Tanjong Katong Secondary School Paper 2

This document consists of 24 printed pages. CANDIDATE NAME MATHEMATICS 4048/02 Paper 2 Monday 22 Aug 2022 2 hours and 30 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/ tape. 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. You are expected to use a scientific calculator to evaluate explicit numerical expressions. 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 . 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 of the marks for this paper is 100. TANJONG KATONG SECONDARY SCHOOL Preliminary Examination 2022 Secondary 4 CLASS INDEX NUMBER www.KiasuExamPaper.com 752

2 4048/2/Sec4Prelim/22 Mathematical Formulae Compound Interest Total Amount = P n r      + 1001 Mensuration Curved surface area of a cone = rl Curved surface area of a sphere = 4r2 Volume of a cone = 3 1 r2 h Volume of a sphere = 3 4 r3 Area of triangle ABC = 2 1 ab sin C Arc length = r, where  is in radians Sector area = 2 1 r2 , where  is in radians Trigonometry A a sin = B b sin = C c sin a2 = b2 + c2 − 2bc cos A Statistics Mean =   f fx Standard Deviation = 22       −     f fx f fx www.KiasuExamPaper.com 753

3 4048/2/Sec4Prelim/22 [Turn over for Question 1] [Turn over www.KiasuExamPaper.com 754

4 4048/2/Sec4Prelim/22 Answer all questions. 1 (a) Solve the inequality 6 2 1 58 yy+−  . Answer ……………..………….. [2] (b) Solve these simultaneous equations. 3x – 7y = −41 4y + 5x = 10 Answer x = ……………..…………. y = ………..………….. [3] www.KiasuExamPaper.com 755

5 4048/2/Sec4Prelim/22 (c) Express as a single fraction in its simplest form 2 23 ( 2) 2 x xx ++−− . Answer ……………..………….. [2] (d) Simplify 32 23 (2 ) 27 9 aa bc b c . Answer ……………..………….. [2] (e) Simplify 2 2 3 31 07 0 3 5 y y y y+ − + + . Answer …………..………...…….[3] [Turn over www.KiasuExamPaper.com 756

6 4048/2/Sec4Prelim/22 2 Deli Burgers sells fish burgers, chicken burgers and beef burgers at Outlets A and B. The table below shows the average number of burgers sold in both outlets on a weekday. Fish burger Chicken burger Beef burger Outlet A 250 280 260 Outlet B 320 300 290 (a) Represent the information in the table above in a 2 × 3 matrix R. Answer R =    [1] (b) (i) Evaluate V = R 1 1 1    . Answer V = [1] (ii) State what each element in V represents. Answer…………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………..………[1] www.KiasuExamPaper.com 757

7 4048/2/Sec4Prelim/22 (c) On average, Outlets A and B expect to sell 20% more fish burgers, 15% more chicken burgers, and 30% more beef burgers per day over the weekend. (i) Write down a 3 × 1 column matrix E, such that RE will give the expected average number of burgers to be sold in the Outlets A and B on a particular day during the weekend. Answer E = [1] (ii) Evaluate the matrix Q = RE. Answer Q = [1] (iii) Hence, represent the total number of burgers sold at each outlet in a week in a 2 × 1 column matrix T. Answer T = [1] (d) Outlets A and B sell each burger at $3.50. Find the total sales for Deli Burgers in a week. Answer $ …………....…….[2] [Turn over www.KiasuExamPaper.com 758

8 4048/2/Sec4Prelim/22 3 (a) Complete the table of values for ( ) 3185 1 x x y− = . x 1− 0 1 2 3 4 5 y 4 . 3− 0 3.4 5.6 5.4 1.6 [1] (b) On the grid, draw the graph of ( ) 3185 1 x x y− = for 1− ≤ x ≤ 5. [3] (c) Use your graph to find the values of x for which 315 18 xx=− in the range 1− ≤ x ≤ 5. Answer x = …………… or …………….. [3] −6 −2 0 2 4 y −1 1 2 3 4 x 5 6 −4 −8 www.KiasuExamPaper.com 759

9 4048/2/Sec4Prelim/22 (d) The line 5y kx=+ where k is a constant, is a tangent to the curve. By drawing a suitable straight line on the graph, find the value of k. Answer k = ………………………….. [2] (e) Explain why the equation ( ) 31 185 x x p−= does not have solutions for some values of p in the range 1− ≤ x ≤ 5. Answer ..………………..………….………………..………...………………..…… ……..………….………………..………...………………..……………………..…...[1] (f) The solutions of the equation 3 0x Ax B+ + = are obtained from the x-coordinates of the points at which the line y = 2 – x intersects with the graph ( ) 3185 1 x x y− = . Find the value of A and the value of B. Answer A =……..… and B =……….… [3] [Turn over www.KiasuExamPaper.com 760

10 4048/2/Sec4Prelim/22 4 In the diagram, A, B, C, D and E are on level ground. Ann and Tony start jogging at the same time from A and from B respectively. Ann jogs in the direction AC at an average speed of 1.5m/s. Tony jogs in the direction BD. Ann and Tony meet after 1.5 minutes at E. The bearing of C from A is 040o. Angle CAB = 65o and AB = 175 m. (a) (i) Calculate AE. Answer …………..…………. m [1] (ii) Calculate BE. Answer …………..…………. m [2] E A C D B 175 65o N www.KiasuExamPaper.com 761