1. Mathematics Level 6

2. Level 6
Number and Algebra

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 3 3³ + 3 = 30
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 3 3³ + 3 = 30 2 2³ + 2 = 10
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 3 3³ + 3 = 30 2 2³ + 2 = 10 2.5
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 =18.125
2.6

7. Fat in a mars bar 28g out of 35g. What percentage is this?
Amounts as a %
Fat in a mars bar 28g out of 35g. What percentage is this?
Write as a fraction
=28/35
Convert to a percentage (top ÷ bottom x 100)
28 ÷ 35 x 100 = 80%
top ÷ bottom converts a fraction to a decimal
Multiply by 100 to make a decimal into a percentage

8. A percentage is a fraction out of 100

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

14. A common multiple of 3 and 11 is 33, so change both fractions to equivalent fractions with a denominator of 33 2 3 11 + = 22 33 6 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 3 1 4 - = 8 12 3 12 - 5 12 =

16. Find the nth term of this sequence
How does it compare to the 7 times table? 7 7 7 7 7
Which times table is this pattern based on?
Each number is 1 less
nth term = 7n - 1

17. Find the nth term of this sequence
How does it compare to the 9 times table? 9 9 9 9 9
Which times table is this pattern based on?
Each number is 3 less
nth term = 9n - 3

19. - -

20. + 5 75 - 4p = 3p
Swap Sides, Swap Signs + 5 5 75 - 3p 3p 4p = 4p + - = 75 = 7p 70 = p 10

21. The y coordinate is always double the x coordinate
y axis
(3,6) 6 5
(2,4) 4 3
(1,2) 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 = 4x y = 3x y = 5x y = 2x y = x y = ½ x y = -x
y axis
y = 3x
y = 5x 10
y = 2x 8
y = x 6
y = -x 4
y = ½ x 2 -4 -3 -2 -1 1 2 3 4
x axis -2 -4 -6 -8
-10

23. y = 2x+6 y = 2x- 2 y = 2x - 5 y = 2x+1 10 8 6 4 2 -4 -3 -2 -1 1 2 3 4
y axis
y = 2x- 2
y = 2x - 5
y = 2x+1 10 8 6 4 2 -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

25. Level 6
Shape, Space and Measures

26. Cuboid
Cube
Triangular Prism
Cylinder
Hexagonal Prism
Square based Pyramid
Cone
Tetrahedron
Sphere

27. Using Isometric Paper
Which Cuboid is the odd one out?

30. Alternate angles are equal50
Alternate angles are equal
a = 50

31. Interior angles add up to 180b 76
Interior angles add up to 180
b = = 104

32. Corresponding angles are equal50
Corresponding angles are equal
c = 50

33. Corresponding angles are equal
114 d
Corresponding angles are equal
d = 114

34. Alternate angles are equal
112
Alternate angles are equal
e = 112

35. Interior angles add up to 180f 50
Interior angles add up to 180
f = 130

36. The Sum of the Interior Angles
Polygon
Sides
(n)
Sum of Interior Angles
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
(n)
Sum of Interior Angles
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
(n)
Sum of Interior Angles
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
(n)
Sum of Interior Angles
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)

41. A regular polygon has equal sides and equal angles

42. If n = number of sides e = 360 ÷ n e + i = 180
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. If n = number of sides e = 360 ÷ n e + i = 180
Regular Polygon
Interior Angle (i)
Exterior Angle (e)
Equilateral Triangle 60
120
Square 90
Regular Pentagon
Regular Hexagon
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180

44. If n = number of sides e = 360 ÷ n e + i = 180
Regular Polygon
Interior Angle (i)
Exterior Angle (e)
Equilateral Triangle 60
120
Square 90
Regular Pentagon
108 72
Regular Hexagon
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180

45. If n = number of sides e = 360 ÷ n e + i = 180
Regular Polygon
Interior Angle (i)
Exterior Angle (e)
Equilateral Triangle 60
120
Square 90
Regular Pentagon
108 72
Regular Hexagon
Regular Heptagon
Regular Octagon
If n = number of sides
e = 360 ÷ n
e + i = 180

47. ( )
Translate the object by -3

48. ( ) Translate the object by 4 -3 Move each corner of the
object 4 squares
across and 3
squares down
Image

49. Rotate by 90 degrees anti-clockwise about c

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 surrounds it
Area = base × height ÷ 2
A = bh/2 h b
Parallelogram
Area = base × height
A = bh h b
Trapezium
A = ½ h(a + b) a h b
The formula for the trapezium is given in the front of the SATs paper

52. Circumference = π × diameter
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
C = π d
C = 3.14 × 60
C = m
r = 30
d = 60

54. Circle Area = πr2

55. π = 3. 141 592 653 589 793 238 462 643 πd πr² Circumference = π × 20
= × 20
= cm
Need radius = distance from the centre of a circle to the edge
10cm πd
πr²
10cm
The distance around the outside of a circle
Area = π × 100
= × 100
= cm²
Need diameter = distance across the middle of a circle

56. V= length × width × height
Volume of a cuboid
V= length × width × height
9 cm
4 cm
10 cm

57. V= length × width × height
Volume of a cuboid
V= length × width × height
9 cm
4 cm
10 cm
V= 9 × 4 × 10
= 360 cm³

60. Level 6
Data Handling

61. Draw a Pie Chart to show the information in the table below
Colour
Frequency
Blue 5
Green 3
Yellow 2
Purple
Pink 4
Orange 1
Red
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
Pink 4
Orange 1
Red
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
Pink 4
Orange 1
Red
TOTAL 20
DIVIDE 360° by the total to find the 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
Green 3
3 × 18 = 54
Yellow 2
2 × 18 = 36
Purple
Pink 4
4 × 18 = 72
Orange 1
1 × 18 = 18
Red
TOTAL 20
Multiply each frequency by the angle for 1 person
DIVIDE 360° by the total to find the 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
Green 3
3 × 18 = 54
Yellow 2
2 × 18 = 36
Purple
Pink 4
4 × 18 = 72
Orange 1
1 × 18 = 18
Red
TOTAL 20

66. Draw a frequency polygon to show the information in the table
Length of string
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100
Draw a frequency polygon to show
the information in the table

67. Use a continuous scale for the x-axis
Length of string (x)
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100
Draw a frequency polygon to show
the information in the table
Plot the point using the midpoint of the interval
frequency
Use a continuous scale for the x-axis

68. Draw a histogram to show the information in the table
Length of string
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100
Draw a histogram to show
the information in the table

69. Use a continuous scale for the x-axis
Length of string (x)
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100
Draw a histogram to show
the information in the table
frequency
Use a continuous scale for the x-axis

70. Describe the correlation between the marks scored in test A and test B

71. Describe the correlation between the marks scored in test A and test B
Positive
The correlation is positive because as marks in test A increase so do the marks in test B

72. y x

73. The sample or probability space shows all 36 outcomes when you add two normal dice together.
Total
Probability 1
1/36 2 3 4 5
4/36 6 7 8 9 10 11 12
Dice 1 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9
Dice 2 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12

74. The sample space shows all 36 outcomes when you find the difference between the scores of two normal dice.
Dice 1 1 2 3 4 5 6
Total
Probability 1
10/36 2 3 4
4/36 5 1 1 2 3 4 5 2 1 1 2 3 4 3 2 1 1 2 3
Dice 2 4 3 2 1 1 2 5 4 3 2 1 1 6 5 4 3 2 1

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?
= 0.34
= 0.66