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:

27

1, 3, 9, 27.

Multiples

Subtract the 4th from the 7th multiples of:

8

24

Polygons

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

Square, Pentagon and Hexagon (all regular)

Rounding (3sf)

Round to three significant figures:
a) 74.38; 74.4
b) 329039; 329000
c) 71; 71.0
d) 0.007195; 0.00720

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 9cm.

18cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 5cm and a top (parallel to base) of 3cm. 40cm²

Fractions (Adding)

Evaluate:

\( \frac{3}{4} + \frac{7}{8}\) \(= 1\frac{5}{8}\)

Fractions (Multiplying)

Evaluate:

\( \frac{2}{3} × \frac{4}{5}\) \(= \frac{8}{15}\)

Fractions (Dividing)

Evaluate:

\( \frac{1}{2} ÷ \frac{5}{3}\) \(= \frac{3}{10}\)

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.

\( \frac{2}{3}\) \(= 66.7\)%

Circle Area

Find the area of a circle that has a radius of 4cm. Give your answer to three significant figures.

50.3cm²

Circle Circumference

Find the circumference of a circle that has a radius of 10cm. Give your answer to three significant figures.

62.8cm

Decimals (Adding)

Calculate the value of:

5.6 + 5.9

= 11.5

Decimals (Subtracting)

Calculate the value of:

7.4 − 4.6

= 2.8

Decimals (Multiplying)

Calculate the value of:

6.7 × 4.9

= 32.83

Decimals (Dividing)

Calculate the value of:

31.2 ÷ 12

= 2.6

Indices (Simple)

What is the value of:

5²

= 25

Indices (Advanced)

What is the value of:

\(4^{\frac{1}{2}}\)

\(= 2\)

Basic Addition

Calculate the value of:

47 + 66

= 113

Basic Subtraction

Calculate the value of:

74 − 26

= 48

Basic Multiplication

Calculate the value of:

73 × 34

= 2482

Basic Division 2

Calculate the value of:

1248 ÷ 24

= 52

Percentage (Of)

Find the value of:

90% of 140

= 126

Standard Form 1

Find the value of:

2.92 × 10³

= 2920

Highest Common Factor

Find the highest common factor of twenty seven 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:

\( \frac{24}{48}\) \(= \frac{1}{2}\)

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find AB if AC = 4.1m and BC = 6m. 4.38m

Trigonometry (Angle)

Find angle BCA if AC = 4m and BC = 5.8m. 46.4^o

Trigonometry (Side)

Find AC if angle BCA = 55^o and AB = 5.5m. 3.85m

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.

\( \frac{1}{6}\) \(= 0.167\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.02\) = \( \frac{1}{50}\)

Percentage (Increase)

Increase £60 by 5%

£63

Lowest Common Multiple

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

= 84

Sequence (Arithmetic)

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

Find the:
a) next term; 54
b) n^th term; 10n - 6
c) term number 48; 474

Sequence (Geometric)

7,28,112,448,1792...

Find the:
a) next term; 7168
b) n^th term; 7 × 4^n-1
c) term number 10; 1835008

Interest (Simple)

If £240 is invested for 8 years with a simple interest rate of 6%, find the amount of interest earned. £115.20

Interest (Compound)

If £120 is invested with an interest rate of 1% compounded annually, find the value of the investment after 4 years. £124.87

Currency Exchange

If £1 is worth $1.34, convert:

a) £120 to dollars; $160.80

b) $140 to pounds; £104.48

Coordinates (Midpoint)

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

\((-3,-2) \text{ and } (3,6)\)

(0,2)

Gradient

What is the gradient of the line joining:

\((-1,7) \text{ and } (2,12)\)

\(\frac{5}{3}\)

Coordinates (Square)

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

\((4,1),(10,4),(1,7)\)

(7,10)

Negative Numbers

a) 10 − 16 = -6
b) 10 × (-6) = -60
c) (9−16)(11−22) = 77
d) 60 ÷ (-6) = -10
e) (-7)² = 49

Substitution

If p = 5, q = 22 and
r = -8 evaluate:

a) 2q − p = 39
b) pq + r = 102
c) p² − 5q - r = -77

Equations (Type 1)

Solve:

\(4x = 8\)

\(x = 2\)

