Number Sequences 1

What is the 5th:
a) Odd number; 9
b) Square number; 25
c) Prime number. 11

Factors

Find all the factors of:

45

1, 3, 5, 9, 15, 45.

Multiples

Subtract the 6th from the 11th multiples of:

4

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) 83.75; 83.8
b) 839944; 840000
c) 56; 56.0
d) 0.005695; 0.00570

Area of a Triangle

Find the area of a triangle that has a base of 3cm and a height of 7cm.

10.5cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 17cm, a height of 12cm and a top (parallel to base) of 7cm. 144cm²

Fractions (Adding)

Evaluate:

\( \frac{4}{7} + \frac{10}{13}\) \(= 1\frac{31}{91}\)

Fractions (Multiplying)

Evaluate:

\( \frac{3}{4} × \frac{5}{6}\) \(= \frac{5}{8}\)

Fractions (Dividing)

Evaluate:

\( \frac{2}{4} ÷ \frac{8}{6}\) \(= \frac{3}{8}\)

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 9cm. Give your answer to three significant figures.

254cm²

Circle Circumference

Find the circumference of a circle that has a radius of 9cm. Give your answer to three significant figures.

56.5cm

Decimals (Adding)

Calculate the value of:

8.5 + 7.7

= 16.2

Decimals (Subtracting)

Calculate the value of:

8.4 − 4.8

= 3.6

Decimals (Multiplying)

Calculate the value of:

5.9 × 3.5

= 20.65

Decimals (Dividing)

Calculate the value of:

64.4 ÷ 14

= 4.6

Indices (Simple)

What is the value of:

2²

= 4

Indices (Advanced)

What is the value of:

\(1^{-2}\)

\(= 1\)

Basic Addition

Calculate the value of:

69 + 99

= 168

Basic Subtraction

Calculate the value of:

74 − 29

= 45

Basic Multiplication

Calculate the value of:

93 × 97

= 9021

Basic Division 2

Calculate the value of:

1248 ÷ 26

= 48

Percentage (Of)

Find the value of:

95% of 100

= 95

Standard Form 1

Find the value of:

4.28 × 10⁴

= 42800

Highest Common Factor

Find the highest common factor of twenty four and fifteen.

= 3

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:

\( \frac{30}{48}\) \(= \frac{5}{8}\)

Fractions (Mixed)

Evaluate:

\( 3\frac{1}{2} − \frac{3}{4}\) \(= 2\frac{3}{4}\)

Pythagoras

Find AB if AC = 3.2m and BC = 4.3m. 2.87m

Trigonometry (Angle)

Find angle BCA if AB = 3.6m and AC = 5m. 35.8^o

Trigonometry (Side)

Find AC if angle ABC = 53^o and BC = 4.8m. 3.83m

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.

\(0.36\) = \( \frac{9}{25}\)

Percentage (Increase)

Increase £100 by 40%

£140

Lowest Common Multiple

What is the lowest common multiple of six and fourteen.

= 42

Sequence (Arithmetic)

6,19,32,45,58...

Find the:
a) next term; 71
b) n^th term; 13n - 7
c) term number 44; 565

Sequence (Geometric)

4,8,16,32,64...

Find the:
a) next term; 128
b) n^th term; 4 × 2^n-1
c) term number 8; 512

Interest (Simple)

If £120 is invested for 8 years with a simple interest rate of 6%, find the amount of interest earned. £57.60

Interest (Compound)

If £200 is invested with an interest rate of 4% compounded annually, find the value of the investment after 9 years. £284.66

Currency Exchange

If £1 is worth $1.32, convert:

a) £240 to dollars; $316.80

b) $160 to pounds; £121.21

Coordinates (Midpoint)

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

\((3,6) \text{ and } (15,12)\)

(9,9)

Gradient

What is the gradient of the line joining:

\((-6,7) \text{ and } (-3,10)\)

1

Coordinates (Square)

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

\((1,1),(7,6),(-4,7)\)

(2,12)

Negative Numbers

a) 7 − 18 = -11
b) 7 × (-8) = -56
c) (7−18)(11−21) = 110
d) 56 ÷ (-8) = -7
e) (-8)² = 64

Substitution

If p = 6, q = 23 and
r = -8 evaluate:

a) 2q − p = 40
b) pq + r = 130
c) p² − 5q - r = -71

Equations (Type 1)

Solve:

\(5x = 40\)

\(x = 8\)

Equations (Type 2)

Solve:

\(4x +2= 38\)

\(x = 9\)

Equations (Type 3)

Solve:

\(7x -6= 2x + 19\)

\(x = 5\)

