Number Sequences 1

What is the 8th:
a) Odd number; 15
b) Square number; 64
c) Prime number. 19

Factors

Find all the factors of:

35

1, 5, 7, 35.

Multiples

Subtract the 6th from the 9th multiples of:

6

18

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) 96.93; 96.9
b) 140020; 140000
c) 61; 61.0
d) 0.006195; 0.00620

Area of a Triangle

Find the area of a triangle that has a base of 7cm and a height of 11cm.

38.5cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 15cm, a height of 9cm and a top (parallel to base) of 7cm. 99cm²

Fractions (Adding)

Evaluate:

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

Fractions (Multiplying)

Evaluate:

\( \frac{1}{2} × \frac{3}{4}\) \(= \frac{3}{8}\)

Fractions (Dividing)

Evaluate:

\( \frac{2}{3} ÷ \frac{6}{5}\) \(= \frac{5}{9}\)

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.

\( \frac{3}{7}\) \(= 42.9\)%

Circle Area

Find the area of a circle that has a radius of 7cm. Give your answer to three significant figures.

154cm²

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:

6.6 + 6.7

= 13.3

Decimals (Subtracting)

Calculate the value of:

8.2 − 4.8

= 3.4

Decimals (Multiplying)

Calculate the value of:

4.6 × 8.8

= 40.48

Decimals (Dividing)

Calculate the value of:

136.8 ÷ 19

= 7.2

Indices (Simple)

What is the value of:

4²

= 16

Indices (Advanced)

What is the value of:

\(9^{\frac{1}{2}}\)

\(= 3\)

Basic Addition

Calculate the value of:

78 + 56

= 134

Basic Subtraction

Calculate the value of:

94 − 29

= 65

Basic Multiplication

Calculate the value of:

73 × 57

= 4161

Basic Division 2

Calculate the value of:

1836 ÷ 27

= 68

Percentage (Of)

Find the value of:

5% of 160

= 8

Standard Form 1

Find the value of:

3.81 × 10³

= 3810

Highest Common Factor

Find the highest common factor of forty five and twenty five.

= 5

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:

\( \frac{9}{18}\) \(= \frac{1}{2}\)

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find AB if AC = 3.6m and BC = 5.2m. 3.75m

Trigonometry (Angle)

Find angle BCA if AC = 5.4m and BC = 7.1m. 40.5^o

Trigonometry (Side)

Find AB if angle ABC = 39^o and BC = 5m. 3.89m

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.

\( \frac{1}{5}\) \(= 0.2\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.51\) = \( \frac{51}{100}\)

Percentage (Increase)

Increase £60 by 40%

£84

Lowest Common Multiple

What is the lowest common multiple of twenty and thirty.

= 60

Sequence (Arithmetic)

7,17,27,37,47...

Find the:
a) next term; 57
b) n^th term; 10n - 3
c) term number 50; 497

Sequence (Geometric)

5,20,80,320,1280...

Find the:
a) next term; 5120
b) n^th term; 5 × 4^n-1
c) term number 10; 1310720

Interest (Simple)

If £120 is invested for 5 years with a simple interest rate of 2%, find the amount of interest earned. £12.00

Interest (Compound)

If £140 is invested with an interest rate of 6% compounded annually, find the value of the investment after 7 years. £210.51

Currency Exchange

If £1 is worth $1.24, convert:

a) £200 to dollars; $248.00

b) $120 to pounds; £96.77

Coordinates (Midpoint)

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

\((5,0) \text{ and } (11,12)\)

(8,6)

Gradient

What is the gradient of the line joining:

\((1,5) \text{ and } (6,9)\)

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

Coordinates (Square)

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

\((2,3),(5,8),(-3,6)\)

(0,11)

Negative Numbers

a) 10 − 18 = -8
b) 10 × (-9) = -90
c) (10−18)(9−19) = 80
d) 90 ÷ (-9) = -10
e) (-12)² = 144

Substitution

If p = 6, q = 24 and
r = -5 evaluate:

a) 2q − p = 42
b) pq + r = 139
c) p² − 5q - r = -79

Equations (Type 1)

