CCHM 4048 02 QP

2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2022 SECONDARY 4 MATHEMATICS 4048/02 Paper 2 Wednesday 31 August 2022 Candidates answer on the Question Paper 2 hours 30 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all the questions. Give non -exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. This document consists of 23 printed pages and 1 blank pages. For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 10 Total Marks

2 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 Mathematical Formulae Compound interest Total amount = 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 Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx nrP      + 1001 lr  2 4 r hr 3 1 2 3 3 4 r Cba sin 2 1 r  2 2 1 r  C c B b A a sin sin sin == Acbcba cos 2 222 −+=

3 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over [Turn over for Question 1]

4 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 1 (a) Express as a single fraction in its simplest form ( )31 68 xx −− . Answer …………………………………….. [2] (b) Simplify 1 6 3 9 27b w −   . Answer …………………………………….. [2] (c) Simplify 2 2 5 12 4 25 20 4 pp pp −+ −+ . Answer …………………………………….. [3]

5 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over (d) Solve the equation 31 122xx +=−− . Answer …………………………………….. [3]

6 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 2 A is the point (−5, −2) and B is the point (−1, 3). (a) Find the distance between point A and point B. Answer ……………………………….. units [2] (b) Line p passes through point A and point B. Show that the equation of line p is 4 5 17yx=+ . Answer [3]

7 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over (c) The equation of line q is 8 7 43yx−= . Find the coordinates of the point of intersection of line p and line q. Answer (…………….…… , ….…….….…) [3] (d) The equation of another line r is 2 2.5y x k−= , where k is a constant and 8.5k  . Without solving algebraically, explain why line p and line r will never meet. Answer ……………………………………………………………………………………………... ……………………………………………………………………………………………... …………………………………………………………………………………………. [2]

8 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 3 An empty pool has a capacity of 20 000 litres. Hose A can fill the pool at a rate of x litres per minute. Hose B can fill the pool at a rate of (x – 8) litres per minute. (a) Write down an expression, in terms of x, for the number of minutes it would take to fill the pool using hose A. Answer …………………………… minutes [1] (b) Write down an expression, in terms of x, for the number of minutes it would take to fill the pool using hose B. Answer …………………………… minutes [1] (c) It takes 2 hours longer to fill the pool using hose B than it does using hose A. Write down an equation to represent this information and show that it reduces to 23 24 4000 0xx− − = .

9 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over (d) Solve the equation 23 24 4000 0xx− − = , giving your solutions correct to two decimal places. Answer x = ………..….… or .………………. [3] (e) Calculate how long it would take to fill the empty pool using hose A and hose B together. Give your answer in hours and minutes, correct to the nearest minute. Answer ....………hours ……………minutes [2]

10 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 4 ABC is a triangle where D is a point on AC. AB= a , AC = b and AD : DC = 3 : 2. X is a point on BD such that BX : XD = 1 : 2 . (a) Express, as simply as possible, in terms of a and/or b, (i) CB , Answer …………………………………….. [1] (ii) DB , Answer …………………………………….. [2] (iii) CX . Answer …………………………………….. [2] A B C D X b a