1. MATHEMATICS REVISION 9-1
WATCH CAREFULLY!

2. 1 – Time/Calendar/Temp/ Conversion
Revision session

3. Metric Imperial Km, m, cm Tonne, kg, g , mg
L, ml
Miles, yards, feet, inches,
Ton, stone, pounds, ounces
Gallons, Fluid ounces

4. Metric Units 1 L = 1 000 ml 1 Tonne = 1 000 kg 1 kg = 1 000 g
1 g = mg
1 km = m
1 m = mm
10 mm = 1 cm
100cm = 1m
1000 = 1km

5. Metric Measures Capacity 1 Litre = 1000ml 330ml = 0.33Litres

6. 30 Days have Sep, Apr, Jun, Nov

7. Density = m/v Speed = Dist/ Time

8. 2-Number
Revision session

9. Thirty one thousand four hundred and seven in figures
31,407
8, 16, 24, 32,…
Multiples 8
Factors 12
1, 2, 3, 4, 6, 12
2, 3, 5, 7, 11, 13…
Prime Number
Square Numbers
1, 4, 9, 16, 25…

11. Percentages 50% is a half so ÷ by 2 25% is a quarter so ÷ by 4
10% is ÷ by 10
40% is ÷ by 10 and x by 4

12. Fractions
Find 25% or a quarter of £12
12 divided by 4
= £3

14. Fractions of amounts
of 20
Split 20 into 5 equal groups 4
So is 4+4=8

15. FRACTIONS
WHEN ADDING FRACTIONS ALL FRACTIONS MUST HAVE THE SAME DENOMINATOR 1 5 2 + = 3 5
Easy!!! 15

16. MULTIPLICATION OF FRACTIONS
FRACTIONS CAN BE MULTIPLIED, BY MULTIPLYING THE DENOMINATORS TOGETHER AND THE NUMERATORS TOGETHER 2 1 5 2 x = 25 16

17. NOTE: IF POSSIBLE ALWAYS CANCEL FRACTIONS DOWN.
DIVISION OF FRACTIONS
WHEN YOU DIVIDE FRACTIONS- TURN THE SECOND FRACTION UPSIDE DOWN AND MULTIPLY.
NOTE: IF POSSIBLE ALWAYS CANCEL FRACTIONS DOWN. 1 2 1 5 ÷ 2 5 10 1 5 2 = x ÷ = 5 17

18. 1 (a) Work out.
x =
1 (b) Work out.
÷ =
Give your answer as a fraction in its simplest form.
[2]
[2]
3 x 1
4 x 4 3 16 = 32 1 6 3 12 1 4 x = = 18

20. . Decimals- Place Value Th H T U 1 4 3 8 5 7 9
What is the value of the...
1,000 1 4 3 8 5 7 9
400 30 8
0.5
0.07
0.009

21. Fractions and Decimals1 5
= 2 10
= 0.2
= 0.7

22. X10 numbers move 1 left Th H t u . 2 3 8

23. X100 numbers move 2 left Th H T U . 6 4 8

24. ÷ 10 numbers move 1 right Th H t u . 3 5 7

25. Bidmas Brackets Indices Division Multiplication Addition Subtraction
This is the order that the questions must be completed in. 25

26. Square and Square Root
√ Square root
√81 = 9
Square of 6 = 62 = 36

27. For example 6 + 2 x 3 And 6 + 6 4 x 22 + (3 x 5) 12 Not 24!!! 31 12
Not 24!!!
4 x
4 x 31 27

28. 11 25 x 5 ( working out the power) = 125 (a) Solve 52 x (3 + 2) =
52 x 5 (working out the brackets)
25 x 5 ( working out the power)
= 125
[2]
(b) Solve =
(working left to right) 11

30. Addition and Subtraction of Decimals
Always keep the decimal point in the same place and then all the numbers will be have the correct place value. 1 1 9 4 1 2 . 5 4 .

31. Multiplication of Decimals
5.3 x 4 =
Notice there is only one decimal place in the question, so there should only be one in the answer. Do
53 x 4 = 212
One decimal place gives 21.2

32. Put in the decimal point gives 1.476
1.23 x 1.2
There are three numbers after the decimal points, so there will be three numbers after the decimal point in the answer. Do
123 x 12 =1476
Put in the decimal point gives 1.476 32

33. 1 Work out.
(a) 0·6 × 0·4
6 x 4 = 24 (2 places in question)
= [1]
2 (a) Work out.
(i) 9·6 – 3·
- 3.42
[1] 1 8 6 . 33