Solve:

\(4x = 20\)

\(x = 5\)

Equations (Type 2)

Solve:

\(3x +4= 25\)

\(x = 7\)

Equations (Type 3)

Solve:

\(7x +2= 2x + 42\)

\(x = 8\)

Equations (Type 4)

Solve:

\(2(4x -2)+10= 30\)

\(x = 3\)

Equations (Type 5)

Solve:

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

\(x = 0\)

Equations (Simultaneous 1)

Solve:

\(3x+2y = 14\)
\(2x+2y = 12\)

\(x = 2, y = 4\)

Equations (Simultaneous 2)

Solve:

\(2x+5y = 22\)
\(7x+15y = 72\)

\(x = 6, y = 2\)

Equations (Simultaneous 3)

Solve:

\(5x+5y = 32.5\)
\(3x-2y = 4.5\)

\(x = 3.5, y = 3\)

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

{1,2,3,4,5} and
{1,3,5,7,9}

{1,3,5}

Bearings

A plane flies from point A to point B on a bearing of 138^o. What bearing would it return on from B to A? 318^o

Probability

A number is picked at random from the set

{1,3,5,7,9}

what is the probability it is even? 0

BIDMAS

Evaluate:

5 + (3 × 2² − 7)

10

Simplify

Simplify the following by collecting like terms:

\(3b+5c+8b+4c\)

\(11b+9c\)

Ratio

Divide 150 in the ratio

8:2

120 and 30

Graph Linear (1)

Draw a rough sketch of the graph of:

\(2y=x\)

Gradient 0.5
y intercept 0

Prime Factors

Express the following number as the product of prime numbers:

36

2 x 2 x 3 x 3

Percentage (Reverse)

In a sale an item costs £54 after a 10% reduction. What was the original price?

£60

Averages

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

2,6,12,6,14

Mean = 8, mode = 6,
median = 6 and range = 12

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.

0.727272... \(\frac{8}{11}\)

Percentage (Decrease)

Decrease £180 by 20%

£144

Brackets (Linear)

Expand:

\(4(3x-6)\)

\(12x-24\)

Brackets (Quadratic)

Expand:

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

\(9x^2+6x-3\)

Factorise (Linear)

Factorise:

\(16x-14\)

\(2(8x-7)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-3x-4\)

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

Factorise (Quadratic 2)

Factorise:

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

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

6.74 × 10^-3

= 0.00674

Standard Form 3

Write in standard form:

619000

= 6.19 × 10⁵

Standard Form 4

Write in standard form:

0.0552

= 5.52 × 10^-2

Sequence (Quadratic)

Find the n^th term:

\(12, 24, 40, 60, 84, \)

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

Standard Form 5

Multiply 8 × 10⁶
by 4 × 10² and give the answer in standard form.

= 3.2 × 10⁹

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:

\(4x^2+3x-5 = 0\)

\(x = 0.804\) and \(-1.55\)

Polygon Angles

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

128.6°

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:

2586 ÷ 6

= 431

Number Sequences 2

What is the 5th:
a) Cube number; 125
b) Triangular number; 15
c) Fibonacci number. 5

Square Numbers

What are the next three square numbers after
81

100, 121, 144

Prime Numbers

What is the difference between the 10th and the 11th prime numbers?

31 - 29 = 2

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

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

g = 122

Angles with Parallels 2

j = 58

Rounding (1sf)

Round to one significant figure:
a) 90.13; 90
b) 606806; 600000
c) 86; 90
d) 0.00178; 0.002

Estimation

Round each value to one significant figure to make an estimate:$$63 + 9.8 \times 61$$\(60 + 10 \times 60 = 660\)

Pie Charts (1)

A pie chart shows the colours of 120 books. What sector angle represents the
59 red books?
177°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 9 hats. How many green hats are represented
by a sector
angle of 80°?
2

Surds (1)

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

Surds (2)

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

Surds (3)

Simplify:
$$\dfrac{3}{4 + \sqrt{2}}$$\(\frac{12 - 3\sqrt{2}}{14} = \frac{6 - \sqrt{2}}{7}\)