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:

37

1, 37.

Multiples

Subtract the 7th from the 11th multiples of:

5

20

Polygons

What are the names of regular polygons with:
a) three sides;
b) four sides;
c) five sides.

Equilateral Triangle, Square and Pentagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 62.73; 62.7
b) 394252; 394000
c) 62; 62.0
d) 0.006295; 0.00630

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 8cm.

16cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 7cm and a top (parallel to base) of 5cm. 63cm²

Fractions (Adding)

Evaluate:

\( \frac{4}{6} + \frac{9}{11}\) \(= 1\frac{16}{33}\)

Fractions (Multiplying)

Evaluate:

\( \frac{3}{4} × \frac{5}{7}\) \(= \frac{15}{28}\)

Fractions (Dividing)

Evaluate:

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

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.

\( \frac{3}{5}\) \(= 60\)%

Circle Area

Find the area of a circle that has a radius of 8cm. Give your answer to three significant figures.

201cm²

Circle Circumference

Find the circumference of a circle that has a radius of 5cm. Give your answer to three significant figures.

31.4cm

Decimals (Adding)

Calculate the value of:

9.7 + 6.4

= 16.1

Decimals (Subtracting)

Calculate the value of:

6.4 − 2.8

= 3.6

Decimals (Multiplying)

Calculate the value of:

7.3 × 9.8

= 71.54

Decimals (Dividing)

Calculate the value of:

68.9 ÷ 13

= 5.3

Indices (Simple)

What is the value of:

1³

= 1

Indices (Advanced)

What is the value of:

\(2^{-1}\)

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

Basic Addition

Calculate the value of:

49 + 39

= 88

Basic Subtraction

Calculate the value of:

91 − 27

= 64

Basic Multiplication

Calculate the value of:

73 × 87

= 6351

Basic Division 2

Calculate the value of:

874 ÷ 19

= 46

Percentage (Of)

Find the value of:

20% of 260

= 52

Standard Form 1

Find the value of:

9.41 × 10³

= 9410

Highest Common Factor

Find the highest common factor of twenty one and nine.

= 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:

\( \frac{7}{21}\) \(= \frac{1}{3}\)

Fractions (Mixed)

Evaluate:

\( 1\frac{3}{4} − \frac{7}{8}\) \(= \frac{7}{8}\)

Pythagoras

Find BC if AB = 4.9m and AC = 6.7m. 8.30m

Trigonometry (Angle)

Find angle BCA if AB = 5.3m and BC = 6.4m. 55.9^o

Trigonometry (Side)

Find BC if angle BCA = 59^o and AB = 3.9m. 4.55m

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.

\( \frac{2}{4}\) \(= 0.5\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.78\) = \( \frac{39}{50}\)

Percentage (Increase)

Increase £100 by 20%

£120

Lowest Common Multiple

What is the lowest common multiple of twelve and twenty four.

= 24

Sequence (Arithmetic)

3,12,21,30,39...

Find the:
a) next term; 48
b) n^th term; 9n - 6
c) term number 29; 255

Sequence (Geometric)

6,18,54,162,486...

Find the:
a) next term; 1458
b) n^th term; 6 × 3^n-1
c) term number 8; 13122

Interest (Simple)

If £120 is invested for 8 years with a simple interest rate of 5%, find the amount of interest earned. £48.00

Interest (Compound)

If £200 is invested with an interest rate of 4% compounded annually, find the value of the investment after 5 years. £243.33

Currency Exchange

If £1 is worth $1.32, convert:

a) £200 to dollars; $264.00

b) $200 to pounds; £151.52

Coordinates (Midpoint)

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

\((-7,4) \text{ and } (1,12)\)

(-3,8)

Gradient

What is the gradient of the line joining:

\((8,8) \text{ and } (14,13)\)

\(\frac{5}{6}\)

Coordinates (Square)

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

\((4,2),(8,8),(-2,6)\)

(2,12)

Negative Numbers

a) 12 − 18 = -6
b) 12 × (-6) = -72
c) (12−21)(12−21) = 81
d) 72 ÷ (-6) = -12
e) (-11)² = 121

Substitution

If p = 6, q = 24 and
r = -7 evaluate:

a) 2q − p = 42
b) pq + r = 137
c) p² − 5q - r = -77

Equations (Type 1)

Solve:

\(4x = 32\)

\(x = 8\)

