Refreshing Revision

Number Sequences 1

What is the 12th:
a) Odd number; 23
b) Square number; 144
c) Prime number. 37

Factors

Find all the factors of:

42

1, 2, 3, 6, 7, 14, 21, 42.

Multiples

Subtract the 4th from the 7th multiples of:

8

24

Polygons

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

Equilateral Triangle, Square and Pentagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 46.34; 46.3
b) 366528; 367000
c) 76; 76.0
d) 0.007695; 0.00770

Area of a Triangle

Find the area of a triangle that has a base of 5cm and a height of 10cm.

25cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 12cm, a height of 8cm and a top (parallel to base) of 4cm. 64cm²

Fractions (Adding)

Evaluate:

$ \frac{1}{3} + \frac{5}{8}$ $= \frac{23}{24}$

Fractions (Multiplying)

Evaluate:

$ \frac{3}{4} × \frac{5}{6}$ $= \frac{5}{8}$

Fractions (Dividing)

Evaluate:

$ \frac{1}{2} ÷ \frac{4}{3}$ $= \frac{3}{8}$

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}{5}$ $= 20$%

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 3cm. Give your answer to three significant figures.

18.8cm

Decimals (Adding)

Calculate the value of:

9.8 + 2.7

= 12.5

Decimals (Subtracting)

Calculate the value of:

7.4 − 3.8

= 3.6

Decimals (Multiplying)

Calculate the value of:

8.2 × 5.9

= 48.38

Decimals (Dividing)

Calculate the value of:

159.6 ÷ 19

= 8.4

Indices (Simple)

What is the value of:

4³

= 64

Indices (Advanced)

What is the value of:

$2^{-1}$

$= \frac{1}{2}$

Basic Addition

Calculate the value of:

96 + 97

= 193

Basic Subtraction

Calculate the value of:

84 − 26

= 58

Basic Multiplication

Calculate the value of:

26 × 85

= 2210

Basic Division 2

Calculate the value of:

630 ÷ 14

= 45

Percentage (Of)

Find the value of:

35% of 300

= 105

Standard Form 1

Find the value of:

8.71 × 10⁵

= 871000

Highest Common Factor

Find the highest common factor of fourteen and four.

= 2

Times Tables (2-5)

3 × 2 = 6	4 × 4 = 16
9 × 2 = 18	8 × 3 = 24
6 × 4 = 24	5 × 4 = 20
7 × 3 = 21	2 × 3 = 6

Times Tables (2-12)

5 × 9 = 45	4 × 2 = 8
9 × 10 = 90	6 × 2 = 12
3 × 11 = 33	8 × 7 = 56
7 × 5 = 35	2 × 5 = 10

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{20}{32}$ $= \frac{5}{8}$

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find BC if AB = 3.7m and AC = 5.5m. 6.63m

Trigonometry (Angle)

Find angle BCA if AC = 5.6m and BC = 7.3m. 39.9^o

Trigonometry (Side)

Find AC if angle ABC = 49^o and BC = 6m. 4.53m

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{3}{8}$ $= 0.375$

Decimal to Fraction

Convert this decimal to a fraction.

$0.48$ = $ \frac{12}{25}$

Percentage (Increase)

Increase £160 by 30%

£208

Lowest Common Multiple

What is the lowest common multiple of four and ten.

= 20

Sequence (Arithmetic)

2,7,12,17,22...

Find the:
a) next term; 27
b) n^th term; 5n - 3
c) term number 30; 147

Sequence (Geometric)

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

Find the:
a) next term; 6144
b) n^th term; 6 × 4^n-1
c) term number 10; 1572864

Interest (Simple)

If £200 is invested for 7 years with a simple interest rate of 3%, find the amount of interest earned. £42.00

Interest (Compound)

If £120 is invested with an interest rate of 5% compounded annually, find the value of the investment after 4 years. £145.86

Currency Exchange

If £1 is worth $1.25, convert:

a) £180 to dollars; $225.00

b) $200 to pounds; £160.00

Coordinates (Midpoint)

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

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

(0,-4)

Gradient

What is the gradient of the line joining:

$(2,6) \text{ and } (8,12)$

1

Coordinates (Square)

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

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

(3,13)

