Refreshing Revision

Number Sequences 1

What is the 11th:
a) Odd number; 21
b) Square number; 121
c) Prime number. 31

Factors

Find all the factors of:

29

1, 29.

Multiples

Subtract the 6th from the 11th multiples of:

6

30

Polygons

What are the names of regular polygons with:
a) eight sides;
b) nine sides;
c) ten sides.

Octagon, Nonagon and Decagon (all regular)

Rounding

Round the following numbers to three significant figures:
a) 14.27; 14.3
b) 588967; 589000
c) 0.003295; 0.00330

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 15cm, a height of 7cm and a top (parallel to base) of 5cm. 70cm2

Fractions (Adding)

Evaluate:

\( \frac{3}{4} + \frac{5}{6}\) \(= 1\frac{7}{12}\)

Fractions (Multiplying)

Evaluate:

\( \frac{3}{4} × \frac{6}{8}\) \(= \frac{9}{16}\)

Fractions (Dividing)

Evaluate:

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

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 12cm. Give your answer to three significant figures.

75.4cm2

Decimals (Adding)

Calculate the value of:

9.9 + 7.8

= 17.7

Decimals (Subtracting)

Calculate the value of:

9.4 − 2.8

= 6.6

Decimals (Multiplying)

Calculate the value of:

4.7 × 7.5

= 35.25

Decimals (Dividing)

Calculate the value of:

79.8 ÷ 19

= 4.2

Indices (Simple)

What is the value of:

52

= 25

Indices (Advanced)

What is the value of:

4-2

= 0.0625

Basic Addition

Calculate the value of:

26 + 69

= 95

Basic Subtraction

Calculate the value of:

81 − 26

= 55

Basic Multiplication

Calculate the value of:

92 × 66

= 6072

Basic Division 2

Calculate the value of:

1584 ÷ 18

= 88

Percentage (Of)

Find the value of:

30% of 80

= 24

Standard Form 1

Find the value of:

9.27 × 105

= 927000

Highest Common Factor

Find the highest common factor of twenty one and nine.

= 3

Times Tables (2-5)

3 × 5 = 15

5 × 3 = 15

6 × 5 = 30

7 × 5 = 35

4 × 3 = 12

9 × 4 = 36

8 × 2 = 16

2 × 2 = 4

Times Tables (2-12)

4 × 11 = 44

7 × 8 = 56

3 × 3 = 9

9 × 12 = 108

6 × 4 = 24

5 × 10 = 50

8 × 11 = 88

2 × 10 = 20

Times Tables (2)

3 × 2 = 6

5 × 2 = 10

4 × 2 = 8

7 × 2 = 14

9 × 2 = 18

6 × 2 = 12

8 × 2 = 16

2 × 2 = 4

Times Tables (3)

5 × 3 = 15

4 × 3 = 12

6 × 3 = 18

9 × 3 = 27

8 × 3 = 24

3 × 3 = 9

7 × 3 = 21

2 × 3 = 6

Times Tables (4)

7 × 4 = 28

9 × 4 = 36

3 × 4 = 12

5 × 4 = 20

8 × 4 = 32

6 × 4 = 24

4 × 4 = 16

2 × 4 = 8

Times Tables (5)

9 × 5 = 45

8 × 5 = 40

5 × 5 = 25

4 × 5 = 20

6 × 5 = 30

7 × 5 = 35

3 × 5 = 15

2 × 5 = 10

Times Tables (6)

4 × 6 = 24

5 × 6 = 30

7 × 6 = 42

6 × 6 = 36

8 × 6 = 48

3 × 6 = 18

9 × 6 = 54

2 × 6 = 12

Times Tables (7)

9 × 7 = 63

6 × 7 = 42

7 × 7 = 49

8 × 7 = 56

5 × 7 = 35

3 × 7 = 21

4 × 7 = 28

2 × 7 = 14

Times Tables (8)

6 × 8 = 48

7 × 8 = 56

5 × 8 = 40

4 × 8 = 32

3 × 8 = 24

8 × 8 = 64

9 × 8 = 72

2 × 8 = 16

Times Tables (9)

6 × 9 = 54

5 × 9 = 45

8 × 9 = 72

9 × 9 = 81

7 × 9 = 63

4 × 9 = 36

3 × 9 = 27

2 × 9 = 18

Times Tables (12)

7 × 12 = 84

8 × 12 = 96

5 × 12 = 60

4 × 12 = 48

3 × 12 = 36

9 × 12 = 108

6 × 12 = 72

2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

\( \frac{4}{16}\) \(= \frac{1}{4}\)

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find BC if AB = 4.4m and AC = 5.7m. 7.20m

Trigonometry (Angle)

Find angle ABC if AC = 3.3m and BC = 4.4m. 48.6o

Trigonometry (Side)

Find AC if angle BCA = 27o and AB = 4.7m. 9.22m

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.

