Mathematics

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Mathematics Foundation Tier
Shape and space
GCSE Revision 2006
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Foundation Tier Shape and space revision 2006
Contents Angle calculations Angles and
polygons Bearings Units Perimeter Area
formulae Area strategy Volume Nets and
surface area Spotting P, A V
formulae Transformations Constructions Pytha
goras Theorem
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Use the rules to work out all angles
Angle calculations
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There are 3 types of angles in regular polygons
Angles and polygons
Interior 180 - e angles
Calculate the value of c, e and i in regular
polygons with 8, 9, 10 and 12 sides
Answers 8 sides 450, 450, 1350 9 sides 400,
400, 1400 10 sides 360, 360, 1440 12 sides
300, 300, 1500
Total i 5 x 180 9000
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Bearings
A bearing is an angle measured in a
clockwise direction from due North
A bearing should always have 3 figures.
What are these bearings ?
Here are the steps to get your answer
2360
Notice that there is a 1800 difference between
the outward journey and the return journey
560
What is the bearing of Bristol from Bath ?
What is the bearing of Bath from Bristol ?
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Units
Learn these metric conversions
Imperial ? Metric 5 miles ? 8 km 1 yard ? 0.9
m 12 inches ? 30 cm 1 inch ? 2.5 cm
Learn these rough imperial to metric conversions
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Perimeter
The perimeter of a shape is the distance around
its outside measured in cm, m, etc.
26m
31.4m
7.85m
4.71m
18.4m
7.85 4.71 1 1 14.56m
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The area of a 2D shape is the amount of space
covered by it measured in cm2, m2 etc.
Area formulae
49m2
40m2
16m2
18m2
24m2
42m2
50.24m2
7.5m2
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Area strategy
What would you do to get the area of each of
these shapes? Do them step by step!
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Volume
The volume of a 3D solid shape is the amount of
space inside it measured in cm3, m3 etc.
27m3
56m3
42m3
384.65m3
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Nets and surface area
12cm2
12cm2
4cm2
2
2
12cm2
4cm2
Cuboid 2 by 2 by 6
Net of the cuboid
12cm2
Volume 2 x 2 x 6 24cm3
Total surface area 12 12 12 12 4 4
56cm2
To find the surface area of a cuboid it helps to
draw the net
Find the volume and surface area of these cuboids
V 5 x 4 x 3 60cm3
V 6 x 6 x 1 60cm3
V 5 x 5 x 5 125cm3
SA 94cm2
SA 96cm2
SA 150cm2
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Spotting P, A V formulae
r(? 3)
4?rl
A
P

• Which of the following
• expressions could be for
• Perimeter
• Area
• Volume

?r(r l)
A
1?d2 4
4?r2 3
4?r3 3
A
A
?r ½r
V
4l2h
P
1?r2h 3
1?rh 3
V
?r 4l
A
V
1?r 3
P
?rl
3lh2
4?r2h
P
V
V
A
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Transformations
1. Reflection
Reflect the triangle using the line y x then
the line y - x then the line x 1
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Transformations
Describe the rotation of A to B and C to D
2. Rotation

• When describing a rotation always state these 3
  things
• No. of degrees
• Direction
• Centre of rotation
• e.g. a rotation of 900 anti-clockwise using a
  centre of (0, 1)

C
B
A
D
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What happens when we translate a shape ? The
shape remains the same size and shape and the
same way up it just. .
Transformations
slides
3. Translation
Horizontal translation
Use a vector to describe a translation
Give the vector for the translation from..
Vertical translation
D
C
A
B
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Enlarge this shape by a scale factor of 2 using
centre O
Transformations
4. Enlargement
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Constructions
Have a look at these constructions and work out
what has been done
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Calculating the Hypotenuse
Pythagoras Theorem
Hyp2 a2 b2
DE2 212 452
How to spot a Pythagoras question
DE2 441 2025
DE2 2466
Right angled triangle
DE 49.659
No angles involved in question
Hyp2 a2 b2
Calculating a shorter side
162 AC2 112
256 AC2 121
256 - 121 AC2
How to spot the Hypotenuse
135 AC2
11.618 AC
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Pythagoras Questions
Look out for the following Pythagoras questions
in disguise