Download Shape and Space 1. A is the point (0,2) and B is the point (3,5). (a

Shape and Space
1.
y
7
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5
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2×
A
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–2
–1
0
1
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8 x
–1
A is the point (0,2) and B is the point (3,5).
(a)
Find the exact length of AB.
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(2)
(b)
Find the equation of the line joining the points A and B.
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(3)
(Total 5 marks)
2.
A container consists of a cylinder on top of a cone.
The container is full of oil.
Non Calc question
4m
1.5 m
0.9 m
The diameter of both the cylinder and the cone is 4 m.
The height of the cone is 0.9 m and the height of the cylinder is 1.5 m.
Calculate the volume of oil in the container.
Give your answer in terms of .
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Wellsway School
1
3.
A, B and C are three points which lie in a straight line on horizontal ground.
BT is a vertical tower.
T
A
13.3°
21.5°
B
C
1200 m
The angle of elevation of T from A is 21.5.
The angle of elevation of T from C is 13.3.
AC = 1200 m.
Calculate the height of the tower.
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Answer .................................................... m
(Total 4 marks)
4.
A firm makes cone shaped containers out of card.
The card is in the shape of a sector of a circle of radius 12 cm.
The angle of the sector is 270°.
The straight edges are brought together to make the cone.
12 cm
270º
12 cm
12 cm
(a)
Find the arc length of the card used to make the cone.
Give your answer in terms of .
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Answer .......................................................... cm
(2)
Wellsway School
2
(b)
Calculate the radius of the base of the cone.
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Answer .......................................................... cm
(2)
(Total 4 marks)
5.
Triangles ADE and ABC are similar.
DE is parallel to BC.
AD = 4 cm, DE = 6 cm and BC = 9 cm.
A
Not to scale
4 cm
D
E
6 cm
B
C
9 cm
Calculate the length of BD.
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Answer ........................................................... cm
(Total 3 marks)
6.
ABCDEFGH is a cuboid with sides of 5 cm, 5 cm and l2 cm as shown.
A
5 cm
B
D
C
E
Not to scale
5 cm
F
H
12 cm
G
Calculate angle DFH.
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Wellsway School
3
7.
Two ships, A and B, leave port at 13 00 hours.
Ship A travels at a constant speed of 18 km per hour on a bearing of 070°.
Ship B travels at a constant speed of 25 km per hour on a bearing of 152°.
N
18 km
A
Port
Not drawn accurately
25 km
B
Calculate the distance between A and B at 14 00 hours.
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Answer ........................................................... km
(Total 4 marks)
8.
The diagram shows a cylinder.
The volume of the cylinder is 320 cm3.
The height of the cylinder is 3.2 cm.
Non Calc question
3.2 cm
Not to scale
Calculate the radius of the base of the cylinder.
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Answer ............................................ cm
(Total 3 marks)
Wellsway School
4
9.
This is a non calculator question
The diagram shows two right-angled triangles.
AD = 15 cm.
CD = 6 cm.
A
Not to scale
15 cm
x°
B
y°
D
6 cm
C
(a)
Given that cos x° = 2 , calculate the length BD.
3
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Answer BD = ............................................
(2)
(b)
Find the value of sin y°.
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Answer sin y° = ............................................
(3)
(Total 5 marks)
10.
The first diagram shows a cone of base radius 12 cm and perpendicular height 10 cm.
A small cone of base radius 6 cm and perpendicular height 5 cm is cut off the bottom
to leave a frustum.
The frustum has a lower radius of 6 cm, an upper radius of 12 cm and a perpendicular
height of 5 cm (see second diagram).
12 cm
12 cm
5 cm
10 cm
6 cm
6 cm
Frustum
5 cm
Not to scale
Wellsway School
5
(a)
Find the volume of the frustum, giving your answer in terms of .
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Answer ....................................... cm3
(4)
(b)
The frustum has the same volume as another cone of perpendicular height 35 cm.
Calculate the radius of this cone.
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Answer ...................................... cm
(3)
(Total 7 marks)
12.
ABCD is a quadrilateral.
AB = 7 cm, AD = 6 cm and BC = 9 cm.
Angle ABC = 75° and angle ADC = 90°
A
7 cm
6 cm
B
75º
Not drawn accurately
D
9 cm
C
Calculate the perimeter of ABCD.
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Answer ........................................................... cm
(Total 5 marks)
Wellsway School
6