Refreshing Revision

Number Sequences 1

What is the 9th:
a) Odd number; 17
b) Square number; 81
c) Prime number. 23

Factors

Find all the factors of:

22

1, 2, 11, 22.

Multiples

Subtract the 7th from the 10th 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

Round the following numbers to three significant figures:
a) 74.63; 74.6
b) 526711; 527000
c) 0.003195; 0.00320

Area of a Triangle

Find the area of a triangle that has a base of 3cm and a height of 8cm.

12cm2

Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 6cm and a top (parallel to base) of 5cm. 48cm2

Fractions (Adding)

Evaluate:

\( \frac{2}{5} + \frac{8}{9}\) \(= 1\frac{13}{45}\)

Fractions (Multiplying)

Evaluate:

\( \frac{1}{3} × \frac{4}{5}\) \(= \frac{4}{15}\)

Fractions (Dividing)

Evaluate:

\( \frac{2}{3} ÷ \frac{7}{5}\) \(= \frac{10}{21}\)

Circle (Vocabulary)

Name the red part.

Circle part Circle part

Venn Diagrams

Describe the red region.

Circle part Circle part

Shape Formulas

What is the formula?

Circle part Circle part

Formulas (Advanced)

What is it?

Circle part Circle part

Fraction to Percentage

Convert this fraction to a percentage to 3 significant figures.

\( \frac{4}{7}\) \(= 57.1\)%

Circle Area

Find the area of a circle that has a radius of 6cm. Give your answer to three significant figures.

113cm2

Circle Circumference

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

50.3cm2

Decimals (Adding)

Calculate the value of:

9.9 + 4.9

= 14.8

Decimals (Subtracting)

Calculate the value of:

9.1 − 1.9

= 7.2

Decimals (Multiplying)

Calculate the value of:

7.6 × 3.9

= 29.64

Decimals (Dividing)

Calculate the value of:

83.6 ÷ 19

= 4.4

Indices (Simple)

What is the value of:

32

= 9

Indices (Advanced)

What is the value of:

30

= 1

Basic Addition

Calculate the value of:

37 + 47

= 84

Basic Subtraction

Calculate the value of:

71 − 27

= 44

Basic Multiplication

Calculate the value of:

97 × 44

= 4268

Basic Division 2

Calculate the value of:

2112 ÷ 22

= 96

Percentage (Of)

Find the value of:

45% of 100

= 45

Standard Form 1

Find the value of:

2.33 × 106

= 2330000

Highest Common Factor

Find the highest common factor of thirty six and twelve.

= 12

Times Tables (2-5)

4 × 4 = 16

3 × 5 = 15

5 × 3 = 15

8 × 5 = 40

9 × 4 = 36

6 × 4 = 24

7 × 3 = 21

2 × 5 = 10

Times Tables (2-12)

4 × 2 = 8

3 × 4 = 12

5 × 10 = 50

9 × 8 = 72

6 × 3 = 18

7 × 8 = 56

8 × 6 = 48

2 × 3 = 6

Times Tables (2)

5 × 2 = 10

6 × 2 = 12

4 × 2 = 8

3 × 2 = 6

7 × 2 = 14

8 × 2 = 16

9 × 2 = 18

2 × 2 = 4

Times Tables (3)

7 × 3 = 21

4 × 3 = 12

9 × 3 = 27

3 × 3 = 9

5 × 3 = 15

6 × 3 = 18

8 × 3 = 24

2 × 3 = 6

Times Tables (4)

9 × 4 = 36

8 × 4 = 32

7 × 4 = 28

4 × 4 = 16

5 × 4 = 20

3 × 4 = 12

6 × 4 = 24

2 × 4 = 8

Times Tables (5)

4 × 5 = 20

6 × 5 = 30

3 × 5 = 15

8 × 5 = 40

5 × 5 = 25

9 × 5 = 45

7 × 5 = 35

2 × 5 = 10

Times Tables (6)

3 × 6 = 18

7 × 6 = 42

4 × 6 = 24

5 × 6 = 30

9 × 6 = 54

8 × 6 = 48

6 × 6 = 36

2 × 6 = 12

Times Tables (7)

6 × 7 = 42

8 × 7 = 56

5 × 7 = 35

4 × 7 = 28

9 × 7 = 63

3 × 7 = 21

7 × 7 = 49

2 × 7 = 14

Times Tables (8)

8 × 8 = 64

5 × 8 = 40

4 × 8 = 32

7 × 8 = 56

9 × 8 = 72

6 × 8 = 48

3 × 8 = 24

2 × 8 = 16

Times Tables (9)

3 × 9 = 27

6 × 9 = 54

8 × 9 = 72

5 × 9 = 45

7 × 9 = 63

9 × 9 = 81

4 × 9 = 36

2 × 9 = 18

Times Tables (12)

7 × 12 = 84

8 × 12 = 96

4 × 12 = 48

6 × 12 = 72

5 × 12 = 60

9 × 12 = 108

3 × 12 = 36

2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

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

Fractions (Mixed)

Evaluate:

\( 2\frac{4}{5} − \frac{7}{8}\) \(= 1\frac{37}{40}\)

Pythagoras

Find BC if AB = 3.1m and AC = 4.9m. 5.80m

Trigonometry (Angle)

Find angle BCA if AC = 4.7m and BC = 6.2m. 40.7o

Trigonometry (Side)

Find AC if angle ABC = 33o and AB = 3.7m. 2.40m

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.

