2024 NCHS Prelim Math P2 QP

Name: Register Number: Class: PRELIMINARY EXAMINATION 2024 SECONDARY FOUR EXPRESS MATHEMATICS 4052/02 Paper 2 Candidates answer on the Question Paper. 19 August 2024, Monday 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and register number in the spaces at the top of this page. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . The number of marks is given in brackets [ ] at the end of each question or part question. The total marks for this paper is 90. ______________________________________________________________________ This document consists of 22 printed pages including the cover page. For Marker’s Use 90

2 Mathematical Formulae Compound interest Total amount = 𝑃 (1 + 𝑟 100) 𝑛 Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry 𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 cos 𝐴 Statistics Mean = Standard deviation = rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == f fx   22        −  f fx f fx

3 Answer all questions. 1 (a) Simplify 9𝑎2−4𝑏2 3𝑎𝑝+6𝑎𝑞−4𝑏𝑞−2𝑏𝑝. Answer ..……………………… [3] (b) Write as a single fraction in its simplest form 𝑥 6−7𝑥−5𝑥2 + 2 5𝑥−3 . Answer ..……………………… [3]

4 (c) Solve the inequality − 1 2 < 2𝑦 5 − 1+𝑦 3 ≤ 5 6 . M1 → A1 → Simplest form (factorised denominator only) Answer ..……………………… [3]

5 2 A closed container, in the shape of a cone, is partially filled with water to a height of 25 cm as shown in Diagram I. The diameter of the container is 38 cm and the height of the container is 40 cm. Diagram I Diagram II (a) Calculate the amount of water in the container, leaving your answer in litres. Answer ……………..……litres [3] The container is subsquently inverted so that the water flows to the base of the cone as shown in Diagram II. (b) Calculate the height of the water, h cm, in the cone as shown in Diagram II. Answer …………….……… cm [4] 40 cm 25 cm 38 cm h

6 3 Sam, Jane and Peter each decided to purchase a new car priced at $108 888. (a) Sam paid for his new car in cash and was given a discount by the salesman. Given that Sam paid $100 176.96, find the percentage discount he received. Answer ………………….… % [2] (b) Jane paid 15% of the cash price as deposit and take a loan for the remaining amount from the bank which charges simple interest at the rate of 2.98% per annum over a period of five years. Calculate the monthly instalment Jane had to pay over the five years period. Answer $………..….………….. [4]

7 (c) Peter paid $18 888 as deposit and take a loan for the remaining amount from the bank which charges compound interest at the rate of R% per annum over a period of ten years. He paid a monthly instalment of $960. Calculate the value of R. Answer ....…………………….. [3]

8 4 Three bakery outlets A, B and C tracked the number of caramel, strawberry and mint cupcakes sold in a week in the table shown below. This information can be represented by the matrix P = ( 60 68 55 49 56 71 53 70 80 ). Caramel Cupcakes Strawberry Cupcakes Mint Cupcakes Outlet A 60 68 55 Outlet B 49 56 71 Outlet C 53 70 80 (a) Caramel cupcakes cost $1.20 each to bake. Strawberry cupcakes cost $1.50 each to bake. Mint cupcakes cost $0.95 each to bake. Represent these costs in a 3 × 1 column matrix Q. Answer Q = [1] (b) Evaluate the matrix R = PQ. Answer R = [2] (c) State what each element of matrix R means. …………………………………………………………………………………………... …………………………………………………………………………………………... [1]

9 (d) The selling price of each caramel, strawberry and mint cupcake are marked up by 200%, 150% and 300% of the respective cost price. Calculate the total amount of profit the three bakery outlets collected in a month. Answer $ ...………...………… [4]

10 5 The diagram shows four points W, X, Y and Z in an open field where W is due north of Y. WZ = 12.5 m and WX = 10.3 m. Angle WZY = 102.6°, angle WYZ = 34° and angle XWY = 45.3°. (a) Calculate XY. Answer ………………….…. m [4] (b) Calculate the bearing of W from Z. Answer ……………………….. [3] W 12.5 m North X Y Z 102.6° 34° 45.3° 10.3 m