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:

37

1, 37.

Multiples

Subtract the 5th from the 9th multiples of:

6

24

Polygons

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

Heptagon, Octagon and Nonagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 31.81; 31.8
b) 815136; 815000
c) 79; 79.0
d) 0.007995; 0.00800

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 9cm, a height of 12cm and a top (parallel to base) of 3cm. 72cm²

Fractions (Adding)

Evaluate:

\( \frac{1}{3} + \frac{4}{6}\) \(= 1\)

Fractions (Multiplying)

Evaluate:

\( \frac{1}{3} × \frac{5}{6}\) \(= \frac{5}{18}\)

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.

\( \frac{3}{6}\) \(= 50\)%

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 6cm. Give your answer to three significant figures.

37.7cm

Decimals (Adding)

Calculate the value of:

7.6 + 2.4

= 10

Decimals (Subtracting)

Calculate the value of:

9.3 − 1.5

= 7.8

Decimals (Multiplying)

Calculate the value of:

7.5 × 7.4

= 55.5

Decimals (Dividing)

Calculate the value of:

36.4 ÷ 14

= 2.6

Indices (Simple)

What is the value of:

4²

= 16

Indices (Advanced)

What is the value of:

\(2^{-3}\)

\(= \frac{1}{8}\)

Basic Addition

Calculate the value of:

77 + 36

= 113

Basic Subtraction

Calculate the value of:

64 − 25

= 39

Basic Multiplication

Calculate the value of:

83 × 35

= 2905

Basic Division 2

Calculate the value of:

871 ÷ 13

= 67

Percentage (Of)

Find the value of:

40% of 340

= 136

Standard Form 1

Find the value of:

1.22 × 10⁵

= 122000

Highest Common Factor

Find the highest common factor of eighteen 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:

\( \frac{14}{28}\) \(= \frac{1}{2}\)

Fractions (Mixed)

Evaluate:

\( 3\frac{4}{5} − \frac{8}{9}\) \(= 2\frac{41}{45}\)

Pythagoras

Find AB if AC = 4.5m and BC = 5.6m. 3.33m

Trigonometry (Angle)

Find angle BCA if AB = 3.5m and BC = 5m. 44.4^o

Trigonometry (Side)

Find AC if angle ABC = 69^o and AB = 4.2m. 10.9m

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.

\(0.41\) = \( \frac{41}{100}\)

Percentage (Increase)

Increase £80 by 40%

£112

Lowest Common Multiple

What is the lowest common multiple of eight and twenty eight.

= 56

Sequence (Arithmetic)

4,14,24,34,44...

Find the:
a) next term; 54
b) n^th term; 10n - 6
c) term number 29; 284

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 9 years with a simple interest rate of 3%, find the amount of interest earned. £43.20

Interest (Compound)

If £180 is invested with an interest rate of 2% compounded annually, find the value of the investment after 5 years. £198.73

Currency Exchange

If £1 is worth $1.31, convert:

a) £100 to dollars; $131.00

b) $240 to pounds; £183.21

Coordinates (Midpoint)

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

\((2,5) \text{ and } (8,15)\)

(5,10)

Gradient

What is the gradient of the line joining:

\((8,-5) \text{ and } (13,-1)\)

\(\frac{4}{5}\)

Coordinates (Square)

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

\((4,3),(7,6),(1,6)\)

(4,9)

Negative Numbers

a) 6 − 12 = -6
b) 6 × (-8) = -48
c) (6−14)(9−15) = 48
d) 48 ÷ (-8) = -6
e) (-8)² = 64

Substitution

If p = 6, q = 17 and
r = -12 evaluate:

a) 2q − p = 28
b) pq + r = 90
c) p² − 5q - r = -37

Equations (Type 1)

Solve:

\(3x = 18\)

\(x = 6\)

Equations (Type 2)

Solve:

\(3x +4= 19\)

\(x = 5\)

Equations (Type 3)

Solve:

\(5x -5= 4x + -1\)

\(x = 4\)

