Number Sequences 1

What is the 7th:
a) Odd number; 13
b) Square number; 49
c) Prime number. 17

Factors

Find all the factors of:

24

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

Multiples

Subtract the 7th from the 11th multiples of:

9

36

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) 68.67; 68.7
b) 511398; 511000
c) 45; 45.0
d) 0.004595; 0.00460

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 14cm, a height of 6cm and a top (parallel to base) of 4cm. 54cm²

Fractions (Adding)

Evaluate:

\( \frac{2}{3} + \frac{4}{6}\) \(= 1\frac{1}{3}\)

Fractions (Multiplying)

Evaluate:

\( \frac{1}{2} × \frac{4}{5}\) \(= \frac{2}{5}\)

Fractions (Dividing)

Evaluate:

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

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 to 3 significant figures.

\( \frac{1}{3}\) \(= 33.3\)%

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 12cm. Give your answer to three significant figures.

75.4cm

Decimals (Adding)

Calculate the value of:

5.6 + 6.5

= 12.1

Decimals (Subtracting)

Calculate the value of:

6.1 − 3.9

= 2.2

Decimals (Multiplying)

Calculate the value of:

7.5 × 5.7

= 42.75

Decimals (Dividing)

Calculate the value of:

123.5 ÷ 13

= 9.5

Indices (Simple)

What is the value of:

2³

= 8

Indices (Advanced)

What is the value of:

\(5^{-3}\)

\(= \frac{1}{125}\)

Basic Addition

Calculate the value of:

37 + 54

= 91

Basic Subtraction

Calculate the value of:

71 − 26

= 45

Basic Multiplication

Calculate the value of:

72 × 76

= 5472

Basic Division 2

Calculate the value of:

676 ÷ 13

= 52

Percentage (Of)

Find the value of:

75% of 200

= 150

Standard Form 1

Find the value of:

6.45 × 10⁴

= 64500

Highest Common Factor

Find the highest common factor of sixteen and ten.

= 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:

\( \frac{40}{48}\) \(= \frac{5}{6}\)

Fractions (Mixed)

Evaluate:

\( 1\frac{1}{2} − \frac{4}{5}\) \(= \frac{7}{10}\)

Pythagoras

Find AC if AB = 5.8m and BC = 7.4m. 4.60m

Trigonometry (Angle)

Find angle ABC if AC = 3.4m and AB = 5.3m. 32.7^o

Trigonometry (Side)

Find AC if angle ABC = 38^o and BC = 4.5m. 2.77m

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.

\( \frac{3}{7}\) \(= 0.429\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.94\) = \( \frac{47}{50}\)

Percentage (Increase)

Increase £80 by 35%

£108

Lowest Common Multiple

What is the lowest common multiple of ten and twenty five.

= 50

Sequence (Arithmetic)

6,15,24,33,42...

Find the:
a) next term; 51
b) n^th term; 9n - 3
c) term number 32; 285

Sequence (Geometric)

5,15,45,135,405...

Find the:
a) next term; 1215
b) n^th term; 5 × 3^n-1
c) term number 8; 10935

Interest (Simple)

If £140 is invested for 8 years with a simple interest rate of 6%, find the amount of interest earned. £67.20

Interest (Compound)

If £140 is invested with an interest rate of 5% compounded annually, find the value of the investment after 6 years. £187.61

Currency Exchange

If £1 is worth $1.25, convert:

a) £100 to dollars; $125.00

b) $140 to pounds; £112.00

Coordinates (Midpoint)

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

\((-7,7) \text{ and } (1,17)\)

(-3,12)

Gradient

What is the gradient of the line joining:

\((-9,-7) \text{ and } (-6,-3)\)

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

Coordinates (Square)

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

\((4,1),(8,4),(1,5)\)

(5,8)

Negative Numbers

a) 12 − 17 = -5
b) 12 × (-11) = -132
c) (5−17)(10−21) = 132
d) 132 ÷ (-11) = -12
e) (-12)² = 144