Equations (Type 4)

Solve:

\(2(3x +6)+7= 67\)

\(x = 8\)

Equations (Type 5)

Solve:

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

\(x = 0.556 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(2x-2y = -4\)
\(4x+2y = 22\)

\(x = 3, y = 5\)

Equations (Simultaneous 2)

Solve:

\(2x-5y = -23\)
\(7x+10y = 112\)

\(x = 6, y = 7\)

Equations (Simultaneous 3)

Solve:

\(2x-7y = -18.5\)
\(5x+3y = -15.5\)

\(x = -4, y = 1.5\)

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

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

{3,5,7}

Bearings

A plane flies from point A to point B on a bearing of 229^o. What bearing would it return on from B to A? 049^o

Probability

A number is picked at random from the set

{1,3,6,10,15}

what is the probability it is even? \(\frac25\)

BIDMAS

Evaluate:

36 ÷ 9 × 36 ÷ 9

16

Simplify

Simplify the following by collecting like terms:

\(6m+7+5m+8\)

\(11m+15\)

Ratio

Divide 77 in the ratio

1:6

11 and 66

Graph Linear (1)

Draw a rough sketch of the graph of:

\(y=-2x+2\)

Gradient -2
y intercept 2

Prime Factors

Express the following number as the product of prime numbers:

108

2 x 2 x 3 x 3 x 3

Percentage (Reverse)

In a sale an item costs £11 after a 45% reduction. What was the original price?

£20

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.

0.666666... \(\frac{2}{3}\)

Percentage (Decrease)

Decrease £140 by 30%

£98

Brackets (Linear)

Expand:

\(3(7x-7)\)

\(21x-21\)

Brackets (Quadratic)

Expand:

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

\(12x^2+3x-9\)

Factorise (Linear)

Factorise:

\(6x-6\)

\(6(x-1)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-x-2\)

\((x+1)(x-2)\)

Factorise (Quadratic 2)

Factorise:

\(x^2-16\)

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

6.42 × 10^-3

= 0.00642

Standard Form 3

Write in standard form:

44700

= 4.47 × 10⁴

Standard Form 4

Write in standard form:

0.0000896

= 8.96 × 10^-5

Sequence (Quadratic)

Find the n^th term:

\(1, 7, 15, 25, 37, \)

\(n^2+3n-3\)

Standard Form 5

Multiply 8 × 10⁵
by 8 × 10² and give the answer in standard form.

= 6.4 × 10⁸

Equations (Quadratic 1)

Solve:

\(x^2-3x-10= 0\)

\(x = 5\) and \(-2\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

\(3x^2-x-5 = 0\)

\(x = 1.47\) and \(-1.14\)

Polygon Angles

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

51.4°

Change The Subject

Make \(h\) the subject of the formula
$$e=\frac{h}{4}-5$$

$$h=4(e+5)$$

Basic Division 1

Calculate the value of:

642 ÷ 2

= 321

Number Sequences 2

What is the 8th:
a) Cube number; 512
b) Triangular number; 36
c) Fibonacci number. 21

Square Numbers

What is the square of

4

16

Prime Numbers

What are the next three prime numbers after
13

17, 19, 23

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: 0.22, 2, 2.22, 2.2, 0.2, 2.02, 0.02, in ascending order.
0.02, 0.2, 0.22, 2, 2.02, 2.2, 2.22,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

c = 81

Angles with Parallels 2

g = 122

Rounding (1sf)

Round to one significant figure:
a) 61.66; 60
b) 374162; 400000
c) 68; 70
d) 0.00840; 0.008

Estimation

Round each value to one significant figure to make an estimate:$$(154 + 2.9) \div 15$$\((200 + 3) \div 20 = 10.15\)

Pie Charts (1)

A pie chart shows the colours of 20 books. What sector angle represents the
3 red books?
54°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 60 hats. How many green hats are represented
by a sector
angle of 222°?
37

Surds (1)

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

Surds (2)

Simplify:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)

Surds (3)

Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)

Speed, Distance, Time

Find the speed of a runner who covers 25 km in 3 hours.
🏃8.33 km/h

Factorising by Grouping

Factorise:

\(xy + 2x + 3y + 6\)

\((x+3)(y+2)\)

Algebraic Fractions

Simplify:

\(\dfrac{1}{x-2} + \dfrac{x+1}{x-3}\)

\(\dfrac{x^{2}-5}{(x-2)(x-3)}\)

Equations with Fractions

Solve:

\(\dfrac{2}{x+2}+\dfrac{3}{2x-1}=1\)

\(x=-1 \text{ or } 3\)