Sec3 WA3 Revision Time Trial 2023 BukitMerah

Secondary 3 Mathematics WA3 Revision Time Trial — Bukit Merah (2023) Duration: 65 minutes Score: / 43 Topics tested: Graphs of Functions; Graphs in Practical Situations; Further Trigonometry; Applications of Trigonometry; Arc Length and Sector Area. Section A: Graphs of Functions [11 marks] 1. (a) Complete the table of values for y = 1 5 x3 − 4 5 x2. [1] x −1.5 −1 0 1 2 3 4 5 y −2.5 −1 0 −0.6 −1.8 0 5 (b) On the grid on the next page, draw the graph of y = 1 5 x3 − 4 5 x2 for −1.5 ≤ x ≤ 5. [3]

x y 0−2 −1 1 2 3 4 5 1 2 3 4 5 6 7 −1 −2 −3

(c) Explain how your graph shows that there is only one solution of the equation 1 5 x3 − 4 5 x2 = 2. [1] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (d) The equation x3 − 4x2 + 10x − 20 = 0 can be solved by finding the points of intersection of the straight line y = ax + b and the curve y = 1 5 x3 − 4 5 x2. (i) Find the value of a and the value of b. [2] Answer a = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,b = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (ii) By drawing the line y = ax + b, solve the equation x3 − 4x2 + 10x − 20 = 0 . [2] Answer x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (e) By drawing a tangent, find the gradient of the curve at (−1, −1). [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Section B: Graphs in Practical Situations [7 marks] 2. The diagram shows the speed-time graph of an object moving in a straight line over a period of 25 seconds. The object travelled 90 m from t = 12 to t = 16. (a) Find the maximum speed of the object. [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s (b) Find the speed of the object at t = 6. [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s

(c) Sketch the distance-time graph for 0 ≤ t ≤ 25. [3] Section C: Further Trigonometry [4 marks] 3. In triangle W XZ, W X = 8 cm. Y is a point on XZ such that W Y = 5 cm, Y Z = 11 cm and sin ∠W Y Z = 4 5 . (a) Find the area of triangle W Y Z. [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2 (b) Find the size of angle W XY . [2]

Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Section D: Applications of Trigonometry [15 marks] 4. The diagram shows three points O, P and Q. The bearing of P from O is 045◦ and P is due north of Q. OP = 90 m and P Q = 120 m. (a) Find the distance of OQ. [3] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m (b) Calculate the bearing of Q from O. [3] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. The diagram shows a triangular court P QR. P R = 20 m, P Q = 48 m and RQ = 52 m. (a) Prove that QP R is a right angle. [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (b) Hence, or otherwise, calculate angle P RQ. [2] Answer ∠P RQ = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (c) Find the shortest distance of P from the line RQ. [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m

(d) If a flag post of height 4.5 m is hoisted up at P and a bird was perched on top of the flag post, calculate (i) the greatest angle of elevation of the bird from a wild chicken walking from Q to R, [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (ii) the greatest angle of depression of the wild chicken from the bird. [1] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Section E: Arc Length and Sector Area [6 marks] 6. The diagram below shows a circle of radius 7 cm, centre O. OE is perpendicular to the chord BC at the point F , OF = 4 cm. (a) Find the angle BOC , in radians. [2] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radians

(b) Express angle BOC , in degrees. [1] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (c) Find the area of the major segment BAC . [3] Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2 — END OF PAPER —