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© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
12 The diagram represents the ski lift in Queenstown New Zealand.
37.1°B
T
h730 m
NOT TOSCALE
(a) The length of the cable from the bottom, B, to the top, T, is 730 metres.
The angle of elevation of T from B is 37.1°.
Calculate the change in altitude, h metres, from the bottom to the top.
Answer(a) m [2]
(b) The lift travels along the cable at 3.65 metres per second.
Calculate how long it takes to travel from B to T.
Give your answer in minutes and seconds.
Answer(b) min s [2]
6
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
12 The diagram represents the ski lift in Queenstown New Zealand.
37.1°B
T
h730 m
NOT TOSCALE
(a) The length of the cable from the bottom, B, to the top, T, is 730 metres.
The angle of elevation of T from B is 37.1°.
Calculate the change in altitude, h metres, from the bottom to the top.
Answer(a) m [2]
(b) The lift travels along the cable at 3.65 metres per second.
Calculate how long it takes to travel from B to T.
Give your answer in minutes and seconds.
Answer(b) min s [2]
6
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
12 The diagram represents the ski lift in Queenstown New Zealand.
37.1°B
T
h730 m
NOT TOSCALE
(a) The length of the cable from the bottom, B, to the top, T, is 730 metres.
The angle of elevation of T from B is 37.1°.
Calculate the change in altitude, h metres, from the bottom to the top.
Answer(a) m [2]
(b) The lift travels along the cable at 3.65 metres per second.
Calculate how long it takes to travel from B to T.
Give your answer in minutes and seconds.
Answer(b) min s [2]
6
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
12 The diagram represents the ski lift in Queenstown New Zealand.
37.1°B
T
h730 m
NOT TOSCALE
(a) The length of the cable from the bottom, B, to the top, T, is 730 metres.
The angle of elevation of T from B is 37.1°.
Calculate the change in altitude, h metres, from the bottom to the top.
Answer(a) m [2]
(b) The lift travels along the cable at 3.65 metres per second.
Calculate how long it takes to travel from B to T.
Give your answer in minutes and seconds.
Answer(b) min s [2]
4
© UCLES 2010 0580/23/M/J/10
For
Examiner's
Use
9 1 second = 106
microseconds.
Change 3 × 1013
microseconds into minutes. Give your answer in standard form.
Answer min [2]
10 The length of each side of an equilateral triangle is 74 mm, correct to the nearest millimetre.
Calculate the smallest possible perimeter of the triangle.
Answer mm [2]
11
P
FAbeach
cliff
55 m
NOT TOSCALE
The diagram shows a point P at the top of a cliff.
The point F is on the beach and vertically below P.
The point A is 55m from F, along the horizontal beach.
The angle of elevation of P from A is 17°.
Calculate PF, the height of the cliff.
Answer PF = m [3]
4
© UCLES 2010 0580/23/M/J/10
For
Examiner's
Use
9 1 second = 106
microseconds.
Change 3 × 1013
microseconds into minutes. Give your answer in standard form.
Answer min [2]
10 The length of each side of an equilateral triangle is 74 mm, correct to the nearest millimetre.
Calculate the smallest possible perimeter of the triangle.
Answer mm [2]
11
P
FAbeach
cliff
55 m
NOT TOSCALE
The diagram shows a point P at the top of a cliff.
The point F is on the beach and vertically below P.
The point A is 55m from F, along the horizontal beach.
The angle of elevation of P from A is 17°.
Calculate PF, the height of the cliff.
Answer PF = m [3]
3.
4.
5.
3
© UCLES 2010 0580/22/O/N/10 [Turn over
For
Examiner's
Use
4
O is the centre of the circle.
DA is the tangent to the circle at A and DB is the tangent to the circle at C.
AOB is a straight line. Angle COB = 50°.
Calculate
(a) angle CBO, Answer(a) Angle CBO = [1]
(b) angle DOC. Answer(b) Angle DOC = [1]
5
JGR is a right-angled triangle. JR = 50m and JG = 20m.
