key stage 3_mathematics_level_6_revision_
TRANSCRIPT
![Page 1: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/1.jpg)
Key Stage 3
Mathematics
Key Facts
Level 6
![Page 2: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/2.jpg)
Level 6
Number and Algebra
![Page 3: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/3.jpg)
Solve the equationx³ + x = 20
Using trial and improvement and give your answer to the nearest tenth
Guess Check Too Big/Too Small/Correct
![Page 4: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/4.jpg)
Solve the equationx³ + 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
![Page 5: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/5.jpg)
Solve the equationx³ + 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
![Page 6: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/6.jpg)
Solve the equationx³ + 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
![Page 7: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/7.jpg)
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
![Page 8: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/8.jpg)
A percentage is a fraction out of 100
![Page 9: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/9.jpg)
![Page 10: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/10.jpg)
![Page 11: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/11.jpg)
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?
![Page 12: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/12.jpg)
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
![Page 13: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/13.jpg)
![Page 14: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/14.jpg)
23
211
+ =2233
633
+
=2833
A common multiple of 3 and 11 is 33, so change both fractions to equivalent
fractions with a denominator of 33
![Page 15: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/15.jpg)
23
14
- = 812
312
-
= 512
A common multiple of 3 and 4 is 12, so change both fractions to equivalent fractions with a
denominator of 12
![Page 16: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/16.jpg)
Find the nth term of this sequence
6 13 20 27 34
7 7 7 7
Which times table is this pattern based on? 7
nth term = 7n - 1
Each number is 1 lessHow does it compare to the 7 times table?
7 14 21 28 35
![Page 17: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/17.jpg)
Find the nth term of this sequence
6 15 24 33 42
9 9 9 9
Which times table is this pattern based on? 9
nth term = 9n - 3
Each number is 3 lessHow does it compare to the 9 times table?
9 18 27 36 45
![Page 18: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/18.jpg)
![Page 19: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/19.jpg)
- -
![Page 20: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/20.jpg)
4p + 5 = 3p75 -
4p + 5 = 3p75 -
Swap Sides, Swap Signs
=4p 75
3p
+ -
5
=7p 70
= p 10
![Page 21: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/21.jpg)
2 4 6-6 -4 -2
2
4
6
-6
-4
-2
y axis
x axis
-5 -3 -1 1 3 5-1
-3
-5
1
3
5
(3,6)
(2,4)
(1,2)
(-3,-6)
The y coordinate is always double the x coordinate
y = 2x
![Page 22: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/22.jpg)
Straight Line Graphs
1 2 3 4-4 -3 -2 -10
2
4
8
6
10
-2
-4
-8
-6
-10
y = ½ x
y = x
y = -x
y = 2x y = 3x
y = 4x
y = 5x
y axis
x axis
![Page 23: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/23.jpg)
1 2 3 4-4 -3 -2 -10
2
4
8
6
10
-2
-4
-8
-6
-10
y = 2x
+1
y = 2x
- 5
y = 2x
+6
y = 2x
- 2y axis
x axis
![Page 24: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/24.jpg)
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
![Page 25: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/25.jpg)
Level 6
Shape, Space and Measures
![Page 26: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/26.jpg)
Cube Cuboid
Triangular Prism
Hexagonal Prism
Cylinder
Square based
PyramidTetrahedron
Cone
Sphere
![Page 27: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/27.jpg)
Using Isometric Paper
Which Cuboid is the odd one out?
![Page 28: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/28.jpg)
![Page 29: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/29.jpg)
![Page 30: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/30.jpg)
50a
Alternate angles are equal
a = 50
![Page 31: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/31.jpg)
76
b
Interior angles add up to 180
b = 180 - 76 = 104
![Page 32: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/32.jpg)
50
c
Corresponding angles are equal
c = 50
![Page 33: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/33.jpg)
114
d
Corresponding angles are equal
d = 114
![Page 34: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/34.jpg)
112
e
Alternate angles are equal
e = 112
![Page 35: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/35.jpg)
50f
Interior angles add up to 180
f = 130
![Page 36: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/36.jpg)
Polygon Sides(n)
Sum of Interior Angles
Triangle 3 180
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
The Sum of the Interior Angles
What is the rule that links the Sum of the Interior Angles to n?
![Page 37: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/37.jpg)
Polygon Sides(n)
Sum of Interior Angles
Triangle 3 180
Quadrilateral 4 360
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
The Sum of the Interior Angles
What is the rule that links the Sum of the Interior Angles to n?
![Page 38: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/38.jpg)
Polygon Sides(n)
Sum of Interior Angles
Triangle 3 180
Quadrilateral 4 360
Pentagon 5 540
Hexagon 6
Heptagon 7
Octagon 8
The Sum of the Interior Angles
What is the rule that links the Sum of the Interior Angles to n?
![Page 39: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/39.jpg)
Polygon Sides(n)
Sum of Interior Angles
Triangle 3 180
Quadrilateral 4 360
Pentagon 5 540
Hexagon 6 720
Heptagon 7
Octagon 8
The Sum of the Interior Angles
What is the rule that links the Sum of the Interior Angles to n?