Equations (Type 2)

Solve:

\(2x +7= 17\)

\(x = 5\)

Equations (Type 3)

Solve:

\(6x +2= 4x + 10\)

\(x = 4\)

Equations (Type 4)

Solve:

\(5(3x -5)+12= 17\)

\(x = 2\)

Equations (Type 5)

Solve:

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

\(x = -0.474 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(2x+3y = 18\)
\(4x+3y = 30\)

\(x = 6, y = 2\)

Equations (Simultaneous 2)

Solve:

\(3x+2y = 24\)
\(5x+4y = 44\)

\(x = 4, y = 6\)

Equations (Simultaneous 3)

Solve:

\(3x-5y = -66.5\)
\(5x-3y = -65.5\)

\(x = -8, y = 8.5\)

Sets (Union)

Find the union of:

{6,7,8,9,10} and
{1,3,6,10,15}

{1,3,6,7,8,9,10,15}

Sets (Intersection)

Find the intersection of:

{2,4,6,8,10} and
{6,7,8,9,10}

{6,8,10}

Bearings

A plane flies from point A to point B on a bearing of 132^o. What bearing would it return on from B to A? 312^o

Probability

A number is picked at random from the set

{3,4,5,6,7,8}

what is the probability it is even? \(\frac12\)

BIDMAS

Evaluate:

9 + 8 × 3 − 6

27

Simplify

Simplify the following by collecting like terms:

\(5a−5−4a−5\)

\(a-10\)

Ratio

Divide 75 in the ratio

4:1

60 and 15

Graph Linear (1)

Draw a rough sketch of the graph of:

\(2y=x+4\)

Gradient 0.5
y intercept 2

Prime Factors

Express the following number as the product of prime numbers:

72

2 x 2 x 2 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:

5,8,8,6,7,8

Mean = 7, mode = 8,
median = 7.5 and range = 3

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.

0.676767... \(\frac{67}{99}\)

Percentage (Decrease)

Decrease £180 by 25%

£135

Brackets (Linear)

Expand:

\(9(8x-7)\)

\(72x-63\)

Brackets (Quadratic)

Expand:

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

\(9x^2-9\)

Factorise (Linear)

Factorise:

\(18x-45\)

\(9(2x-5)\)

Factorise (Quadratic 1)

Factorise:

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

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

Factorise (Quadratic 2)

Factorise:

\(12x^2+5x-3\)

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

4.36 × 10^-2

= 0.0436

Standard Form 3

Write in standard form:

92200

= 9.22 × 10⁴

Standard Form 4

Write in standard form:

0.000388

= 3.88 × 10^-4

Sequence (Quadratic)

Find the n^th term:

\(3, 15, 33, 57, 87, \)

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

Standard Form 5

Multiply 8 × 10²
by 4 × 10⁵ and give the answer in standard form.

= 3.2 × 10⁸

Equations (Quadratic 1)

Solve:

\(x^2-2x-8= 0\)

\(x = 4\) and \(-2\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

\(x = 1.18\) and \(-0.847\)

Polygon Angles

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

120°

Change The Subject

Make \(f\) the subject of the formula
$$h=g(e-f)$$

$$f=e-\frac{h}{g}$$

Basic Division 1

Calculate the value of:

6181 ÷ 7

= 883

Number Sequences 2

What is the 7th:
a) Cube number; 343
b) Triangular number; 28
c) Fibonacci number. 13

Square Numbers

What are the three largest square numbers less than
144

121, 100, 81

Prime Numbers

What is the difference between the 11th and the 12th prime numbers?

37 - 31 = 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: 1, 0.1, 1.1, 1.01, 1.11, 0.11, 0.01, in ascending order.
0.01, 0.1, 0.11, 1, 1.01, 1.1, 1.11,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

i = 54

Angles with Parallels 2

e = 63

Rounding (1sf)

Round to one significant figure:
a) 71.51; 70
b) 508759; 500000
c) 49; 50
d) 0.00783; 0.008

Estimation

Round each value to one significant figure to make an estimate:$$(193 + 2.7) \div 16$$\((200 + 3) \div 20 = 10.15\)

Pie Charts (1)

A pie chart shows the colours of 60 books. What sector angle represents the
7 red books?
42°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 40 hats. How many green hats are represented
by a sector
angle of 135°?
15

Surds (1)

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

Surds (2)

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

Surds (3)

Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)