -45
c) (9−21)(9−16) = 84
d) 45 ÷ (-9) = -5
e) (-8)² = 64

Substitution

If p = 6, q = 17 and
r = -6 evaluate:

a) 2q − p = 28
b) pq + r = 96
c) p² − 5q - r = -43

Equations (Type 1)

Solve:

$2x = 4$

$x = 2$

Equations (Type 2)

Solve:

$5x +4= 14$

$x = 2$

Equations (Type 3)

Solve:

$3x +5= 2x + 11$

$x = 6$

Equations (Type 4)

Solve:

$2(3x +6)+9= 63$

$x = 7$

Equations (Type 5)

Solve:

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

$x = 0.2$

Equations (Simultaneous 1)

Solve:

$3x-3y = -6$
$2x+3y = 31$

$x = 5, y = 7$

Equations (Simultaneous 2)

Solve:

$3x-3y = 0$
$7x-12y = -15$

$x = 3, y = 3$

Equations (Simultaneous 3)

Solve:

$2x+7y = -30$
$5x+3y = -31.5$

$x = -4.5, y = -3$

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:

{5,6,7,8,9,10} and
{1,3,6,10,15}

{6,10}

Bearings

A plane flies from point A to point B on a bearing of 089^o. What bearing would it return on from B to A? 269^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:

3 + 4 × 8 − 4

31

Simplify

Simplify the following by collecting like terms:

$3a+5b-3a+4b^2$

$5b+4b^2$

Ratio

Divide 48 in the ratio

3:1

36 and 12

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:

120

2 x 2 x 2 x 3 x 5

Percentage (Reverse)

In a sale an item costs £152 after a 5% reduction. What was the original price?

£160

Averages

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

1,3,1,10,5

Mean = 4, mode = 1,
median = 3 and range = 9

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.

0.626262... $\frac{62}{99}$

Percentage (Decrease)

Decrease £60 by 15%

£51

Brackets (Linear)

Expand:

$6(7x-6)$

$42x-36$

Brackets (Quadratic)

Expand:

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

$4x^2-8x-12$

Factorise (Linear)

Factorise:

$16x-20$

$4(4x-5)$

Factorise (Quadratic 1)

Factorise:

$x^2-x-12$

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

Factorise (Quadratic 2)

Factorise:

$5x^2+6x-8$

$(x+2)(5x-4)$

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

8.28 × 10^-3

= 0.00828

Standard Form 3

Write in standard form:

9540

= 9.54 × 10³

Standard Form 4

Write in standard form:

0.0292

= 2.92 × 10^-2

Sequence (Quadratic)

Find the n^th term:

$10, 23, 42, 67, 98, $

$3n^2+4n+3$

Standard Form 5

Multiply 6 × 10²
by 5 × 10⁴ and give the answer in standard form.

= 3 × 10⁷

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:

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

$x = 0.643$ and $-1.24$

Polygon Angles

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

144°

Change The Subject

Make $e$ the subject of the formula
$$f=g(e+h)$$

$$e=\frac{f}{g}-h$$

Basic Division 1

Calculate the value of:

3892 ÷ 4

= 973

Number Sequences 2

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

Square Numbers

What is the difference between the 5th and the 6th square numbers?

11

Prime Numbers

What is the 4th prime number?

7

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, 0.6, 6.06, 6.66, 6.6, 0.06, in ascending order.
0.06, 0.6, 0.66, 6, 6.06, 6.6, 6.66,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram b = 52

Angles with Parallels 2

Angle diagram c = 78

Rounding (1sf)

Round to one significant figure:
a) 95.26; 100
b) 881198; 900000
c) 66; 70
d) 0.00932; 0.009

Estimation

Round each value to one significant figure to make an estimate:$$(154 + 5.9) \div 19$$$(200 + 6) \div 20 = 10.3$

Pie Charts (1)

A pie chart shows the colours of 10 books. What sector angle represents the
4 red books?
144°

Graph Linear (2)

What is the equation?

$y=x-4$

Pie Charts (2)

A pie chart shows the colours of 60 hats. How many green hats are represented
by a sector
angle of 186°?
31

Surds (1)

Simplify:
$$\sqrt{18}$$
$3\sqrt{2}$

Surds (2)

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

Surds (3)

Simplify:
$$\dfrac{7}{4 + \sqrt{3}}$$$\frac{28 - 7\sqrt{3}}{13}$