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:

24

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

Multiples

Subtract the 4th from the 7th multiples of:

7

21

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) 37.44; 37.4
b) 515318; 515000
c) 23; 23.0
d) 0.002395; 0.00240

Area of a Triangle

Find the area of a triangle that has a base of 6cm and a height of 11cm.

33cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 17cm, a height of 6cm and a top (parallel to base) of 7cm. 72cm²

Fractions (Adding)

Evaluate:

\( \frac{3}{6} + \frac{9}{12}\) \(= 1\frac{1}{4}\)

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

\( \frac{3}{5} ÷ \frac{9}{7}\) \(= \frac{7}{15}\)

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.

\( \frac{1}{5}\) \(= 20\)%

Circle Area

Find the area of a circle that has a radius of 3cm. Give your answer to three significant figures.

28.3cm²

Circle Circumference

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

50.3cm

Decimals (Adding)

Calculate the value of:

7.9 + 7.4

= 15.3

Decimals (Subtracting)

Calculate the value of:

6.1 − 1.9

= 4.2

Decimals (Multiplying)

Calculate the value of:

7.7 × 7.9

= 60.83

Decimals (Dividing)

Calculate the value of:

84.6 ÷ 18

= 4.7

Indices (Simple)

What is the value of:

2²

= 4

Indices (Advanced)

What is the value of:

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

\(= 3\)

Basic Addition

Calculate the value of:

86 + 97

= 183

Basic Subtraction

Calculate the value of:

81 − 25

= 56

Basic Multiplication

Calculate the value of:

38 × 28

= 1064

Basic Division 2

Calculate the value of:

1375 ÷ 25

= 55

Percentage (Of)

Find the value of:

15% of 40

= 6

Standard Form 1

Find the value of:

9.71 × 10²

= 971

Highest Common Factor

Find the highest common factor of forty and twenty.

= 20

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:

\( \frac{18}{36}\) \(= \frac{1}{2}\)

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find AB if AC = 5.1m and BC = 6.2m. 3.53m

Trigonometry (Angle)

Find angle ABC if AC = 6m and BC = 7.5m. 53.1^o

Trigonometry (Side)

Find AB if angle ABC = 26^o and BC = 3.2m. 2.88m

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.

\(0.8\) = \( \frac{4}{5}\)

Percentage (Increase)

Increase £120 by 35%

£162

Lowest Common Multiple

What is the lowest common multiple of nine and eighteen.

= 18

Sequence (Arithmetic)

7,18,29,40,51...

Find the:
a) next term; 62
b) n^th term; 11n - 4
c) term number 42; 458

Sequence (Geometric)

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

Find the:
a) next term; 1458
b) n^th term; 6 × 3^n-1
c) term number 9; 39366

Interest (Simple)

If £180 is invested for 8 years with a simple interest rate of 4%, find the amount of interest earned. £57.60

Interest (Compound)

If £200 is invested with an interest rate of 6% compounded annually, find the value of the investment after 5 years. £267.65

Currency Exchange

If £1 is worth $1.37, convert:

a) £240 to dollars; $328.80

b) $240 to pounds; £175.18

Coordinates (Midpoint)

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

\((-8,-2) \text{ and } (2,6)\)

(-3,2)

Gradient

What is the gradient of the line joining:

\((6,-2) \text{ and } (10,2)\)

1

Coordinates (Square)

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

\((4,2),(10,5),(1,8)\)

(7,11)

Negative Numbers

a) 10 − 21 = -11
b) 10 × (-6) = -60
c) (12−18)(10−20) = 60
d) 60 ÷ (-6) = -10
e) (-11)² = 121

Substitution

If p = 5, q = 26 and
r = -5 evaluate:

a) 2q − p = 47
b) pq + r = 125
c) p² − 5q - r = -100

Equations (Type 1)

Solve:

\(4x = 24\)

\(x = 6\)

Equations (Type 2)

Solve:

\(4x +4= 20\)

\(x = 4\)

Equations (Type 3)

Solve:

\(5x -6= 2x + 0\)

\(x = 2\)

Equations (Type 4)

Solve:

\(4(2x +4)-12= 60\)

\(x = 7\)

Equations (Type 5)

Solve:

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

\(x = -0.308 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(2x-4y = -16\)
\(5x+4y = 30\)