\( \frac{3}{8}\) \(= 0.375\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.14\) = \( \frac{7}{50}\)

Percentage (Increase)


Increase £60 by 45%

£87

Lowest Common Multiple

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

= 42

Sequence (Arithmetic)

7,20,33,46,59...

Find the:
a) next term; 72
b) nth term; 13n - 6
c) term number 31; 397

Sequence (Geometric)

5,20,80,320,1280...

Find the:
a) next term; 5120
b) nth term; 5 × 4n-1
c) term number 9; 327680

Interest (Simple)

If £200 is invested for 7 years with a simple interest rate of 6%, find the amount of interest earned. £84.00

Interest (Compound)

If £160 is invested with an interest rate of 3% compounded annually, find the value of the investment after 5 years. £185.48

Currency Exchange

If £1 is worth $1.48, convert:

a) £100 to dollars; $148.00

b) $160 to pounds; £67.57

Coordinates (Midpoint)

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

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

(-2,5)

Gradient

What is the gradient of the line joining:

\((4,-8) \text{ and } (9,-3)\)

1

Coordinates (Square)

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

\((1,3),(5,6),(-2,7)\)

(2,10)

Negative Numbers

a) 8 − 15 = -7
b) 8 × (-6) = -48
c) (5−17)(12−22) = 120
d) 48 ÷ (-6) = -8
e) (-6)2 = 36

Substitution

If p = 6, q = 20 and
r = -7 evaluate:

a) 2q − p = 34
b) pq + r = 113
c) p2 − 5q - r = -57

Equations (Type 1)

Solve:

\(5x = 25\)

\(x = 5\)

Equations (Type 2)

Solve:

\(2x +7= 15\)

\(x = 4\)

Equations (Type 3)

Solve:

\(10x -4= 5x + 36\)

\(x = 8\)

Equations (Type 4)

Solve:

\(5(2x +6)-5= 55\)

\(x = 3\)

Equations (Type 5)

Solve:

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

\(x = -1.625\)

Equations (Simultaneous 1)

Solve:

\(6x-3y = 9\)
\(5x+3y = 46\)

\(x = 5, y = 7\)

Equations (Simultaneous 2)

Solve:

\(4x-4y = 0\)
\(5x-16y = -44\)

\(x = 4, y = 4\)

Equations (Simultaneous 3)

Solve:

\(5x-7y = 79\)
\(4x-7y = 69.5\)

\(x = 9.5, y = -4.5\)

Sets (Union)

Find the union of:

{2,4,6,8,10} and
{1,3,6,10,15}

{1,2,3,4,6,8,10,15}

Sets (Intersection)

Find the intersection of:

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

{5,7}

Bearings

A plane flies from point A to point B on a bearing of 083o. What bearing would it return on from B to A? 263o

Probability

A number is picked at random from the set

{2,6,12}

what is the probability it is even? 1

BIDMAS

Evaluate:

82 − 9 × 7 + 5

6

Simplify

Simplify the following by collecting like terms:

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

\(11m+15\)

Ratio

Divide 104 in the ratio

7:1

91 and 13

Graph (Linear)

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:

39

3 x 13

Percentage (Reverse)

In a sale an item costs £85 after a 15% reduction. What was the original price?

£100

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?

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.

0.454545... \(\frac{5}{11}\)

Percentage (Decrease)


Decrease £140 by 35%

£91

Brackets (Linear)

Expand:

\(2(5x-6)\)

\(10x-12\)

Brackets (Quadratic)

Expand:

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

\(3x^2-8x-16\)

Factorise (Linear)

Factorise:

\(9x-27\)

\(9(1x-3)\)

Factorise (Quadratic 1)

Factorise:

\(x^2+x-2\)

\((x+2)(x-1)\)

Factorise (Quadratic 2)

Factorise:

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

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

Circle Theorems

Which theorem?

Circle part Circle part

Standard Form 2

Find the value of:

6.07 × 10-3

= 0.00607

Standard Form 3

Write in standard form:

8000

= 8 × 103

Standard Form 4

Write in standard form:

0.000297

= 2.97 × 10-4

Sequence (Quadratic)

Find the nth term:

\(1, 12, 29, 52, 81, \)

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

Standard Form 5

Multiply 8 × 105
by 9 × 103 and give the answer in standard form.

= 7.2 × 109

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:

\(2x^2+4x-2 = 0\)

\(x = 0.414\) and \(-2.41\)

Polygon Angles

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

144°

Interior and Exterior angles

Change The Subject

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

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

Basic Division 1

Calculate the value of:

7308 ÷ 9

= 812

Number Sequences 2

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


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