Refreshing Revision

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:

36

1, 2, 3, 4, 6, 9, 12, 18, 36.

Multiples

Subtract the 6th from the 11th multiples of:

10

50

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) 90.44; 90.4
b) 475266; 475000
c) 89; 89.0
d) 0.008995; 0.00900

Area of a Triangle

Find the area of a triangle that has a base of 5cm and a height of 9cm.

22.5cm²

Area of a Trapezium

Find the area of a trapezium that has a base of 13cm, a height of 11cm and a top (parallel to base) of 5cm. 99cm²

Fractions (Adding)

Evaluate:

$ \frac{4}{6} + \frac{9}{12}$ $= 1\frac{5}{12}$

Fractions (Multiplying)

Evaluate:

$ \frac{1}{2} × \frac{4}{6}$ $= \frac{1}{3}$

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 10cm. Give your answer to three significant figures.

314cm²

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:

7.5 + 3.5

= 11

Decimals (Subtracting)

Calculate the value of:

8.3 − 2.8

= 5.5

Decimals (Multiplying)

Calculate the value of:

5.2 × 3.6

= 18.72

Decimals (Dividing)

Calculate the value of:

109.2 ÷ 14

= 7.8

Indices (Simple)

What is the value of:

4³

= 64

Indices (Advanced)

What is the value of:

$3^{1}$

$= 3$

Basic Addition

Calculate the value of:

47 + 27

= 74

Basic Subtraction

Calculate the value of:

92 − 28

= 64

Basic Multiplication

Calculate the value of:

54 × 94

= 5076

Basic Division 2

Calculate the value of:

688 ÷ 16

= 43

Percentage (Of)

Find the value of:

50% of 280

= 140

Standard Form 1

Find the value of:

8.03 × 10³

= 8030

Highest Common Factor

Find the highest common factor of twenty one and six.

= 3

Times Tables (2-5)

6 × 4 = 24	5 × 4 = 20
8 × 4 = 32	4 × 4 = 16
7 × 3 = 21	3 × 5 = 15
9 × 5 = 45	2 × 2 = 4

Times Tables (2-12)

4 × 3 = 12	9 × 11 = 99
8 × 8 = 64	5 × 4 = 20
6 × 10 = 60	7 × 4 = 28
3 × 11 = 33	2 × 9 = 18

Times Tables (2)

9 × 2 = 18	5 × 2 = 10
7 × 2 = 14	6 × 2 = 12
4 × 2 = 8	3 × 2 = 6
8 × 2 = 16	2 × 2 = 4

Times Tables (3)

6 × 3 = 18	9 × 3 = 27
8 × 3 = 24	7 × 3 = 21
5 × 3 = 15	3 × 3 = 9
4 × 3 = 12	2 × 3 = 6

Times Tables (4)

6 × 4 = 24	5 × 4 = 20
9 × 4 = 36	7 × 4 = 28
3 × 4 = 12	4 × 4 = 16
8 × 4 = 32	2 × 4 = 8

Times Tables (5)

6 × 5 = 30	5 × 5 = 25
3 × 5 = 15	4 × 5 = 20
7 × 5 = 35	9 × 5 = 45
8 × 5 = 40	2 × 5 = 10

Times Tables (6)

6 × 6 = 36	8 × 6 = 48
4 × 6 = 24	7 × 6 = 42
5 × 6 = 30	3 × 6 = 18
9 × 6 = 54	2 × 6 = 12

Times Tables (7)

9 × 7 = 63	5 × 7 = 35
6 × 7 = 42	7 × 7 = 49
8 × 7 = 56	4 × 7 = 28
3 × 7 = 21	2 × 7 = 14

Times Tables (8)

7 × 8 = 56	8 × 8 = 64
6 × 8 = 48	9 × 8 = 72
3 × 8 = 24	4 × 8 = 32
5 × 8 = 40	2 × 8 = 16

Times Tables (9)

5 × 9 = 45	9 × 9 = 81
8 × 9 = 72	7 × 9 = 63
6 × 9 = 54	4 × 9 = 36
3 × 9 = 27	2 × 9 = 18

Times Tables (12)

8 × 12 = 96	9 × 12 = 108
4 × 12 = 48	5 × 12 = 60
6 × 12 = 72	3 × 12 = 36
7 × 12 = 84	2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

$ \frac{6}{9}$ $= \frac{2}{3}$

Fractions (Mixed)

Evaluate:

$ 1\frac{2}{3} − \frac{6}{7}$ $= \frac{17}{21}$

Pythagoras

Find BC if AB = 6m and AC = 7.2m. 9.37m

Trigonometry (Angle)

Find angle ABC if AC = 4.7m and BC = 6.1m. 50.4^o

Trigonometry (Side)

Find AC if angle BCA = 20^o and AB = 3.7m. 10.2m

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}{8}$ $= 0.5$

Decimal to Fraction

Convert this decimal to a fraction.

$0.26$ = $ \frac{13}{50}$

Percentage (Increase)

Increase £160 by 30%

£208

Lowest Common Multiple

What is the lowest common multiple of six and ten.

= 30

Sequence (Arithmetic)

5,12,19,26,33...

Find the:
a) next term; 40
b) n^th term; 7n - 2
c) term number 34; 236

Sequence (Geometric)

5,10,20,40,80...

