1.
The triangles A and B are congruent.
8 cm
B
10 cm
x
A
y
30°
38°
30°
15 cm
(a)
112°
Not drawn
accurately
Write down the values of x and y.
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Answer x =...................... cm, y = ………………… cm
(2)
(b)
Given that sin 30° = 0.5, calculate the area of triangle A.
State the units of your answer.
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Answer ................................................................
(3)
(Total 5 marks)
2.
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
B
6 cm
9 cm
E
C
Calculate the length of BD.
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1
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Answer ........................................................... cm
(Total 3 marks)
3.
Triangles ABC and PQR are similar.
AC = 3.2 cm, AB = 4 cm and PR = 4.8 cm.
P
A
Not drawn accurately
4.8 cm
3.2 cm
C
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4 cm
x
B
R
Q
2
(a)
Explain why sin x = 0.8
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(1)
(b)
Calculate the length of PQ.
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Answer .......................................................cm
(3)
(Total 4 marks)
4.
Triangles ABC and APQ are similar.
PQ is parallel to BC.
AQ = 6 cm, QC = 2 cm and BC = 12 cm
A
not drawn accurately
6 cm
Q
P
B
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12 cm
2 cm
C
3
Calculate the length of PQ.
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Answer...............................................................................................................................cm
(Total 3 marks)
5.
A square-based pyramid A is divided into two parts:
a square-based pyramid B and a frustum C, as shown.
Pyramid B
Pyramid A
Frustum C
Pyramid A is similar to pyramid B.
The base of pyramid A is a square of side 10 cm.
The base of pyramid B is a square of side 5 cm.
The vertical height of pyramid A is 12 cm.
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4
(a)
You are given the formula
Volume of a pyramid =
1
 area of base × vertical height
3
Calculate the volume of the frustum C.
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Answer .......................................................... cm3
(4)
(b)
Express the volume of the frustum C as a fraction of the volume of the larger pyramid A.
Give your answer in its simplest form.
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Answer ..................................................................
(2)
(Total 6 marks)
1.
(a)
(b)
x=8
B1
y= 10
B1
1
M1
2
× 10 × 15 × 0.5
oe
37.5
A1
cm2
B1
Units mark
[5]
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5
2.
Scale factor
9 6 6 4
or or or
6 9 4 6
oe
M1
AB = (their 1.5) × 4
Or 9 ÷ (their 1.5)
A1
DB = 2
A1
Alternative:
4
6 4 x 9
 or

4 x 9
4
6
36 = 24 + 6x
x=2
M1
M1
A1
[3]
3.
(a)
(sin x =) 3.2/4 or 4.8/6
oe eg 4× 0.8 = 3.2
B1
(b)
4.8/3.2 or 1.5
oe 0.8 =4.8/PQ
M1
1.5 × 4
M1 dep
oe 4.8/0.8
6
A1
[4]
4.
Scale factor
6
8
M1
6
 12
8
M1
9
A1
[3]
5.
(a)
1
× 10 × 10 × 12
3
M1
400
A1
Accept 399.6 or better
1
7
× 5 × 5 × 6 or 50 or
× 400
3
8
Allow 0.3(3)
350
M1
A1
Accept 349.6 or better
(b)
350
400
or their
M1
350
400
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Allow
7
8
1
for M1
8
A1
[6]
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7