Sec 3 Express Peicai 2023 Paper 2

[Turn over PEICAI SECONDARY SCHOOL SECONDARY 3 EXPRESS END-OF-YEAR EXAMINATION 2023 CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS 4052/02 Paper 2 3 October 2023 2 hours 15 minutes Candidates answer on Question Paper READ THESE INSTRUCTIONS FIRST Write your register number, class and name on all the work you hand in. Write in dark blue or black pen. You may use an 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 𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋. 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 90. For Examiner’s Use ANnotations ACcuracy Marks Deducted 1 1 This document consists of 19 printed pages and 1 blank page. Setter: Mr Lim Jit Chong

2 Mathematical Formulae Compound Interest Total Amount 1 100 n rP=+  Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where θ is in radians Sector area = 21 2 r  , where θ is in radians Trigonometry sin sin sin a b c A B C== Abccba cos2222 −+= Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

[Turn over 3 Answer all questions 1 (a) It is given that (3 ) 3m x y y k+ + = . (i) Find the value of k when 5x= , 7y=− and 2m= . Answer k = ............................ [1] (ii) Express y in terms of k, m and x. Answer y = ............................ [3] (b) Solve 2(2 7) 25x−= Answer k = ........... or ............ [2] (c) Simplify (i) 2 3 62 25 5 ac ac xx Answer .................................. [2] (ii) 2 23 93 x xx −−− Answer .................................. [3] __________________________________________________________________________

4 2 (a) The straight lines AD and BC intersect at O. AB is parallel to DC. AO = 6 cm, OD = 18 cm, CD = 15 cm and OC = 24 cm. (i) Show that AOB is similar to DOC . Answer: [2] (ii) Find the length of AB. Answer ............................ cm [2] (iii) Given that the area of DOC is 126 cm2, find the area of AOB . Answer ........................... cm2 [2] 18 cm 15 cm 24 cm 6 cm A B C D O

[Turn over 5 (b) In the diagram below, EFGH is a parallelogram. (i) Show that EHF is congruent to GFH . Answer: [2] (ii) Given that : 2 :1HK KF = , find Area of Area of EKF EHK   . Answer .................................. [1] (iii) Find Area of Area of EKF EFGH  . Answer .................................. [1] __________________________________________________________________________ E F G H K

6 3 On his holiday trip, Mr Lim drove 230km from town A to town B at an average speed of x km/h. (a) Write an expression in terms of x for the time that he had taken to drive from town A to town B. Answer ........................ hours [1] (b) On his return trip from town B to town A, Mr Lim increased his average speed by 10 km/h. Write an expression in terms of x for the time that he had taken for his return trip. Answer ........................ hours [1] (c) Mr Lim took 45 minutes less for his return journey. Form an equation and show that it reduces to 23 30 9200 0xx+ − = . Answer: [2]

[Turn over 7 (d) Solve the equation 23 30 9200 0xx+ − = , correct to 3 significant figures. Answer x = ................. or .................. [3] (e) Hence, find the time that Mr Lim reached town A for his return trip given that he left town B at 09 00. Answer ............................ [2] __________________________________________________________________________

8 4 The diagram, not drawn to scale, shows a field ABC. AB = 5 m and AC = 8.6 m. The bearing of A from B is 049 and the bearing of C from A is 141 . (a) Show that 88BAC= . State your reasons clearly. Answer: [2] (b) Find the length of BC. Answer ............................. m [2] 5 m 8.6 m m A B C N

[Turn over 9 (c) Calculate ACB . Answer ............................... o [2] (d) Find the shortest distance from A to BC. Answer ............................. m [2] (e) A kite is hovering 6 m vertically above A. Mr Lim is walking along BC. Find the greatest angle of elevation of the kite from Mr Lim. Answer ............................... o [2] __________________________________________________________________________

10 O A B X Y 12 cm 5 In the diagram below, OAB and XYB are sectors of two circles with centres O and Y respectively. 0.6YOX= radians, 12OY = cm and XY is perpendicular to OX. (a) Show that the length of XY = 6.78 cm. Answer: [1] (b) Show that 2.17BYX= rad. Answer: [1] (c) Hence, find the perimeter of the shaded region ABX. Answer ............................ cm [4] 0.6 rad