3. Solve the equation
x³ + x = 20
Using trial and improvement and give your answer to the nearest tenth
Guess Check Too Big/Too
Small/Correct
4. Solve the equation
x³ + x = 20
Using trial and improvement and give your answer to the nearest tenth
Guess Check Too Big/Too
Small/Correct
3 3³ + 3 = 30 Too Big
5. Solve the equation
x³ + x = 20
Using trial and improvement and give your answer to the nearest tenth
Guess Check Too Big/Too
Small/Correct
3 3³ + 3 = 30 Too Big
2 2³ + 2 = 10 Too Small
6. Solve the equation
x³ + x = 20
Using trial and improvement and give your answer to the nearest tenth
Guess Check Too Big/Too
Small/Correct
3 3³ + 3 = 30 Too Big
2 2³ + 2 = 10 Too Small
2.5 2.5³ + 2.5 =18.125 Too Small
2.6
7. Amounts as a %
• Fat in a mars bar 28g out of 35g. What percentage
is this?
Write as a fraction top ÷ bottom
converts a
fraction to a
• =28/35 decimal
Convert to a percentage (top ÷ bottom x 100)
• 28 ÷ 35 x 100 = 80% Multiply by 100
to make a
decimal into a
percentage
11. The ratio of boys to girls in a class is 3:2
Altogether there are 30 students in the class.
How many boys are there?
12. The ratio of boys to girls in a class is 3:2
Altogether there are 30 students in the class.
How many boys are there?
The ratio 3:2 represents 5 parts (add 3 + 2)
Divide 30 students by the 5 parts (divide)
30 ÷ 5 = 6
Multiply the relevant part of the ratio by the
answer (multiply)
3 × 6 = 18 boys
13.
14. A common multiple of 3 and
11 is 33, so change both
fractions to equivalent
fractions with a denominator
of 33
2 2 22 6
+ = +
3 11 33 33
28
=
33
15. A common multiple of 3 and 4
is 12, so change both fractions
to equivalent fractions with a
denominator of 12
2 1 8 3
- = -
3 4 12 12
5
=
12
16. Find the nth term of this sequence
7 14 21 28 35
6 13 20 27 34
7 7 7 7
Which times table is this pattern based on? 7
How does it compare to the 7 times table? Each number is 1 less
nth term = 7n - 1
17. Find the nth term of this sequence
9 18 27 36 45
6 15 24 33 42
9 9 9 9
Which times table is this pattern based on? 9
How does it compare to the 9 times table? Each number is 3 less
nth term = 9n - 3
21. y axis
6 (3,6)
5
4 (2,4)
3
2 (1,2)
1
x axis
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-1
-2
-3
-4
-5
(-3,-6) -6
The y coordinate is always double the x coordinate
y = 2x
22. Straight Line Graphs
y axis y = 4x
y = 3x
10
y = 5x y = 2x
8
6 y=x
4
2 y=½x
0
-4 -3 -2 -1 1 2 3 4 x axis
-2
-4
y = -x
-6
-8
-10
23. +6 1 x- 2
y axis 2x + 2 -5
10 y = 2x = 2x
y= y y=
8
6
4
2
0
-4 -3 -2 -1 1 2 3 4 x axis
-2
-4
-6
-8
-10
24. All straight line graphs can be expressed in the form
y = mx + c
m is the gradient of the line
and c is the y intercept
The graph y = 5x + 4 has gradient 5 and cuts the
y axis at 4
36. The Sum of the Interior Angles
Polygon Sides Sum of Interior Angles
(n)
Triangle 3 180
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
What is the rule that links the Sum of the Interior Angles to n?
37. The Sum of the Interior Angles
Polygon Sides Sum of Interior Angles
(n)
Triangle 3 180
Quadrilateral 4 360
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
What is the rule that links the Sum of the Interior Angles to n?
38. The Sum of the Interior Angles
Polygon Sides Sum of Interior Angles
(n)
Triangle 3 180
Quadrilateral 4 360
Pentagon 5 540
Hexagon 6
Heptagon 7
Octagon 8
What is the rule that links the Sum of the Interior Angles to n?
39. The Sum of the Interior Angles
Polygon Sides Sum of Interior Angles
(n)
Triangle 3 180
Quadrilateral 4 360
Pentagon 5 540
Hexagon 6 720
Heptagon 7
Octagon 8
What is the rule that links the Sum of the Interior Angles to n?
40. For a polygon with n sides
Sum of the Interior Angles = 180 (n – 2)
42. Regular Polygon Interior Angle (i) Exterior Angle (e)
Equilateral Triangle 60 120
Square
Regular Pentagon
Regular Hexagon
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180
43. Regular Polygon Interior Angle (i) Exterior Angle (e)
Equilateral Triangle 60 120
Square 90 90
Regular Pentagon
Regular Hexagon
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180
44. Regular Polygon Interior Angle (i) Exterior Angle (e)
Equilateral Triangle 60 120
Square 90 90
Regular Pentagon 108 72
Regular Hexagon
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180
45. Regular Polygon Interior Angle (i) Exterior Angle (e)
Equilateral Triangle 60 120
Square 90 90
Regular Pentagon 108 72
Regular Hexagon 120 60
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180
50. Rotate by 90 degrees anti-clockwise about C
Image
C
Remember to ask for tracing paper
51. We divide by 2 because the area of the
triangle is half that of the rectangle that Triangle
surrounds it Area = base × height ÷ 2
h
A = bh/2
b
Parallelogram
Area = base × height
h
A = bh
b
a Trapezium
h
A = ½ h(a + b)
b
The formula for the trapezium is given in
the front of the SATs paper
52. The circumference
of a circle is the
distance around the
outside
diameter
Circumference = π × diameter
Where π = 3.14 (rounded to 2 decimal places)
53. The radius of a circle is
30m. What is the
circumference?