![Page 40: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/40.jpg)
For a polygon with n sides
Sum of the Interior Angles = 180 (n – 2)
![Page 41: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/41.jpg)
A regular polygon has equal sides and equal angles
![Page 42: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/42.jpg)
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
![Page 43: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/43.jpg)
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
![Page 44: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/44.jpg)
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
![Page 45: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/45.jpg)
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
![Page 46: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/46.jpg)
![Page 47: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/47.jpg)
Translate the object by 4-3 ( )
![Page 48: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/48.jpg)
Translate the object by 4-3 ( )
Image
Move each corner of theobject 4 squaresacross and 3 squares down
![Page 49: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/49.jpg)
C
Rotate by 90 degrees anti-clockwise about c
![Page 50: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/50.jpg)
C
Rotate by 90 degrees anti-clockwise about C
Image
Remember to ask for tracing paper
![Page 51: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/51.jpg)
Triangle
Area = base × height ÷ 2
A = bh/2
Parallelogram
Area = base × height
A = bhTrapezium
A = ½ h(a + b)h
b
ab
h
h
b
The formula for the trapezium is given in the front of the SATs paper
We divide by 2 because the area of the triangle is half that of the rectangle that surrounds it
![Page 52: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/52.jpg)
Circumference = π × diameter
Where π = 3.14 (rounded to 2 decimal places)
diameter
The circumference of a circle is the distance around the outside
![Page 53: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/53.jpg)
The radius of a circle is 30m. What is the circumference?
r=30, d=60
C = π d
C = 3.14 × 60
C = 18.84 m
r = 30d = 60
![Page 54: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/54.jpg)
Circle Area = πr2
![Page 55: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/55.jpg)
πd πr²
π = 3. 141 592 653 589 793 238 462 643
Need diameter = distance across the middle of a circle
Need radius = distance from the centre of a circle to the edge
Area = π × 100= 3.142 × 100= 314.2 cm²
10cm
Circumference = π × 20= 3.142 × 20= 62.84 cm
10cm
The distance around the outside of a circle
![Page 56: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/56.jpg)
9 cm4 cm
10 cm
Volume of a cuboid
V= length × width × height
![Page 57: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/57.jpg)
9 cm4 cm
10 cm
Volume of a cuboid
V= length × width × height
V= 9 × 4 × 10
= 360 cm³
![Page 58: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/58.jpg)
![Page 59: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/59.jpg)
![Page 60: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/60.jpg)
Level 6
Data Handling
![Page 61: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/61.jpg)
Colour Frequency
Blue 5
Green 3
Yellow 2
Purple 2
Pink 4
Orange 1
Red 3
Draw a Pie Chart to show the information in the table below
A pie chart to show the favourite colour in our class
![Page 62: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/62.jpg)
Colour Frequency
Blue 5
Green 3
Yellow 2
Purple 2
Pink 4
Orange 1
Red 3
TOTAL 20
Draw a Pie Chart to show the information in the table below
A pie chart to show the favourite colour in our class
Add the frequencies to find the total
![Page 63: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/63.jpg)
Colour Frequency
Blue 5
Green 3
Yellow 2
Purple 2
Pink 4
Orange 1
Red 3
TOTAL 20
Draw a Pie Chart to show the information in the table below
A pie chart to show the favourite colour in our class
DIVIDE 360° by the total to find the angle for 1 person
360 ÷ 20 = 18Add the frequencies to find the total
![Page 64: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/64.jpg)
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
Draw a Pie Chart to show the information in the table below
A pie chart to show the favourite colour in our class
DIVIDE 360° by the total to find the angle for 1 person
360 ÷ 20 = 18Add the frequencies to find the total
Multiply each frequency by the angle for 1 person
![Page 65: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/65.jpg)
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
Draw a Pie Chart to show the information in the table below
A bar chart to show the favourite colour in our class
Blue
Green
YellowPurple
Pink
Orange
Red
![Page 66: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/66.jpg)
Length of string
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
Draw a frequency polygon to show
the information in the table
![Page 67: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/67.jpg)
frequency
x
f
Length of string (x)
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
Draw a frequency polygon to show
the information in the table
Plot the point using the midpoint of the interval
Use a continuous scale for the x-axis
![Page 68: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/68.jpg)
Length of string
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
Draw a histogram to show
the information in the table
![Page 69: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/69.jpg)
x
ffrequency
Length of string (x)
Frequency
0 < x ≤ 20 10
20 < x ≤ 40 20
40 < x ≤ 60 45
60 < x ≤ 80 32
80 < x ≤ 100 0
Draw a histogram to show
the information in the table
Use a continuous scale for the x-axis
![Page 70: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/70.jpg)
A Scatter Diagram to compare the marks of students in 2 maths tests
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Test A
Te
st
B
Describe the correlation between the marks scored in test A and test B
![Page 71: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/71.jpg)
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
0
20
40
60
80
100
120
140
160
0 20 40 60 80 100 120 140 160
Test A
Te
st
B
The correlation is positive because as marks in test A increase so do the marks in test B
![Page 72: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/72.jpg)
Negative Correlation
0
2
4
6
8
10
12
0 2 4 6 8 10 12
y
x
![Page 73: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/73.jpg)
The sample or probability space shows all 36 outcomes when you add two normal dice together.
2 3 4 5 6 7
3 4 5 6 7 8
7 8 9 10 11 12
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
1 2 3 4 5 6
1
2
6
3
4
5
Dice 1
Dice 2
Total Probability
1 1/36
2
3
4
5 4/36
6
7
8
9
10
11
12
![Page 74: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/74.jpg)
Dice 1
Dice 2
Total Probability
0
1 10/36
2
3
4 4/36
5
The sample space shows all 36 outcomes when you find the difference between the scores of two normal dice.
0 1 2 3 4 5
1 0 1 2 3 4
5 4 3 2 1 0
2 1 0 1 2 3
3 2 1 0 1 2
4 3 2 1 0 1
1 2 3 4 5 6
1
2
6
3
4
5
![Page 75: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/75.jpg)
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?
![Page 76: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/76.jpg)
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
![Page 77: Key stage 3_mathematics_level_6_revision_](https://reader038.vdocuments.mx/reader038/viewer/2022102815/55672d43d8b42a986b8b49df/html5/thumbnails/77.jpg)
© Dave Cavill