Calculate angle JRG.
Answer Angle JRG = [2]
6 Write 0.00658
(a) in standard form,
Answer(a) [1]
(b) correct to 2 significant figures.
Answer(b) [1]
J
G R
50 m20 mNOT TOSCALE
50°OA
D
C
B
NOT TOSCALE
9
© UCLES 2010 0580/22/O/N/10 [Turn over
For
Examiner's
Use
19
M
C B
P
D A
8 cm
10 cm
10 cm
NOT TOSCALE
The diagram represents a pyramid with a square base of side 10 cm.
The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm.
(a) Calculate the length of BD.
Answer(a) BD = cm [2]
(b) Calculate MP, the height of the pyramid.
Answer(b) MP = cm [3]
9
© UCLES 2010 0580/22/O/N/10 [Turn over
For
Examiner's
Use
19
M
C B
P
D A
8 cm
10 cm
10 cm
NOT TOSCALE
The diagram represents a pyramid with a square base of side 10 cm.
The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm.
(a) Calculate the length of BD.
Answer(a) BD = cm [2]
(b) Calculate MP, the height of the pyramid.
Answer(b) MP = cm [3]
9
© UCLES 2010 0580/22/O/N/10 [Turn over
For
Examiner's
Use
19
M
C B
P
D A
8 cm
10 cm
10 cm
NOT TOSCALE
The diagram represents a pyramid with a square base of side 10 cm.
The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm.
(a) Calculate the length of BD.
Answer(a) BD = cm [2]
(b) Calculate MP, the height of the pyramid.
Answer(b) MP = cm [3]
9
© UCLES 2010 0580/22/O/N/10 [Turn over
For
Examiner's
Use
19
M
C B
P
D A
8 cm
10 cm
10 cm
NOT TOSCALE
The diagram represents a pyramid with a square base of side 10 cm.
The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm.
(a) Calculate the length of BD.
Answer(a) BD = cm [2]
(b) Calculate MP, the height of the pyramid.
Answer(b) MP = cm [3]
2
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
1 In the right-angled triangle ABC, cos C =
5
4
. Find angle A.
A
B C
NOT TOSCALE
Answer Angle A = [2]
2 Which of the following numbers are irrational?
3
2
36 3 + 6 π 0.75 48% 83
1
Answer [2]
3 Show that 1
9
5
÷ 1
9
7
=
8
7
.
Write down all the steps in your working.
Answer
[2]
6.
7.
11
© UCLES 2011 0580/23/M/J/11 [Turn over
For
Examiner's
Use
21
4 cm
6 cm
6 cm
DC
BA
P
M
NOT TOSCALE
The diagram shows a pyramid with a square base ABCD of side 6 cm.
The height of the pyramid, PM, is 4 cm, where M is the centre of the base.
Calculate the total surface area of the pyramid.
Answer cm2
[5]
Question 22 is printed on the next page.
11
© UCLES 2011 0580/23/M/J/11 [Turn over
For
Examiner's
Use
21
4 cm
6 cm
6 cm
DC
BA
P
M
NOT TOSCALE
The diagram shows a pyramid with a square base ABCD of side 6 cm.
The height of the pyramid, PM, is 4 cm, where M is the centre of the base.
Calculate the total surface area of the pyramid.
Answer cm2
[5]
Question 22 is printed on the next page.
10
© UCLES 2011 0580/21/O/N/11
For
Examiner's
Use
16
y
xO
A (1,3)
B (3,0)
C (9,7)
NOT TOSCALE
The co-ordinates of A, B and C are shown on the diagram, which is not to scale.
(a) Find the length of the line AB.
Answer(a) AB = [3]
(b) Find the equation of the line AC.