Find the:
a) next term; 160
b) n^th term; 5 × 2^n-1
c) term number 11; 5120

Interest (Simple)

If £140 is invested for 8 years with a simple interest rate of 4%, find the amount of interest earned. £44.80

Interest (Compound)

If £140 is invested with an interest rate of 3% compounded annually, find the value of the investment after 4 years. £157.57

Currency Exchange

If £1 is worth $1.36, convert:

a) £120 to dollars; $163.20

b) $240 to pounds; £176.47

Coordinates (Midpoint)

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

$(-4,-4) \text{ and } (6,8)$

(1,2)

Gradient

What is the gradient of the line joining:

$(4,8) \text{ and } (7,11)$

1

Coordinates (Square)

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

$(5,2),(11,5),(2,8)$

(8,11)

Negative Numbers

a) 5 − 13 = -8
b) 5 × (-6) = -30
c) (11−16)(6−16) = 50
d) 30 ÷ (-6) = -5
e) (-7)² = 49

Substitution

If p = 5, q = 18 and
r = -11 evaluate:

a) 2q − p = 31
b) pq + r = 79
c) p² − 5q - r = -54

Equations (Type 1)

Solve:

$3x = 24$

$x = 8$

Equations (Type 2)

Solve:

$2x -3= 5$

$x = 4$

Equations (Type 3)

Solve:

$8x +5= 5x + 29$

$x = 8$

Equations (Type 4)

Solve:

$5(4x +3)-11= 104$

$x = 5$

Equations (Type 5)

Solve:

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

$x = -0.5$

Equations (Simultaneous 1)

Solve:

$3x-5y = -16$
$2x+5y = 31$

$x = 3, y = 5$

Equations (Simultaneous 2)

Solve:

$4x-2y = -4$
$6x-6y = -24$

$x = 2, y = 6$

Equations (Simultaneous 3)

Solve:

$3x+5y = 37.5$
$5x-3y = 28.5$

$x = 7.5, y = 3$

Sets (Union)

Find the union of:

{6,7,8,9,10} and
{2,6,12}

{2,6,7,8,9,10,12}

Sets (Intersection)

Find the intersection of:

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

{6,10}

Bearings

A plane flies from point A to point B on a bearing of 297^o. What bearing would it return on from B to A? 117^o

Probability

A number is picked at random from the set

{2,6,12}

what is the probability it is even? 1

BIDMAS

Evaluate:

3² − 9 × 8 + 7

-56

Simplify

Simplify the following by collecting like terms:

$3y+2w+7y$

$10y+2w$

Ratio

Divide 25 in the ratio

4:1

20 and 5

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:

72

2 x 2 x 2 x 3 x 3

Percentage (Reverse)

In a sale an item costs £133 after a 5% reduction. What was the original price?

£140

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.

0.747474... $\frac{74}{99}$

Percentage (Decrease)

Decrease £140 by 10%

£126

Brackets (Linear)

Expand:

$3(9x-2)$

$27x-6$

Brackets (Quadratic)

Expand:

$(2x+3)(4x-1)$

$8x^2+10x-3$

Factorise (Linear)

Factorise:

$6x-27$

$3(2x-9)$

Factorise (Quadratic 1)

Factorise:

$x^2+3x-4$

$(x+4)(x-1)$

Factorise (Quadratic 2)

Factorise:

$16x^2-1$

$(4x+1)(4x-1)$

Circle Theorems

Which theorem?

Standard Form 2

Find the value of:

1.69 × 10^-5

= 0.0000169

Standard Form 3

Write in standard form:

5490

= 5.49 × 10³

Standard Form 4

Write in standard form:

0.0017

= 1.7 × 10^-3

Sequence (Quadratic)

Find the n^th term:

$6, 13, 22, 33, 46, $

$n^2+4n+1$

Standard Form 5

Multiply 7 × 10³
by 8 × 10³ and give the answer in standard form.

= 5.6 × 10⁷

Equations (Quadratic 1)

Solve:

$x^2-2x-15= 0$

$x = 5$ and $-3$

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

$5x^2+x-5 = 0$

$x = 0.905$ and $-1.10$

Polygon Angles

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

144°

Change The Subject

Make $d$ the subject of the formula
$$e=\frac{2d-1}{3}$$

$$d=\frac{3e+1}{2}$$

Basic Division 1

Calculate the value of:

4975 ÷ 5

= 995

Number Sequences 2

What is the 10th:
a) Cube number; 1000
b) Triangular number; 55
c) Fibonacci number. 55

Square Numbers

What is the square root of

16

4

Prime Numbers

What is the 4th prime number?

7

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: 0.99, 9.9, 9.99, 0.9, 9, 9.09, 0.09, in ascending order.
0.09, 0.9, 0.99, 9, 9.09, 9.9, 9.99,

Lengths (Ordering)

Write down these lengths: 18mm, 1.08m, 1.8m, 17cm, 107cm, 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

Angle diagram j = 97

Angles with Parallels 2

Angle diagram j = 58

Rounding (1sf)

Round to one significant figure:
a) 74.86; 70
b) 157681; 200000
c) 94; 90
d) 0.00857; 0.009

Estimation

Round each value to one significant figure to make an estimate:$$7.6 \times 74 - 192$$$8 \times 70 - 200 = 360$

Pie Charts (1)

A pie chart shows the colours of 6 books. What sector angle represents the
4 red books?
240°

Graph Linear (2)

What is the equation?

$y=2-0.5x$

Pie Charts (2)

A pie chart shows the colours of 30 hats. How many green hats are represented
by a sector
angle of 252°?
21

Surds (1)

Simplify:
$$\sqrt{32}$$
$4\sqrt{2}$

Surds (2)

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

Surds (3)

Simplify:
$$\dfrac{5}{2 - \sqrt{3}}$$$\frac{10 + 5\sqrt{3}}{1} = 10 + 5\sqrt{3}$

Speed, Distance, Time

What distance is covered by a jogger running at 40 km/h for 8 hours?
👟320 km