35. 3- Standard Form
Revision session

36. Standard Form
(A number between 1 & 10) x 10? 5.2 x x 10-5

37. Negative power means a small number so divide by 10
0.12
0.012
1 250
125
12.5
1.25
1.25 x 104
60 052
600.52
60.052
x 106

38. 4- Money & Problems
Revision session

39. Multiplcation
=128
32 x 4 = X 30 2 4
120 8

40. seats
_851
200
651
651 x 8
+1200
5208
6408
6408 Is close to 6500

42. Ratio Simplify Ratio is the same as cancelling down fractions.
20:30 Both numbers can be divided by 10.
Giving
2:3
7:35
Gives 1: 5 Both numbers can be divided by 7

43. (a) In a lottery, Martin won £1800 and Pat won £4200.
Work out the ratio of Martin’s winnings to Pat’s winnings.
Give your answer in its simplest form.
: [2]
Martin
Pat
1800
4200
÷100
18 : 42 ÷6
3 : 7

44. Finding quantities using Ratios
Red paint is added to white paint in the ratio
3:2.
How much of each colour paint will I need if I
need 40 litres in total.
Total
Red : White
Altogether there are 5
parts (3 + 2)
3:2 x8 : 40
40 ÷ 5 = 8
Red paint (3 parts) = 3 x 8 = 24
Litres
White paint (2 parts) = 2 x 8 = 16
Litres 44

45. Peter
Marion
(b) Marion and Peter won £200 in a raffle.
They shared the £200 between them in the ratio 1 : 4.
How much was Peter’s share?
£ [2] : 1 : 4
5 parts
X 40 40 :
160
200 parts

46. Algebra
Revision session

47. INDICES a + a + a = a x a x a = 23 X 26 = 45 ÷ 42 = 3a a3 29
(ADD POWERS) 43
(SUBTRACT POWERS) 47

48. (a) Sam simplifies p × p × p × p × p.
She thinks the answer is 5p.
Explain why her answer is wrong.
[1]

49. p + p + p + p + p = 5p, whereas p x p x p x p x p = p5
(a) Sam simplifies p × p × p × p × p.
She thinks the answer is 5p.
Explain why her answer is wrong.
p + p + p + p + p = 5p, whereas
p x p x p x p x p = p5
[1]

50. 4+8 12
(a) simplify 54 x 5 8
[2]
(b) Simplify 74 ÷ 7 2 = 5 = 5
4-2 2 = 7 = 7 50

51. A Sequence is a set of numbers linked by a pattern.
…… Rule is +8
…… Rule is +5

52. nth term of a sequence -5 n + 8 20 17 14 11 8 5 …… +23 n -3 -5
……. n
+ 8 ……
+23 n -3

53. Basic Algebra
3( 4 + f)
There is a secret x between the 3 and the bracket.
Everything in the bracket has to be x by 3.
3( 4 + f) = 12
+ 3f 53

54. 4x - 24 5 x f =5f 5f-15 --------- [1] 4 x x = 4x 4 x - 6 = -24
Expand
4(x − 6)
4 x x = 4x
4 x - 6 = -24
4x - 24
[1]
5(f – 3)
5 x f =5f
5 x -3 = -15
5f-15
[1] 54

55. Following the rules Weekly pay = £210
Rate of pay per hour
x hours worked
+ bonus
Jody worked 30 hours at a rate of £6 and gained a bonus of £30. 30 £6
£30
Weekly pay = x +
Weekly pay =
£180 + £30
Weekly pay = £210

56. Equations
Remember 3a
means
3 x a

57. Solving Equations Solving an equation means finding the unknown. (×) x
+ 3
= 15
Subtract 3 2 x = 12
Divide by 2 x = 6

58. 5× = 2× + 6
5× - 2× =
3× = 9
× = 9 / 3
× = 3 58

59. Solve.
(a) 2x – 7 = 5
[2]
2x = 5
(add 7 to both sides or bring over and swap sign)
2x = 5+ 7
2x = 12
x = 12 2
x = 6 59

60. 7x - 2 = 4x – 11 (get x’s on one side) 7x – 4x – 2 = - 11 3x -2 = -11
(b) 7x - 2 = 4x – 11
7x - 2 = 4x – 11
(get x’s on one side)
7x – 4x – 2 = - 11
3x = -11
(get numbers over to the other side)
3x =
( divide both sides by 3)
3x = -9
x = -9 3
x = -3 60

61. 2x – 6 = 7 (multiply out brackets)
Solve
2(x − 3) = 7
2x – 6 = 7 (multiply out brackets)
2x = (collect numbers on one side)
2x = 13
x = 13/2 (divide by 2)
x = 6.5
[3] 61

