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:

28

1, 2, 4, 7, 14, 28.

Multiples

Subtract the 7th from the 11th multiples of:

5

20

Polygons

What are the names of regular polygons with:
a) eight sides;
b) nine sides;
c) ten sides.

Octagon, Nonagon and Decagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 57.22; 57.2
b) 129169; 129000
c) 20; 20.0
d) 0.002095; 0.00210

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 13cm, a height of 10cm and a top (parallel to base) of 7cm. 100cm²

Fractions (Adding)

Evaluate:

\( \frac{3}{6} + \frac{8}{9}\) \(= 1\frac{7}{18}\)

Fractions (Multiplying)

Evaluate:

\( \frac{3}{5} × \frac{7}{8}\) \(= \frac{21}{40}\)

Fractions (Dividing)

Evaluate:

\( \frac{2}{4} ÷ \frac{6}{5}\) \(= \frac{5}{12}\)

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.

\( \frac{5}{10}\) \(= 50\)%

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 6cm. Give your answer to three significant figures.

37.7cm

Decimals (Adding)

Calculate the value of:

3.8 + 6.6

= 10.4

Decimals (Subtracting)

Calculate the value of:

5.1 − 2.9

= 2.2

Decimals (Multiplying)

Calculate the value of:

7.4 × 3.2

= 23.68

Decimals (Dividing)

Calculate the value of:

73.6 ÷ 16

= 4.6

Indices (Simple)

What is the value of:

1³

= 1

Indices (Advanced)

What is the value of:

\(5^{-2}\)

\(= \frac{1}{25}\)

Basic Addition

Calculate the value of:

25 + 58

= 83

Basic Subtraction

Calculate the value of:

54 − 29

= 25

Basic Multiplication

Calculate the value of:

62 × 54

= 3348

Basic Division 2

Calculate the value of:

1386 ÷ 18

= 77

Percentage (Of)

Find the value of:

90% of 60

= 54

Standard Form 1

Find the value of:

7.03 × 10⁵

= 703000

Highest Common Factor

Find the highest common factor of fourteen and eight.

= 2

Times Tables (2-5)

Times Tables (2-12)

Times Tables (2)

Times Tables (3)

Times Tables (4)

Times Tables (5)

Times Tables (6)

Times Tables (7)

Times Tables (8)

Times Tables (9)

Times Tables (12)

Fractions (Equivalent)

Write this fraction in its simplest form:

\( \frac{16}{28}\) \(= \frac{4}{7}\)

Fractions (Mixed)

Evaluate:

\( 2\frac{2}{3} − \frac{5}{6}\) \(= 1\frac{5}{6}\)

Pythagoras

Find AC if AB = 5.6m and BC = 6.8m. 3.86m

Trigonometry (Angle)

Find angle ABC if AC = 3.6m and BC = 5.6m. 40.0^o

Trigonometry (Side)

Find AC if angle ABC = 23^o and BC = 3.8m. 1.48m

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.

\( \frac{2}{3}\) \(= 0.667\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.34\) = \( \frac{17}{50}\)

Percentage (Increase)

Increase £140 by 40%

£196

Lowest Common Multiple

What is the lowest common multiple of six and twelve.

= 12

Sequence (Arithmetic)

2,8,14,20,26...

Find the:
a) next term; 32
b) n^th term; 6n - 4
c) term number 41; 242

Sequence (Geometric)

4,12,36,108,324...

Find the:
a) next term; 972
b) n^th term; 4 × 3^n-1
c) term number 10; 78732

Interest (Simple)

If £160 is invested for 8 years with a simple interest rate of 2%, find the amount of interest earned. £25.60

Interest (Compound)

If £120 is invested with an interest rate of 6% compounded annually, find the value of the investment after 4 years. £151.50

Currency Exchange

If £1 is worth $1.31, convert:

a) £100 to dollars; $131.00

b) $180 to pounds; £137.40

Coordinates (Midpoint)

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

\((-4,-3) \text{ and } (2,7)\)

(-1,2)

Gradient

What is the gradient of the line joining:

\((3,9) \text{ and } (7,12)\)

\(\frac{3}{4}\)

Coordinates (Square)

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

\((2,5),(6,9),(-2,9)\)

(2,13)

Negative Numbers

a) 5 − 17 = -12
b) 5 × (-9) = -45
c) (6−15)(5−16) = 99
d) 45 ÷ (-9) = -5
e) (-6)² = 36

Substitution

If p = 6, q = 23 and
r = -10 evaluate:

a) 2q − p = 40
b) pq + r = 128
c) p² − 5q - r = -69

Equations (Type 1)

