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 th