ABSTRACT
Plot a graph of y (vertically) against x (horizontally) to scales of 1 cm = 1 for the horizontal x-axis and 1 cm = 2 for the vertical y-axis. From the graph find:
(a) the value of y when x = 3 (b) the value of y when x = −4 (c) the value of x when y = 1 (d) the value of x when y = −20 (8)
3. If graphs of y against x were to be plotted for each of the following, state (i) the gradient, and (ii) the y-axis intercept. (a) y = −5x + 3 (b) y = 7x (c) 2y + 4 = 5x (d) 5x + 2y = 6 (e) 2x − y
3 = 7
6 (10)
4. The resistance R ohms of a copper winding is measured at various temperatures t◦C and the results are as follows:
R () 38 47 55 62 72 t (◦C) 16 34 50 64 84
Plot a graph of R (vertically) against t (horizontally) and find from it (a) the temperature when the resistance is 50 (b) the resistance when the temperature is 72◦C (c) the gradient (d) the equation of the graph. (10)
5. In triangle JKL in Figure RT5.1, find (a) length KJ correct to 3 significant figures, (b) sin L and tan K , each correct to 3 decimal places. (4)
6. Two ships leave a port at the same time. Ship X travels due west at 30 km/h and ship Y travels due north.After 4 hours the two ships are 130 km apart. Calculate the velocity of ship Y . (4)
7. If sin A = 12 37
find tan A in fraction form. (3) 8. Evaluate 5 tan 62◦11′ correct to 3 significant
figures. (2) 9. Determine the acute angle cos−1 0.3649 in degrees
and minutes. (2) 10. In triangle PQR in Figure RT5.2, find angle P in
decimal form, correct to 2 decimal places. (2)
figures: 3 tan 81.27◦ − 5 cos 7.32◦ − 6 sin 54.81◦ (2)
12. In triangle ABC in Figure RT5.3, find lengths AB and AC, correct to 2 decimal places. (4)
13. From a point P, the angle of elevation of a 40 m high electricity pylon is 20◦ . How far is point P from the base of the pylon, correct to the nearest metre? (3)
14. A triangular plot of land ABC is shown in Figure RT5.4. Solve the triangle and determine its area. (10)
travels 500 correct to now above
16. Figure RT5.5 shows a roof truss PQR with rafter PQ = 3 m. Calculate the length of (a) the roof rise PP′, (b) rafter PR, and (c) the roof span QR. Find also (d) the cross-sectional area of the roof truss. (11)
17. Solve triangle ABC given b = 10 cm, c = 15 cm and A = 60◦ . (10)