Equations (Type 4)

Solve:

\(4(3x +2)+6= 110\)

\(x = 8\)

Equations (Type 5)

Solve:

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

\(x = 1.67 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(4x-4y = 0\)
\(5x-4y = 3\)

\(x = 3, y = 3\)

Equations (Simultaneous 2)

Solve:

\(4x-4y = -8\)
\(7x+12y = 62\)

\(x = 2, y = 4\)

Equations (Simultaneous 3)

Solve:

\(3x+7y = -20.5\)
\(5x+2y = 4.5\)

\(x = 2.5, y = -4\)

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:

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

∅

Bearings

A plane flies from point A to point B on a bearing of 231^o. What bearing would it return on from B to A? 051^o

Probability

A number is picked at random from the set

{2,6,12}

what is the probability it is even? 1

BIDMAS

Evaluate:

4 ÷ 2 × 24 ÷ 4

12

Simplify

Simplify the following by collecting like terms:

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

\(8c-6b\)

Ratio

Divide 54 in the ratio

1:5

9 and 45

Graph Linear (1)

Draw a rough sketch of the graph of:

\(y=-2x-1\)

Gradient -2
y intercept -1

Prime Factors

Express the following number as the product of prime numbers:

270

2 x 3 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £42 after a 30% reduction. What was the original price?

£60

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.

0.737373... \(\frac{73}{99}\)

Percentage (Decrease)

Decrease £180 by 40%

£108

Brackets (Linear)

Expand:

\(2(9x-8)\)

\(18x-16\)

Brackets (Quadratic)

Expand:

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

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

Factorise (Linear)

Factorise:

\(21x-14\)

\(7(3x-2)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-x-2\)

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

Factorise (Quadratic 2)

Factorise:

\(15x^2+7x-2\)

\((3x+2)(5x-1)\)

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

8.21 × 10^-3

= 0.00821

Standard Form 3

Write in standard form:

474000

= 4.74 × 10⁵

Standard Form 4

Write in standard form:

0.000217

= 2.17 × 10^-4

Sequence (Quadratic)

Find the n^th term:

\(5, 13, 23, 35, 49, \)

\(n^2+5n-1\)

Standard Form 5

Multiply 8 × 10⁴
by 4 × 10² and give the answer in standard form.

= 3.2 × 10⁷

Equations (Quadratic 1)

Solve:

\(x^2-x-12= 0\)

\(x = 4\) and \(-3\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

\(5x^2-3x-1 = 0\)

\(x = 0.839\) and \(-0.239\)

Polygon Angles

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

51.4°

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:

3954 ÷ 6

= 659

Number Sequences 2

What is the 11th:
a) Cube number; 1331
b) Triangular number; 66
c) Fibonacci number. 89

Square Numbers

What is the square root of

36

6

Prime Numbers

What are the three largest prime numbers less than
11

7, 5, 3

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

Capacities (Ordering)

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

Angles with Parallels 1

d = 99

Angles with Parallels 2

j = 58

Rounding (1sf)

Round to one significant figure:
a) 65.95; 70
b) 517107; 500000
c) 62; 60
d) 0.00765; 0.008

Estimation

Round each value to one significant figure to make an estimate:$$(192 + 3.5) \div 19$$\((200 + 4) \div 20 = 10.2\)

Pie Charts (1)

A pie chart shows the colours of 24 books. What sector angle represents the
6 red books?
90°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 18 hats. How many green hats are represented
by a sector
angle of 200°?
10

Surds (1)

Simplify:
$$\sqrt{12}$$
\(2\sqrt{3}\)

Surds (2)

Simplify:
$$\dfrac{5}{2\sqrt{3}}$$\(\frac{5\sqrt{3}}{6}\)

Surds (3)

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

Speed, Distance, Time

How long does it take to drive 130 km at a speed of 100 km/h?
🚗1 hours 18 minutes

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:

\(\dfrac{1}{x+1}+\dfrac{x}{2x-4}=1\)

\(x=0 \text{ or}\ x=5\)