\(x = 2, y = 5\)

Equations (Simultaneous 2)

Solve:

\(3x+2y = 14\)
\(6x+6y = 36\)

\(x = 2, y = 4\)

Equations (Simultaneous 3)

Solve:

\(3x+3y = 28.5\)
\(7x-2y = 26\)

\(x = 5, y = 4.5\)

Sets (Union)

Find the union of:

{5,6,7,8,9,10} and
{2,3,5,7,11,13}

{2,3,5,6,7,8,9,10,11,13}

Sets (Intersection)

Find the intersection of:

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

{4,6,8}

Bearings

A plane flies from point A to point B on a bearing of 327^o. What bearing would it return on from B to A? 147^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:

(15 − 8)² + 3 × 9

76

Simplify

Simplify the following by collecting like terms:

\(3a+5b-3a+4b^2\)

\(5b+4b^2\)

Ratio

Divide 135 in the ratio

4:5

60 and 75

Graph Linear (1)

Draw a rough sketch of the graph of:

\(y=2x+2\)

Gradient 2
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 £99 after a 45% reduction. What was the original price?

£180

Averages

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

7,7,2,7,7

Mean = 6, mode = 7,
median = 7 and range = 5

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.

0.979797... \(\frac{97}{99}\)

Percentage (Decrease)

Decrease £60 by 45%

£33

Brackets (Linear)

Expand:

\(6(6x-6)\)

\(36x-36\)

Brackets (Quadratic)

Expand:

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

\(4x^2-2x-12\)

Factorise (Linear)

Factorise:

\(21x-9\)

\(3(7x-3)\)

Factorise (Quadratic 1)

Factorise:

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

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

Factorise (Quadratic 2)

Factorise:

\(12x^2-x-1\)

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

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

4.46 × 10^-2

= 0.0446

Standard Form 3

Write in standard form:

735

= 7.35 × 10²

Standard Form 4

Write in standard form:

0.00657

= 6.57 × 10^-3

Sequence (Quadratic)

Find the n^th term:

\(0, 8, 18, 30, 44, \)

\(n^2+5n-6\)

Standard Form 5

Multiply 7 × 10³
by 6 × 10⁵ and give the answer in standard form.

= 4.2 × 10⁹

Equations (Quadratic 1)

Solve:

\(x^2+x-6= 0\)

\(x = 2\) and \(-3\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

\(4x^2-5x-1 = 0\)

\(x = 1.43\) and \(-0.175\)

Polygon Angles

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

36°

Change The Subject

Make \(b\) the subject of the formula
$$c=3b-5$$

$$b=\frac{c+5}{3}$$

Basic Division 1

Calculate the value of:

2544 ÷ 4

= 636

Number Sequences 2

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

Square Numbers

What are the next three square numbers after
9

16, 25, 36

Prime Numbers

What are the next three prime numbers after
31

37, 41, 43

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: 1.01, 1.11, 0.1, 1, 1.1, 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, 107cm, 17cm, 18mm, 1.8m, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

Write down these capacities: 21cl, 173ml, 17cl, 200ml, 18cl, 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) 37.69; 40
b) 677272; 700000
c) 78; 80
d) 0.00554; 0.006

Estimation

Round each value to one significant figure to make an estimate:$$6.8 \times 44 - 191$$\(7 \times 40 - 200 = 80\)

Pie Charts (1)

A pie chart shows the colours of 45 books. What sector angle represents the
6 red books?
48°

Graph Linear (2)

What is the equation?

Pie Charts (2)

A pie chart shows the colours of 180 hats. How many green hats are represented
by a sector
angle of 146°?
73

Surds (1)

Simplify:
$$\sqrt{75}$$
\(5\sqrt{3}\)

Surds (2)

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

Surds (3)

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

Speed, Distance, Time

Find the time needed to travel 120 km at 50 km/h.
🛴2:24

Factorising by Grouping

Factorise:

\(xy + 2x + 3y + 6\)

\((x+3)(y+2)\)

Algebraic Fractions

Simplify:

\(\dfrac{3a}{4} \div \dfrac{9a}{10}\)

\(\dfrac{5}{6}\)

Equations with Fractions

Solve:

\(\dfrac{2}{x+2}+\dfrac{3}{2x-1}=1\)

\(x=-1 \text{ or } 3\)