Answer(b) [3]
10
© UCLES 2011 0580/21/O/N/11
For
Examiner's
Use
16
y
xO
A (1,3)
B (3,0)
C (9,7)
NOT TOSCALE
The co-ordinates of A, B and C are shown on the diagram, which is not to scale.
(a) Find the length of the line AB.
Answer(a) AB = [3]
(b) Find the equation of the line AC.
Answer(b) [3]
8.
9.
10
© UCLES 2011 0580/23/O/N/11
For
Examiner's
Use
21
North
North
A
C
B
4.5 km
2.7 km
5 km
NOT TOSCALE
The diagram shows 3 ships A, B and C at sea.
AB = 5 km, BC = 4.5 km and AC = 2.7 km.
(a) Calculate angle ACB.
Show all your working.
Answer(a) Angle ACB = [4]
(b) The bearing of A from C is 220°.
Calculate the bearing of B from C.
Answer(b) [1]
10
© UCLES 2011 0580/23/O/N/11
For
Examiner's
Use
21
North
North
A
C
B
4.5 km
2.7 km
5 km
NOT TOSCALE
The diagram shows 3 ships A, B and C at sea.
AB = 5 km, BC = 4.5 km and AC = 2.7 km.
(a) Calculate angle ACB.
Show all your working.
Answer(a) Angle ACB = [4]
(b) The bearing of A from C is 220°.
Calculate the bearing of B from C.
Answer(b) [1]
10
© UCLES 2011 0580/23/O/N/11
For
Examiner's
Use
21
North
North
A
C
B
4.5 km
2.7 km
5 km
NOT TOSCALE
The diagram shows 3 ships A, B and C at sea.
AB = 5 km, BC = 4.5 km and AC = 2.7 km.
(a) Calculate angle ACB.
Show all your working.
Answer(a) Angle ACB = [4]
(b) The bearing of A from C is 220°.
Calculate the bearing of B from C.
Answer(b) [1]
10
© UCLES 2011 0580/23/O/N/11
For
Examiner's
Use
21
North
North
A
C
B
4.5 km
2.7 km
5 km
NOT TOSCALE
The diagram shows 3 ships A, B and C at sea.
AB = 5 km, BC = 4.5 km and AC = 2.7 km.
(a) Calculate angle ACB.
Show all your working.
Answer(a) Angle ACB = [4]
(b) The bearing of A from C is 220°.
Calculate the bearing of B from C.
Answer(b) [1]
6
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
11 y varies directly as the square of (x – 3).
y = 16 when x = 1.
Find y when x = 10.
Answer y = [3]
12
North 5 km
8 km
150°
C
B
A
NOT TOSCALE
A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A.
Angle ABC = 150°.
(a) Calculate the area of triangle ABC.
Answer(a) km2
[2]
(b) Find the bearing of B from C.
Answer(b) [2]
6
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
11 y varies directly as the square of (x – 3).
y = 16 when x = 1.
Find y when x = 10.
Answer y = [3]
12
North 5 km
8 km
150°
C
B
A
NOT TOSCALE
A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A.
Angle ABC = 150°.
(a) Calculate the area of triangle ABC.
Answer(a) km2
[2]
(b) Find the bearing of B from C.
Answer(b) [2]
6
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
11 y varies directly as the square of (x – 3).
y = 16 when x = 1.
Find y when x = 10.
Answer y = [3]
12
North 5 km
8 km
150°
C
B
A
NOT TOSCALE
A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A.
Angle ABC = 150°.
(a) Calculate the area of triangle ABC.
Answer(a) km2
[2]
(b) Find the bearing of B from C.
Answer(b) [2]
6
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
11 y varies directly as the square of (x – 3).
y = 16 when x = 1.
Find y when x = 10.
Answer y = [3]
12
North 5 km
8 km
150°
C
B
A
NOT TOSCALE
A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A.
Angle ABC = 150°.
(a) Calculate the area of triangle ABC.
Answer(a) km2
[2]
(b) Find the bearing of B from C.
Answer(b) [2]