Negative Numbers

a) 9 − 21 = -12
b) 9 × (-10) = -90
c) (5−11)(10−15) = 30
d) 90 ÷ (-10) = -9
e) (-8)² = 64

Substitution

If p = 6, q = 26 and
r = -5 evaluate:

a) 2q − p = 46
b) pq + r = 151
c) p² − 5q - r = -89

Equations (Type 1)

Solve:

$3x = 9$

$x = 3$

Equations (Type 2)

Solve:

$2x -2= 6$

$x = 4$

Equations (Type 3)

Solve:

$6x +5= 3x + 32$

$x = 9$

Equations (Type 4)

Solve:

$4(2x +4)-5= 43$

$x = 4$

Equations (Type 5)

Solve:

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

$x = 0.4$

Equations (Simultaneous 1)

Solve:

$5x-2y = 25$
$4x-2y = 18$

$x = 7, y = 5$

Equations (Simultaneous 2)

Solve:

$3x-2y = -1$
$5x-8y = -25$

$x = 3, y = 5$

Equations (Simultaneous 3)

Solve:

$3x-2y = -46.5$
$5x-7y = -110.5$

$x = -9.5, y = 9$

Sets (Union)

Find the union of:

{1,3,5,7,9} and
{2,6,12}

{1,2,3,5,6,7,9,12}

Sets (Intersection)

Find the intersection of:

{1,3,5,7,9} and
{2,6,12}

∅

Bearings

A plane flies from point A to point B on a bearing of 185^o. What bearing would it return on from B to A? 005^o

Probability

A number is picked at random from the set

{1,2,3,4,5}

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

BIDMAS

Evaluate:

5² − 7 × 6 + 4

-13

Simplify

Simplify the following by collecting like terms:

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

$11b+9c$

Ratio

Divide 110 in the ratio

9:1

99 and 11

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:

360

2 x 2 x 2 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £33 after a 45% reduction. What was the original price?

£60

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.

0.141414... $\frac{14}{99}$

Percentage (Decrease)

Decrease £160 by 45%

£88

Brackets (Linear)

Expand:

$5(3x-8)$

$15x-40$

Brackets (Quadratic)

Expand:

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

$8x^2+2x-6$

Factorise (Linear)

Factorise:

$63x-49$

$7(9x-7)$

Factorise (Quadratic 1)

Factorise:

$x^2+2x-3$

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

Factorise (Quadratic 2)

Factorise:

$3x^2+4x-4$

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

5.81 × 10^-2

= 0.0581

Standard Form 3

Write in standard form:

1200

= 1.2 × 10³

Standard Form 4

Write in standard form:

0.000837

= 8.37 × 10^-4

Sequence (Quadratic)

Find the n^th term:

$3, 13, 29, 51, 79, $

$3n^2+n-1$

Standard Form 5

Multiply 4 × 10⁵
by 5 × 10⁶ and give the answer in standard form.

= 2 × 10¹²

Equations (Quadratic 1)

Solve:

$x^2+x-6= 0$

$x = 2$ and $-3$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

$x = 1.72$ and $-0.387$

Polygon Angles

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

140°

Change The Subject

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

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

Basic Division 1

Calculate the value of:

2715 ÷ 3

= 905

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

64

8

Prime Numbers

What is the difference between the 6th and the 7th prime numbers?

17 - 13 = 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, 7.7, 7.07, 7, 7.77, 0.77, 0.07, in ascending order.
0.07, 0.7, 0.77, 7, 7.07, 7.7, 7.77,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

Angle diagram a = 48

Angles with Parallels 2

Angle diagram g = 122

Rounding (1sf)

Round to one significant figure:
a) 49.76; 50
b) 419844; 400000
c) 21; 20
d) 0.00584; 0.006

Estimation

Round each value to one significant figure to make an estimate:$$9.5 \times 61 - 182$$$10 \times 60 - 200 = 400$

Pie Charts (1)

A pie chart shows the colours of 180 books. What sector angle represents the
21 red books?
42°

Graph Linear (2)

What is the equation?

$y=4-0.5x$

Pie Charts (2)

A pie chart shows the colours of 120 hats. How many green hats are represented
by a sector
angle of 348°?
116

Surds (1)

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

Surds (2)

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

Surds (3)

Simplify:
$$\dfrac{5}{3 - \sqrt{2}}$$$\frac{15 + 5\sqrt{2}}{7}$