62. Substitution
Substitution means replacing an unknown (×), with a number.
If × =2, solve
3 × + 4
We replace the × with the 2
(3 x 2) + 4 = 10

63. Formulae
S = 45 – 3p
If p = 5
Then S = 45 – 3 x 5
S = 45 – 15
S = 30

64. If × = 3
Solve
×2 + 4
Answer
32 + 4
= 13 64

65. 16 + 20 36 4 - 10 -6 Work out the value of x2 + 5x when (a) x = 4,
[1]
(b) x = – 2.
x -2
4 - 10 -6
[2] 65

66. PYTHAGORAS x = 5 PYTHAGORAS SAID 3 4 LONGEST 2 = SHORTEST2 + MIDDLE2 x
c2 = a2 + b2
LONGEST 2 = SHORTEST2 + MIDDLE2
x2 =
x2 =
x2 = 25
x = √25
x = 5

67. PYTHAGORAS ALSO SAID.. x = 3 5 x 4 SHORTEST 2 = LONGEST2 - MIDDLE2
c2 = a2 - b2
SHORTEST 2 = LONGEST2 - MIDDLE2
x2 =
x2 =
x2 = 9
x = √9
x = 3

68. LINES ON GRAPHS
THE LINE y = 3 CUTS THROUGH THE y AXIS Y 3 X

69. THE LINE x = 4 CUTS THROUGH THE x AXIS AT 4Y X 4

70. THE LINE y = x MEANS THAT EACH POINT ON THE LINE HAS THE SAME x AND y CO-ORDINATE

71. GRADIENTS AND INTERCEPTS
THE GENERAL EQUATION OF A STRAIGHT LINE IS Y = MX + C
M IS THE GRADIENT OF THE LINE
C IS THE Y-INTERCEPT
Y = 4X + 6
HAS A GRADIENT OF 4 AND CUTS THE Y AXIS AT (0, 6) 4 6 1

72. If you don’t have a table MAKE one! x -1 11 y 2 3 -2 2 6
y = 4x + 2
y = x3
y =
y = 14 Y
y = 4x + 2
y = x2
y = 10
x is -1 up to 3 4

73. INDICES
23 X 26 = 29 (ADD POWERS)
45 ÷ 42 = 43 (SUBTRACT POWERS)

74. Shape
Revision session

75. Angles between 180º and 360º are REFLEX
Angles less than 90º are ACUTE
Angles more than 90º are OBTUSE
90º angles are RIGHT ANGLES
Angles between 180º and 360º are REFLEX

76. AREA OF A RECTANGLE = LENGTH X WIDTH WIDTH LENGTH
REMEMBER THE UNITS CM2

77. AREA OF A RIGHT ANGLED TRIANGLE
BASE X HEIGHT 2
HEIGHT
BASE
REMEMBER THE UNITS CM2

78. Find the area of the shaded region
Base x Height 2
Area of a Triangle =
9 x 8 2
Area of a Rectangle =
Length x Width 72 2
2.5 x 8 20 36
cm2 36 - 20 16
cm2

79. AREA OF A TRAPEZIUM Note: This formulae is NOT given 5 cm 3 cm 7 cm
= ½(5 + 7)3
= ½(12)3
= 6x3
= 18
cm2
Remember the units for area cm2

80. SURFACE AREA OF A CUBOID
The Surface area is the area of all the faces!!!
Area Front
Back
Left
Right
Top
Bottom
4 x 3 =
12 cm2
3cm
12 cm2
2 x 3 =
6 cm2
2cm
6 cm2
4cm
4 x 2 =
8 cm2
8 cm2
52 cm2
REMEMBER THE UNITS CM2

81. VOLUME OF A CUBOID LENGTH X WIDTH X HEIGHT HEIGHT WIDTH LENGTH
REMEMBER THE UNITS CM3

82. QWC means Quality of Written Communication Clear working out!!!
2 cubes
12 cm
3 cubes
5 cubes
5 cm
5 x 3 = 15 cubes
5 cm
5 cm
5 x 3 x 2 = 30 cubes
QWC means Quality of Written Communication
Clear working out!!!
Then... Write your Answer in a sentence
No, He can only fit 30 Cubes in the box