Equations (Type 2)

Solve:

\(4x -2= 10\)

\(x = 3\)

Equations (Type 3)

Solve:

\(7x -2= 2x + 8\)

\(x = 2\)

Equations (Type 4)

Solve:

\(2(3x +3)+9= 45\)

\(x = 5\)

Equations (Type 5)

Solve:

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

\(x = -0.429 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(5x+2y = 26\)
\(4x+2y = 22\)

\(x = 4, y = 3\)

Equations (Simultaneous 2)

Solve:

\(3x-3y = 12\)
\(5x-6y = 17\)

\(x = 7, y = 3\)

Equations (Simultaneous 3)

Solve:

\(5x-3y = -5.5\)
\(3x+2y = -37.5\)

\(x = -6.5, y = -9\)

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

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

{2,4}

Bearings

A plane flies from point A to point B on a bearing of 241^o. What bearing would it return on from B to A? 061^o

Probability

A number is picked at random from the set

{2,4,6,8,10}

what is the probability it is even? 1

BIDMAS

Evaluate:

6 + (5 × 2² − 7)

19

Simplify

Simplify the following by collecting like terms:

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

\(11m+15\)

Ratio

Divide 130 in the ratio

7:6

70 and 60

Graph Linear (1)

Draw a rough sketch of the graph of:

\(2y=x-2\)

Gradient 0.5
y intercept -1

Prime Factors

Express the following number as the product of prime numbers:

24

2 x 2 x 2 x 3

Percentage (Reverse)

In a sale an item costs £153 after a 15% reduction. What was the original price?

£180

Averages

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

1,3,1,10,5

Mean = 4, mode = 1,
median = 3 and range = 9

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.

0.262626... \(\frac{26}{99}\)

Percentage (Decrease)

Decrease £100 by 35%

£65

Brackets (Linear)

Expand:

\(5(8x-4)\)

\(40x-20\)

Brackets (Quadratic)

Expand:

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

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

Factorise (Linear)

Factorise:

\(14x-7\)

\(7(2x-1)\)

Factorise (Quadratic 1)

Factorise:

\(x^2+x-6\)

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

Factorise (Quadratic 2)

Factorise:

\(5x^2+14x-3\)

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

6.56 × 10^-2

= 0.0656

Standard Form 3

Write in standard form:

90500

= 9.05 × 10⁴

Standard Form 4

Write in standard form:

0.000906

= 9.06 × 10^-4

Sequence (Quadratic)

Find the n^th term:

\(15, 27, 45, 69, 99, \)

\(3n^2+3n+9\)

Standard Form 5

Multiply 8 × 10⁴
by 7 × 10⁵ and give the answer in standard form.

= 5.6 × 10¹⁰

Equations (Quadratic 1)

Solve:

\(x^2+2x-15= 0\)

\(x = 3\) and \(-5\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

\(x = 1.43\) and \(0.232\)

Polygon Angles

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

135°

Change The Subject

Make \(c\) the subject of the formula
$$d=\frac{3c+1}{2}$$

$$c=\frac{2d-1}{3}$$

Basic Division 1

Calculate the value of:

3141 ÷ 9

= 349

Number Sequences 2

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

Square Numbers

What are the three largest square numbers less than
81

64, 49, 36

Prime Numbers

What is the 11th prime number?

31

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, 0.11, 1.01, 1.11, 0.01, in ascending order.
0.01, 0.1, 0.11, 1, 1.01, 1.1, 1.11,

Lengths (Ordering)

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

Capacities (Ordering)

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

Angles with Parallels 1

b = 52

Angles with Parallels 2

b = 48

Rounding (1sf)

Round to one significant figure:
a) 77.31; 80
b) 343292; 300000
c) 27; 30
d) 0.00895; 0.009

Estimation

Round each value to one significant figure to make an estimate:$$74 + 6.8 \times 93$$\(70 + 7 \times 90 = 700\)

Pie Charts (1)

A pie chart shows the colours of 12 books. What sector angle represents the
7 red books?
210°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 36 hats. How many green hats are represented
by a sector
angle of 240°?
24

Surds (1)

Simplify:
$$\sqrt{45}$$
\(3\sqrt{5}\)

Surds (2)

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

Surds (3)

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