r=30, d=60
r = 30
C= πd d = 60
C = 3.14 × 60
C = 18.84 m
55. π = 3. 141 592 653 589 793 238 462 643
Circumference = π × 20 Need radius = distance
= 3.142 × 20 from the centre of a
= 62.84 cm circle to the edge
10cm
πd πr²
10cm
The distance around
Area = π × 100
the outside of a circle
= 3.142 × 100
= 314.2 cm²
Need diameter = distance
across the middle of a circle
56. Volume of a cuboid
V= length × width × height
10 cm
4 cm 9 cm
57. Volume of a cuboid
V= length × width × height
V= 9 × 4 × 10 10 cm
= 360 cm³
4 cm 9 cm
61. Draw a Pie Chart to show the information in the table below
Colour Frequency
Blue 5
Green 3
Yellow 2
Purple 2
Pink 4
Orange 1
Red 3
A pie chart to show the favourite colour in our class
62. Draw a Pie Chart to show the information in the table below
Colour Frequency
Blue 5
Green 3
Yellow 2
Purple 2
Pink 4
Orange 1
Red 3
TOTAL 20
Add the frequencies to
find the total
A pie chart to show the favourite colour in our class
63. Draw a Pie Chart to show the information in the table below
Colour Frequency
Blue 5
Green 3
Yellow 2
Purple 2
Pink 4
Orange 1 DIVIDE 360° by
Red 3 the total to find the
TOTAL 20 angle for 1 person
360 ÷ 20 = 18
Add the frequencies to
find the total
A pie chart to show the favourite colour in our class
64. Draw a Pie Chart to show the information in the table below
Colour Frequency Angle
Blue 5 5 × 18 = 90 Multiply each frequency by the angle
Green 3 3 × 18 = 54
for 1 person
Yellow 2 2 × 18 = 36
Purple 2 2 × 18 = 36
Pink 4 4 × 18 = 72
Orange 1 1 × 18 = 18 DIVIDE 360° by
Red 3 3 × 18 = 54 the total to find the
TOTAL 20 angle for 1 person
360 ÷ 20 = 18
Add the frequencies to
find the total
A pie chart to show the favourite colour in our class
65. Draw a Pie Chart to show the information in the table below
Colour Frequency Angle
Blue 5 5 × 18 = 90
A bar chart to show the favourite colour in our class
Green 3 3 × 18 = 54
Yellow 2 2 × 18 = 36 Red
Blue
Purple 2 2 × 18 = 36
Orange
Pink 4 4 × 18 = 72
Orange 1 1 × 18 = 18
Pink
Green
Red 3 3 × 18 = 54
TOTAL 20 Purple Yellow
66. Length of Frequency
Draw a frequency polygon to show string
the information in the table 0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
67. Length of Frequency
Draw a frequency polygon to show string (x)
the information in the table 0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
Plot the point using the 80 < x ≤ 100 0
midpoint of the interval
50 frequency
f
40
30
20
10
Use a continuous scale
for the x-axis x
10 20 30 40 50 60 70 80 90 100
68. Length of Frequency
Draw a histogram to show string
the information in the table 0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
69. Length of Frequency
Draw a histogram to show string (x)
the information in the table 0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
50 frequency
f
40
30
20
10
Use a continuous scale
for the x-axis x
10 20 30 40 50 60 70 80 90 100
70. Describe the correlation between the marks scored in test A and test B
A Scatter Diagram to compare the marks of students in 2 maths tests
140
120
100
80
Test B
60
40
20
0
0 20 40 60 80 100 120 140
Test A
71. Describe the correlation between the marks scored in test A and test B
A Scatter Diagram to compare the marks of students in 2 maths tests
160
140
120
100
Test B
80
The correlation is
positive because as
60
40
marks in test A
increase so do the
20
marks in test B
0
0 20 40 60 80 100 120 140 160
Test A
72. y Negative Correlation
12
10
8
6
4
2
x
0
0 2 4 6 8 10 12
73. The sample or probability space shows all 36 outcomes
when you add two normal dice together.
Total Probability
1 1
/36
Dice 1
2
1 2 3 4 5 6 3
4
1 2 3 4 5 6 7
5 4
/36
2 3 4 5 6 7 8 6
7
3 4 5 6 7 8 9
Dice 2 8
4 5 6 7 8 9 10 9
5 6 7 8 9 10 11 10
11
6 7 8 9 10 11 12 12
74. The sample space shows all 36 outcomes when you find the
difference between the scores of two normal dice.
Dice 1
Total Probability
1 2 3 4 5 6
0
1 0 1 2 3 4 5
1 10
/36
2 1 0 1 2 3 4
2
3 2 1 0 1 2 3 3
Dice 2
4 3 2 1 0 1 2 4 4
/36
5 4 3 2 1 0 1 5
6 5 4 3 2 1 0
75. The total probability of all the mutually exclusive outcomes of
an experiment is 1
A bag contains 3 colours of beads, red, white and blue.
The probability of picking a red bead is 0.14
The probability of picking a white bead is 0.2
What is the probability of picking a blue bead?
76. The total probability of all the mutually exclusive outcomes of
an experiment is 1
A bag contains 3 colours of beads, red, white and blue.
The probability of picking a red bead is 0.14
The probability of picking a white bead is 0.2
What is the probability of picking a blue bead?
0.14 + 0.2 = 0.34
1 - 0.34 = 0.66