83. VOLUME OF A TRIANGULAR PRISM
AREA OF CROSS-SECTION X LENGTH
CROSS SECTION
LENGTH
REMEMBER THE UNITS OF LENGTH CM3

84. ANGLES IN A TRIANGLE
ADD UP TO 180o
50o
40o

85. ANGLES AROUND A POINT
ADD UP TO 360O
70O
180O
110O

86. OPPOSITE ANGLES
ARE EQUAL b a a b

87. CORRESPONDING ANGLES
ARE EQUAL

88. ALTERNATE ANGLES
ARE EQUAL

89. SUPPLEMENTARY ANGLES
ADD UP TO 1800
a + b = 180O a b

90. EXTERIOR ANGLES OF A POLYGON
EXTERIOR (OUTSIDE) ANGLES OF A POLYGON ADD UP TO 360O 90

91. BEARINGS ALWAYS INCLUDE 3 DIGITS 095O 2750 ALWAYS MEASURE FROM NORTH
ALWAYS MEASURE CLOCKWISE
ALWAYS INCLUDE 3 DIGITS N N
095O
2750

92. CIRCLES CIRCUMFERENCE = π X DIAMETER AREA = π X RADIUS2
REMEMBER TO CHECK WHETHER YOU ARE GIVEN THE RADIUS OR THE DIAMETER
RADIUS
DIAMETER 92

93. CO-ORDINATES x IS HORIZONTAL AND COMES FIRST
y IS VERTICAL AND FOLLOWS THE x y
(x, y) x

94. Reflective Symmetry A shape that has reflective symmetry can be split
exactly in half.

95. Maps & Plans N E W S
Clockwise
Anti clockwise
LEFT
RIGHT

96. Estimating People just under 2m So tree is about 4 times bigger
Tree 8m

97. Shapes rhombus Parallelogram Cube Trapezium Cuboid Cylinder Cone
Sphere

98. 3D Shape
What shape are the faces of this pyramid?
Square
Triangles

99. Views
What is the plan view of this pyramid?

100. Enlargement The green rectangle has been enlarged by Scale factor 3
2cms
6cms
4cms
12cms

101. Interior angles of a quadrilateral
Add up to 3600
1000
800
800
1000

102. The sum of the interior angles of any Polygon
Split the shape into the minimum number of triangles
Angles in a triangle add up to 1800
So, the number of triangles x 1800 = sum of interior angles of a polygon.
6 X 1800 = 10800

103. Work out angle x.
Give reasons for your answer.
x = because…
angles in quadrilateral add up to 3600
so = 3250
=350...
[4]
1270
1150
350
830 x
Angles on a straight line add up to 1800,
1450
so 180 – 35 =

104. CIRCLES CIRCUMFERENCE = Π X DIAMETER AREA = Π X RADIUS2
REMEMBER TO CHECK WHETHER YOU ARE GIVEN THE RADIUS OR THE DIAMETER
RADIUS
DIAMETER

105. Circumference = Π x 6 (twice the radius) = 18.86 cm ( 2.d.p)
Area = Π x 32 (radius2)
= CM2

106. The picture shows a circular coffee table.
The radius of the top of the table is 55 cm.
Calculate the area of the top of the table.
Give the units of your answer and to two decimal places..
[3]

107. The picture shows a circular coffee table.
The radius of the top of the table is 55 cm.
Calculate the area of the top of the table.
Give the units of your answer.
Area = Π x 552
= Π x 3025
= cm2 ( 2 dp)
[3]

108. Plans and Elevations A 3D shape has three different views.
The above view is called the plan
The side view is called the side elevation
The front view is called the front elevation.
108

109. Plan from above Plan Side elevation Side Front elevation
109

110. Here is a plan and front elevation of a prism.
The front elevation shows the cross section of the prism.
On the grid below draw the side elevation

111. Here is a plan and front elevation of a prism.
The front elevation shows the cross section of the prism.
On the grid below draw the side elevation

112. Transformations There are several types of transformations Reflections
Rotations
Translations
Enlargements
112

113. Enlargements
An enlargement changes the size of an object. It does not change its shape.
It can be made bigger or smaller.
The amount by which it is made bigger is called the scale factor.
113

114. The image is 3 times bigger than the object, so this shape has been enlarged by scale factor 3.
114

115. Shape A is shown in the diagram. Shape A is enlarged to obtain the
shape B.
Write down the scale factor of the enlargement.
Complete the drawing of shape B on the diagram.
115

116. Scale factor of enlargement is 1/3
Shape A is shown in the diagram.
Shape A is enlarged to obtain the
shape B.
Write down the scale factor of the enlargement.
Complete the drawing of shape B on the diagram.
Scale factor of enlargement is 1/3
116

117. Rotations To describe a rotation you have to give
The angle of rotation (degrees)
The direction of rotation (clockwise or anticlockwise)
The centre of rotation (give the coordinate).
117

118. Example
To rotate triangle A onto triangle B the centre of rotation is crossed, the angle of rotation is 90° and the direction of rotation is anti-clockwise. (Could say 270° clockwise instead). A B
118

