Year 10 General Maths – Exam Revision – Pythagoras and Trigonometry 1
Part A – Multiple-choice(10 marks)
1Which of the following mathematical statements is false?
ABC
DE
2For the right-angled triangle shown, the value of x is given by:
ABC
DE
3The slant height, s cm, of the following cone, correct to one decimal place, is:
A11.3 cmB5.5 cmC3.4 cm
D2.3 cmE2.1 cm
4Which of the following triangles has its sides labelled correctly?
ABC
DE
5The value of tan 29, correct to four decimal places, is:
A0.4848B0.8746C0.1307
D0.5543E0.2591
Questions 6 and 7 refer to the following diagram:
6For the given triangle:
ABC
DE
7For the given triangle:
ABC
DE
8From the top of a lighthouse, John spots a boat out at sea. If the lighthouse is 18 m above sea level and the boat is 60 m away from its base, John’s angle of depression to the boat is closest to:
A54B72C73
D16E17
Questions 9 and 10 refer to the following diagram:
9The true bearing of A from O is:
A130 TB140 TC220 T
D230 TE310 T
10The true bearing of O from A is:
A040 TB050 TC130 T
D140 TE220 T
Part B – Short-answer(16 marks)
1Find the length of the hypotenuse in each of the following right-angled triangles, leaving your answer to part b as an exact value.
a b
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______
______
(1 + 1 = 2 marks)
2Find the value of the pronumeral in each of the following right-angled triangle, leaving your answer to part b as an exact value.
ab
______
______
______
(1 + 1 = 2 marks)
3Consider the following rectangular prism.
aFind the length AC
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bHence, find the length AD as an exact value.
______
______
(1 + 1 = 2 marks)
4In each of the following, find the value of x correct to two decimal places.
acos 70 = b = tan 28
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______
csin 34 = d = cos 59.6
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______
______
(4 1 = 4 marks)
5For each of the following, find the value of x correct to two decimal places.
ab
______
______
______
cd
______
______
______
(4 1 = 4 marks)
6Find the value of to the nearest degree.
ab
______
______
______
(1 + 1 = 2 marks)
Part C – Extended-response(14 marks)
1A pilot flying a plane at an altitude of 1790 m sees a mountain peak 2540 m high, 2800 m away from him in the horizontal direction.
aWhat is the difference in the vertical height between the plane and mountain peak?
______
______
______
bFind the direct distance between the plane and the mountain peak, correct to the nearest metre.
______
______
______
cFind the pilot’s angle of elevation to the mountain peak to the nearest
degree.
______
______
______
The pilot quickly starts to climb so as to fly the plane over the mountain peak. When he is 2000 m away from the mountain peak in the horizontal direction, and at an altitude of 1850 m, he is flying at an angle of 17 to the horizontal.
dIf the pilot continues to fly at this angle, will he clear the mountain peak?
______
______
______
eWhat is the smallest angle of inclination, to the nearest degree, that the pilot can fly at and still clear the mountain peak?
______
______
______
(1 + 2 + 2 + 3 + 1 = 9 marks)
2Alice starts from point O and walks 3 km on a true bearing of 140 to point A.
aDraw a diagram to represent this scenario.
bHow far south of the starting point is Alice? Give your answer correct to two decimal places.
______
______
______
cWhat is the bearing of point O from point A?
______
______
______
(1 + 2 + 2 = 5 marks)