Substitution

If p = 6, q = 22 and
r = -7 evaluate:

a) 2q − p = 38
b) pq + r = 125
c) p² − 5q - r = -67

Equations (Type 1)

Solve:

\(3x = 21\)

\(x = 7\)

Equations (Type 2)

Solve:

\(2x -4= 2\)

\(x = 3\)

Equations (Type 3)

Solve:

\(5x +2= 2x + 14\)

\(x = 4\)

Equations (Type 4)

Solve:

\(2(5x -6)-5= 33\)

\(x = 5\)

Equations (Type 5)

Solve:

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

\(x = -4.67 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(5x+4y = 58\)
\(4x+4y = 52\)

\(x = 6, y = 7\)

Equations (Simultaneous 2)

Solve:

\(2x-2y = -4\)
\(5x+6y = 56\)

\(x = 4, y = 6\)

Equations (Simultaneous 3)

Solve:

\(5x-5y = -40\)
\(3x+2y = 1\)

\(x = -3, y = 5\)

Sets (Union)

Find the union of:

{6,7,8,9,10} and
{3,6,9,12,15}

{3,6,7,8,9,10,12,15}

Sets (Intersection)

Find the intersection of:

{6,7,8,9,10} and
{3,6,9,12,15}

{6,9}

Bearings

A plane flies from point A to point B on a bearing of 280^o. What bearing would it return on from B to A? 100^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:

63 ÷ 7 × 20 ÷ 5

36

Simplify

Simplify the following by collecting like terms:

\(3n+7−2n+8\)

\(n+15\)

Ratio

Divide 55 in the ratio

4:1

44 and 11

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:

108

2 x 2 x 3 x 3 x 3

Percentage (Reverse)

In a sale an item costs £34 after a 15% reduction. What was the original price?

£40

Averages

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

1,2,3,4,5

Mean = 3, no mode,
median = 3 and range = 4

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.

0.686868... \(\frac{68}{99}\)

Percentage (Decrease)

Decrease £20 by 25%

£15

Brackets (Linear)

Expand:

\(8(4x-5)\)

\(32x-40\)

Brackets (Quadratic)

Expand:

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

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

Factorise (Linear)

Factorise:

\(4x-4\)

\(4(x-1)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-x-6\)

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

Factorise (Quadratic 2)

Factorise:

\(3x^2-8x-16\)

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

4.3 × 10^-4

= 0.00043

Standard Form 3

Write in standard form:

4530

= 4.53 × 10³

Standard Form 4

Write in standard form:

0.00419

= 4.19 × 10^-3

Sequence (Quadratic)

Find the n^th term:

\(11, 20, 31, 44, 59, \)

\(n^2+6n+4\)

Standard Form 5

Multiply 8 × 10²
by 9 × 10⁶ and give the answer in standard form.

= 7.2 × 10⁹

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:

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

\(x = 0.468\) and \(-2.14\)

Polygon Angles

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

40°

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:

3160 ÷ 5

= 632

Number Sequences 2

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

Square Numbers

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

13

Prime Numbers

What are the next three prime numbers after
17

19, 23, 29

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: 8.88, 8, 0.88, 8.8, 8.08, 0.8, 0.08, in ascending order.
0.08, 0.8, 0.88, 8, 8.08, 8.8, 8.88,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

b = 52

Angles with Parallels 2

e = 63

Rounding (1sf)

Round to one significant figure:
a) 81.28; 80
b) 734079; 700000
c) 27; 30
d) 0.00285; 0.003

Estimation

Round each value to one significant figure to make an estimate:$$(154 + 3.8) \div 15$$\((200 + 4) \div 20 = 10.2\)

Pie Charts (1)

A pie chart shows the colours of 72 books. What sector angle represents the
32 red books?
160°

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 100°?
5

Surds (1)

Simplify:
$$\sqrt{50}$$
\(5\sqrt{2}\)

Surds (2)

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

Surds (3)

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