119. (a) Find the centre of rotation and mark it on the diagram. B
(a) Find the centre of rotation and mark it on the diagram.
(b) Give the direction of rotation.
(c) Give the angle of rotation.
119

120. x A B
(a) Find the centre of rotation and mark it on the diagram.
(b) Give the direction of rotation.
(c) Give the angle of rotation.
Clockwise
900
120

121. TRANSLATIONS -3 THIS MEANS 3 LEFT -4 THIS MEANS 4 DOWN
TRANSLATIONS ARE WRITTEN AS VECTORS
THIS MEANS 3 RIGHT
THIS MEANS 4 UP
THIS MEANS 3 LEFT
THIS MEANS 4 DOWN

122. Data
Revision session

123. Mode & Median
Mode is the most popular, the most common number in the set.
Median put numbers in order of size then find the middle value.

124. 2 Way Tables 35 20 55 25 30 80 15 10 50 Hockey Not Hockey Total
Netball 35 20 55
Not Netball 25 30 80
How many play
Hockey?
How many play
Hockey but not
netball? 15 10
How many don’t
Want to play? 50

125. Averages Mean and Range Mean
add up the values ÷ by the number of values
Range
Largest value – smallest value

126. 3,5,6,7,9
Mean = ( )÷ 5
=30 ÷ 5 =6
Range = 9 – 3
= 6

127. Conversion Graphs
Find what 80Kmph is in mph.
80Kmph = 50 mph

128. Probability - CHANCE
impossible
certain
unlikely
evens 1
likely

129. Probability Probability of an event is Number of favourable events
Total number of outcomes

130. Probability
What is the probability of choosing a letter E from the word REPRESENT?

131. PROBABILITY REMEMBER PROBABILITY IS A NUMBER BETWEEN 0 AND 1
ALL PROBABILITIES ADD UP TO 1
For example,
if the probability that it will rain tomorrow is 0.8,
the probability that it won’t rain tomorrow is 0.2
= 1
131

132. Tom puts one party hat into each Christmas cracker.
The hats are red, yellow or green.
The probability that a cracker contains a red hat is 0·35.
The probability that a cracker contains a yellow hat is 0·4.
What is the probability that a cracker contains a green hat?
= 0.75
= [2]
132

133. There are no green pens so probability is 0
Jasinder has some pens in his school bag.
Some are red, some are black and the rest are blue.
He chooses a pen at random from his bag.
The probability that it is red is 0·2.
The probability that it is black is 0·5.
(a) What is the probability that it is blue?
1 – = 0.3
[2]
(b) What is the probability that it is green?
There are no green pens so probability is 0
[2]
133

134. Scatter diagrams
A scatter diagram shows how two pieces of data are related (correlate).
For example.
x x
xxx x
Xxx xx
X x x x x
This is a positive correlation, both values increase. Height and shoe size
This is a negative correlation as one value increases the other decreases. i.e. car age and car price
This has no correlation between the date. i.e. IQ and hair colour.
134

135. -----------negative correlation------- (1)
Joe has twelve cars for sale.
The scatter diagram shows the ages and prices of the twelve cars.
Describe the correlation between the ages of the cars and their prices
negative correlation (1)
135

136. A line of best fit can be drawn, that runs down the middle of the points, giving a good spread of points either side of the line.
This line shows that a car aged 4 years will have a price of approximately …
£2250
136

137. (a) Draw a line of best fit onto the scatter graph. (1)
The scattergraph shows the Age of children in relation to the number of hours sleep they get at night.
(a) Draw a line of best fit onto the scatter graph. (1)
(b) Use your line of best fit to estimate the amount of sleep a child of 10 years would be expected to get a night?
(2) x x x x
137

138. The scattergraph shows the Age of children in relation to the number of hours sleep they get at night.
(a) Draw a line of best fit onto the scatter graph. (1)
(b) Use your line of best fit to estimate the amount of sleep a child of 8 years would be expected to get a night?
(2) x x x x
10 hours
138

139. IMPORTANT NOTES REMEMBER ALWAYS PUT THE CORRECT UNITS OF WORKING
CM2 FOR AREA
CM3 FOR VOLUME

140. ALWAYS CHECK WHETHER YOU NEED TO ROUND TO A GIVEN NUMBER OF SIGNIFICANT FIGURES OR DECIMAL PLACES
If required it will be worth an extra mark.

141. PROBABILITY AND = X (MULTIPLY) OR = + (ADD)
REMEMBER PROBABILITY IS A NUMBER BETWEEN 0 AND 1
ALL PROBABILITIES ADD UP TO 1

142. THE END
GOOD LUCK
TRY YOUR BEST