Download Year 10 Level Name: Department of Mathematics 2014 Parade

Year 10 Level
Department of Mathematics 2014
Parade College
TEST:
Name:
CHAPTER 5: TRIGONOMETRY I
Section
A: Vocabulary knowledge
B: Multiple Choice
C: Short Answer
D: Analysis Problem
Marks
5
11
19
10
Your mark
Total Marks = 45
Instructions
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

Read questions carefully
CAS calculators may be used.
No sharing of equipment, including calculators.
Section A:
Vocabulary Knowledge (5 marks)
Complete the following using the words and phrases from the list where appropriate.
1. To find the size of an angle whose sine, cosine or tangent is given, perform an __________ operation.
2. True bearings are measured from north in a __________ direction and expressed as 3 digits and with a T.
3. The __________ is the longest side of the triangle and is opposite the right angle.
4. The angle of elevation is measured up from the _________ line to the line of__________.
Word List
hypotenuse
vision
Inverse
Clockwise
horizontal
vertical
1
Anticlockwise
adjacent
Section B:
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1
10 questions worth 1 mark each
Working out is not necessary
CAS Calculators may be used.
The most accurate measure for the length of the third side in the triangle below is:
A
B
C
D
E
2
Multiple Choice (10 mark)
3.68 m
26.3 cm
3681 mm
2632 mm
5.02 m
The value of cos 1322ʹ correct to four decimal places is:
A 0.2311
B 0.2312
C 0.9734
D 0.9735
E 0.9729
2
3
The length x in the diagram below is:
18
x
A
B
C
D
E
4
The size of the angle a in the figure below is:
A
B
C
D
E
5
18 sin 53º
18 tan 53º
18 cos53º
18
tan 53
18
sin 53
4244ʹ
4215ʹ
4745ʹ
3355ʹ
4755ʹ
The length of the side b in the figure below is:
A
B
C
D
E
98.3
63.4
181.5
63.5
89.3
3
6
285T is the same bearing as:
A N85W
B N75W
C W75N
D S75W
E S85W
7
The diameter of a vertical cone is 23 cm and the length of the slant edge is 43 cm. The semivertical angle of the cone is:
A 3015ʹ
B 3220ʹ
C 1610ʹ
D 3715ʹ
E 1531ʹ
8
What is the length of the sloping edge (in mm) of this prism? The cross section is an
isosceles triangle.
A
B
C
D
E
9
65 mm
80 mm
85 mm
120 mm
130 mm
What is the length of HD (the diagonal of the base) in this prism?
A
B
C
D
E
5.39
4.29
3.76
2.4
1.75
4
10
From the top of a vertical cliff 125 m high, the angle of depression to a ship is 348ʹ. From
the base of the cliff, the distance to the ship is closest to:
A 1880 m
B 1350 m
C 1250 m
D 1080 m
E 1450 m
11
A tree 34 m high casts a shadow 12 m long. The angle of elevation of the sun is closest to:
A 71
B 21
C 69
D 19
E 79
5
Section C Short Answer Section

1.
Working out must be shown to gain full marks.
CAS may be used to check answers and must be used when asked in the question.
A plane flies for 419 km on a bearing of 14853ʹT.
a) Draw a labelled diagram showing the plane’s journey.
b) How far south is the plane from its starting point? Give your answer to the nearest kilometre.
2 + 2 = 4 marks
2. From the top of a building 202 m high, the angle of depression to the top of another building is 25. The
buildings are separated by a horizontal distance of 120 m.
a. Draw a diagram to illustrate this situation.
b. Calculate the height of the second building. Give your answer to the nearest metre.
6
3.
2 + 2 = 4 marks
Damian was drinking his can of Sprite when his 10.8 cm straw fell inside the can. The can has a radius of
4.4 cm and height 13 cm as shown.
(a) How far below the top of the can does the top of the straw lie? Give your answer correct to 1 decimal place.
(b) What is the angle the straw makes with the base of the can? Give your answer correct to the nearest degree.
3+2 = 5 marks
7
4.
A triangular rug as shown below, where the angle at A is acute, is being laid in the foyer of a building. The
height of the triangle is h, as also indicated on the diagram.
h
5.
a) Calculate the height h of the triangle, correct to two decimal places.
b)
Calculate the length of AC, correct to two decimal places.
c)
State the area of the rug, in square metres, correct to one decimal place.
2+ 3+ 1 = 6 marks
8
Section D:
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
ANALYSIS
(10 marks)
Working out must be shown to gain full marks
CAS calculator may be used to check your answer.
From a point A on level ground, the angle of elevation to the top of a pine tree is 60°. From a point B, also on
the ground, 20 m away from point A and in line with A and the foot of the pine tree, the angle of elevation to
the top of the pine tree is 30°.
Let h be the height of the pine tree and let d be the distance between A and the foot of the pine tree.
(a) Draw a labelled diagram and mark the size of all the angles.
(b) Write an equation using point A to express the height of the pine tree h in terms of the distance d
(c) Write another equation using point B this time to express the height of the pine tree in terms of d.
(d) Use your two equations from parts (b) and (c) to find the distance from B to the pine tree. You may use
technology to achieve your solution.
(e) How high is the pine tree? Give your answer correct to two decimal places.
9
(2+2+2+2+2= 10 marks)
10