\( \frac{2}{7}\) \(= 0.286\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.49\) = \( \frac{49}{100}\)

Percentage (Increase)


Increase £20 by 15%

£23

Lowest Common Multiple

What is the lowest common multiple of twenty and thirty.

= 60

Sequence (Arithmetic)

5,17,29,41,53...

Find the:
a) next term; 65
b) nth term; 12n - 7
c) term number 50; 593

Sequence (Geometric)

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

Find the:
a) next term; 160
b) nth term; 5 × 2n-1
c) term number 10; 2560

Interest (Simple)

If £100 is invested for 4 years with a simple interest rate of 3%, find the amount of interest earned. £12.00

Interest (Compound)

If £120 is invested with an interest rate of 3% compounded annually, find the value of the investment after 5 years. £139.11

Currency Exchange

If £1 is worth $1.45, convert:

a) £200 to dollars; $290.00

b) $120 to pounds; £137.93

Coordinates (Midpoint)

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

\((1,5) \text{ and } (13,17)\)

(7,11)

Gradient

What is the gradient of the line joining:

\((8,-4) \text{ and } (13,1)\)

1

Coordinates (Square)

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

\((2,2),(5,7),(-3,5)\)

(0,10)

Negative Numbers

a) 7 − 15 = -8
b) 7 × (-7) = -49
c) (10−21)(7−17) = 110
d) 49 ÷ (-7) = -7
e) (-9)2 = 81

Substitution

If p = 6, q = 21 and
r = -7 evaluate:

a) 2q − p = 36
b) pq + r = 119
c) p2 − 5q - r = -62

Equations (Type 1)

Solve:

\(5x = 30\)

\(x = 6\)

Equations (Type 2)

Solve:

\(5x +3= 13\)

\(x = 2\)

Equations (Type 3)

Solve:

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

\(x = 2\)

Equations (Type 4)

Solve:

\(4(2x +4)+10= 90\)

\(x = 8\)

Equations (Type 5)

Solve:

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

\(x = 0.143 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(3x-5y = 8\)
\(2x-5y = 2\)

\(x = 6, y = 2\)

Equations (Simultaneous 2)

Solve:

\(4x+2y = 28\)
\(3x-8y = -36\)

\(x = 4, y = 6\)

Equations (Simultaneous 3)

Solve:

\(3x-7y = -36\)
\(6x-4y = -42\)

\(x = -5, y = 3\)

Sets (Union)

Find the union of:

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

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

Sets (Intersection)

Find the intersection of:

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

{5,7,9}

Bearings

A plane flies from point A to point B on a bearing of 199o. What bearing would it return on from B to A? 019o

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:

4 + (9 × 82 − 2)

578

Simplify

Simplify the following by collecting like terms:

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

\(11m+15\)

Ratio

Divide 165 in the ratio

2:9

30 and 135

Graph (Linear)

Draw a rough sketch of the graph of:

\(y=-x+1\)

Gradient -1
y intercept 1

Prime Factors

Express the following number as the product of prime numbers:

31

31

Percentage (Reverse)

In a sale an item costs £64 after a 20% reduction. What was the original price?

£80

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?

Circle part Circle part

Time (Digital)

Sketch a clock face:

Circle part Circle part

Decimals (Recurring)

Write the following recurring decimal as a fraction in its lowest terms.

0.666666... \(\frac{2}{3}\)

Percentage (Decrease)


Decrease £120 by 35%

£78

Brackets (Linear)

Expand:

\(8(5x-8)\)

\(40x-64\)

Brackets (Quadratic)

Expand:

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

\(4x^2+4x-8\)

Factorise (Linear)

Factorise:

\(9x-72\)

\(9(1x-8)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-x-6\)

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

Factorise (Quadratic 2)

Factorise:

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

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

Circle Theorems

Which theorem?

Circle part Circle part

Standard Form 2

Find the value of:

8.25 × 10-2

= 0.0825

Standard Form 3

Write in standard form:

8090000

= 8.09 × 106

Standard Form 4

Write in standard form:

0.00655

= 6.55 × 10-3

Sequence (Quadratic)

Find the nth term:

\(5, 13, 25, 41, 61, \)

\(2n^2+2n+1\)

Standard Form 5

Multiply 7 × 105
by 5 × 105 and give the answer in standard form.

= 3.5 × 1011

Equations (Quadratic 1)

Solve:

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

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

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

\(x = 0.358\) and \(-0.558\)

Polygon Angles

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

51.4°

Interior and Exterior angles

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:

5382 ÷ 6

= 897

Number Sequences 2

What is the 12th:
a) Cube number; 1728
b) Triangular number; 78
c) Fibonacci number. 144


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