Mathematics Level 6

1
MathematicsLevel 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 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
• 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
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9
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10
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11
The ratio of boys to girls in a class is
32 Altogether there are 30 students in the
class. How many boys are there?
12
The ratio of boys to girls in a class is
32 Altogether there are 30 students in the
class. How many boys are there? The ratio 32
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
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14
A common multiple of 3 and 11 is 33, so change
both fractions to equivalent fractions with a
denominator of 33
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
8 12
3 12
-
5 12

16
Find the nth term of this sequence 6 13 20 27
34
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 6 15 24 33
42
9
Which times table is this pattern based on?
Each number is 3 less
nth term 9n - 3
18
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19
-
-
20
-

5
75

• 4p

3p
Swap Sides, Swap Signs
3p
3p
-

5
5
75
4p

4p
-

75

21
y axis
(3,6)
6
5
(2,4)
4
3
(1,2)
2
1
x axis
2
4
6
-6
-2
-3
1
3
-4
-5
-1
5
-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
10
8
6
4
2
0
-4
-3
-2
-1
1
2
3
4
x axis
-2
-4
-6
-8
-10
23
y axis
10
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
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?
28
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29
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30
a
50
Alternate angles are equal a 50
31
b
76
Interior angles add up to 180 b 180 - 76 104
32
c
50
Corresponding angles are equal c 50
33
114
d
Corresponding angles are equal d 114
34
e
112
Alternate angles are equal e 112
35
f
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
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
46
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47
( )
Translate the object by 4 -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
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
Triangle 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
The circumference of a circle is the distance
around the outside
diameter
Circumference p diameter Where p 3.14
(rounded to 2 decimal places)
53
The radius of a circle is 30m. What is the
circumference?
r30, d60 C p d C 3.14 60 C 18.84 m
r 30
d 60
54
Circle Area pr2
55
p 3. 141 592 653 589 793 238 462 643
Circumference p 20 3.142 20 62.84
cm
Need radius distance from the centre of a
circle to the edge
10cm
pd
pr²
10cm
The distance around the outside of a circle
Area p 100 3.142 100 314.2 cm²
Need diameter distance across the middle of a
circle
56
Volume of a cuboid V length width height
57
Volume of a cuboid V length width height
V 9 4 10 360 cm³
58
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59
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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 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
Red 3
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 2 2 18 36
Pink 4 4 18 72
Orange 1 1 18 18
Red 3 3 18 54
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 2 2 18 36
Pink 4 4 18 72
Orange 1 1 18 18
Red 3 3 18 54
TOTAL 20
66
Length of string Frequency
0 lt x 20 10
20 lt x 40 20
40 lt x 60 45
60 lt x 80 32
80 lt x 100 0
Draw a frequency polygon to show the information
in the table
67
Length of string (x) Frequency
0 lt x 20 10
20 lt x 40 20
40 lt x 60 45
60 lt x 80 32
80 lt x 100 0
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
Length of string Frequency
0 lt x 20 10
20 lt x 40 20
40 lt x 60 45
60 lt x 80 32
80 lt x 100 0
Draw a histogram to show the information in the
table
69
Length of string (x) Frequency
0 lt x 20 10
20 lt x 40 20
40 lt x 60 45
60 lt x 80 32
80 lt x 100 0
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
2
3
4
5
6
7
1
3
4
5
6
7
8
2
4
5
6
7
8
9
3
Dice 2
5
6
7
8
9
10
4
6
7
8
9
10
11
5
7
8
9
10
11
12
6
74
The sample space shows all 36 outcomes when you
find the difference between the scores of two
normal dice.
Dice 1
Total Probability
0
1 10/36
2
3
4 4/36
5
1
2
3
4
5
6
0
1
2
3
4
5
1
1
0
1
2
3
4
2
2
1
0
1
2
3
3
Dice 2
3
2
1
0
1
2
4
4
3
2
1
0
1
5
5
4
3
2
1
0
6
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