Solve:

\(2x = 6\)

\(x = 3\)

Equations (Type 2)

Solve:

\(5x -5= 30\)

\(x = 7\)

Equations (Type 3)

Solve:

\(8x +4= 6x + 14\)

\(x = 5\)

Equations (Type 4)

Solve:

\(4(4x +4)-6= 106\)

\(x = 6\)

Equations (Type 5)

Solve:

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

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

Equations (Simultaneous 1)

Solve:

\(3x+5y = 40\)
\(5x+5y = 50\)

\(x = 5, y = 5\)

Equations (Simultaneous 2)

Solve:

\(3x+3y = 12\)
\(5x-9y = -8\)

\(x = 2, y = 2\)

Equations (Simultaneous 3)

Solve:

\(2x-2y = 9\)
\(3x+5y = -10.5\)

\(x = 1.5, y = -3\)

Sets (Union)

Find the union of:

{2,4,6,8,10} and
{1,3,6,10,15}

{1,2,3,4,6,8,10,15}

Sets (Intersection)

Find the intersection of:

{5,6,7,8,9,10} and
{2,6,12}

{6}

Bearings

A plane flies from point A to point B on a bearing of 104^o. What bearing would it return on from B to A? 284^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:

(16 − 4)² + 4 × 6

168

Simplify

Simplify the following by collecting like terms:

\(b+4c-7b+4c\)

\(8c-6b\)

Ratio

Divide 120 in the ratio

7:1

105 and 15

Graph Linear (1)

Draw a rough sketch of the graph of:

\(y=2x\)

Gradient 2
y intercept 0

Prime Factors

Express the following number as the product of prime numbers:

54

2 x 3 x 3 x 3

Percentage (Reverse)

In a sale an item costs £84 after a 30% reduction. What was the original price?

£120

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.

0.919191... \(\frac{91}{99}\)

Percentage (Decrease)

Decrease £120 by 45%

£66

Brackets (Linear)

Expand:

\(7(6x-8)\)

\(42x-56\)

Brackets (Quadratic)

Expand:

\((2x+3)(2x-2)\)

\(4x^2+2x-6\)

Factorise (Linear)

Factorise:

\(9x-9\)

\(9(x-1)\)

Factorise (Quadratic 1)

Factorise:

\(x^2+x-12\)

\((x+4)(x-3)\)

Factorise (Quadratic 2)

Factorise:

\(9x^2+9x-4\)

\((3x+4)(3x-1)\)

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

6.94 × 10^-5

= 0.0000694

Standard Form 3

Write in standard form:

80200

= 8.02 × 10⁴

Standard Form 4

Write in standard form:

0.0426

= 4.26 × 10^-2

Sequence (Quadratic)

Find the n^th term:

\(0, 8, 20, 36, 56, \)

\(2n^2+2n-4\)

Standard Form 5

Multiply 7 × 10⁶
by 5 × 10³ and give the answer in standard form.

= 3.5 × 10¹⁰

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:

\(2x^2-2x-1 = 0\)

\(x = 1.37\) and \(-0.366\)

Polygon Angles

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

140°

Change The Subject

Make \(a\) the subject of the formula
$$b=2a-3$$

$$a=\frac{b+3}{2}$$

Basic Division 1

Calculate the value of:

4669 ÷ 7

= 667

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

9

3

Prime Numbers

What is the difference between the 9th and the 10th prime numbers?

29 - 23 = 6

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: 0.9, 0.99, 9, 9.9, 9.09, 9.99, 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, 17cm, 18mm, 1.08m, 107cm, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

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

Angles with Parallels 1

h = 75

Angles with Parallels 2

j = 58

Rounding (1sf)

Round to one significant figure:
a) 44.31; 40
b) 363010; 400000
c) 98; 100
d) 0.00154; 0.002

Estimation

Round each value to one significant figure to make an estimate:$$(153 + 4.9) \div 18$$\((200 + 5) \div 20 = 10.25\)

Pie Charts (1)

A pie chart shows the colours of 20 books. What sector angle represents the
7 red books?
126°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 45 hats. How many green hats are represented
by a sector
angle of 264°?
33

Surds (1)

Simplify:
$$\sqrt{48}$$
\(4\sqrt{3}\)

Surds (2)

Simplify:
$$\dfrac{4}{5\sqrt{3}}$$\(\frac{4\sqrt{3}}{15}\)

Surds (3)

Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$\(\frac{10 + 2\sqrt{7}}{18}\)