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Tak Sun Secondary School Marks Form 3 Mathematics (Applications in Trigonometry) Revision Exercise 2016-2017 Name : ___________________________ Class : /35 _________ No. :_______ Section A : Multiple Choices (2 marks each, 10 marks in Total) Choose the most suitable answer and write down into the corresponding boxes. Time Allowed: 35 minutes 1. B 1. 2. C 3. A 4. A Caroline rides a bicycle and moves up a road with gradient 5. A 1 . If her horizontal run is 2.4 km, 12 find her vertical rise. A. B. C. D. 2. 3. 0.05 km 0.2 km 5 km 12 km If the gradient of a road is 0.23, what is the inclination of the road? (Give the answer correct to 3 significant figures.) A. B. 12.0 12.9 C. D. 13.0 13.9 The figure shows a contour map of scale 1 : 20 000. If the horizontal run of AB is 1 cm on the map, find the inclination of AB, correct to the nearest degree. A. B. C. 27 30 45 D. 60 1 4. The angle of elevation of the top C of the building CD from the top of the building AB is 30°. The angle of depression of the bottom D of the building CD from the top of the building AB is 50°. If the height of the building AB is 80 m, find the height of the building CD, correct to 3 significant figures. 5. A. B. 119 m 135 m C. D. 165 m 245 m In the figure, E and F are two lifeguard towers 200 m apart along the shore. Given that the bearings of the swimmer C from E and F are 045° and 315° respectively, find the shortest distance from C to the shore. A. B. C. D. 100 m 150 m 200 m 300 m Section B : (Short Questions) Total 25 marks Please write all answers with steps in the spaces provided. 6. Jane walks 12 m up a slope and her vertical rise is 5 m. Find the gradient of the stair, correct to 3 significant figures. (4 marks) In △ABC, BC 2 + AC 2 = AB 2 AC 1M AB 2 BC 2 12 2 5 2 m 119 m BC Gradient of the stair AC 5m 119 m 0.458 , cor. to 3 sig. fig. 1A 1M 1A 2 7. The figure shows a contour map. Now a straight road is going to be constructed to connect E and F. If the actual horizontal run between E and F is 420 m, find the gradient of the straight road. Express your answer as a fraction. 100 m 80 m 60 m 40 m F 20 m 0m E (5 marks) 1M+1A Vertical rise of EF = (80 – 20) m = 60 m Refer to the figure. 1M FD Gradient of the straight road ED 60 m 420 m 1 7 1M 1A 3 8. Cindy stands on the belvedere of the peak to see the pier on the opposite bank. Her eye level is 450 m above the horizontal. If the horizontal distance between Cindy and the pier is 5 400 m, find the angle of depression of the pier from Cindy. (Give the answer correct to 3 significant figures.) (4 marks) Refer to the figure. Let the angle of depression required be θ. 1M In △ABC, ∠ABC = 450 m AC tan BC 5 400 m 1M 1M = 4.76, cor. to 3 sig. fig. The angle of depression required is 4.76°. 4 1A 9.A boy rides a bicycle from position A to B in a direction of 056°, then he turns 74° left to C which is due north of A. Find the whole circle bearing of B from C. (5 marks) With the notation in the figure, In △ABC, ∠ACB + 56 = 74 ∠ACB = 18 = 180 – ∠ACB 1M 1A 1M = 180 – 18 = 162 The whole circle bearing of B from C is 162°. 1A 1A 5 10.Two speedboats A and B sail from the same position X at the same time. Speedboat A sails at a speed of 40 km/h due south and speedboat B sails at a speed of 60 km/h due west. Find the reduced bearing of A from B after 15 minutes, correct to the nearest degree. N B 60 km/h X 40 km/h A (7 marks) After 15 minutes, distance between B and X = 60 15 km 60 = 15 km 15 distance between A and X = 40 km 60 = 10 km With the notation in the figure, 1A 1A In △AXB, ∠AXB = 90 AX tan BX 10 km 15 km = 33.69, cor. to 2 d.p. = 90 – 1A 1M = 90 – 33.69 = 56, cor. to the nearest degree The reduced bearing of A from B is S56°E. 1A 1A 1M End of Paper 6