2025 MSHS Math Prelim P1 Question

This document consists of 24 printed pages. [Turn over For Examiner’s Use Subtotal Statement Presentation Units Rounding off Class/ Index Number Centre Number/ ‘O’ Level Index Number Name / / MARIS STELLA HIGH SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR MATHEMATICS 4052/1 Paper 1 18 August 2025 Candidates answer on the Question Paper. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, index number 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 the questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. 90

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  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry A a sin = B b sin = C c sin 2 2 2 2 cosa b c bc A= + − Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 1 Simplify ( )( ) 3 22x x x x− + − . Answer ............................................. [2] 2 Represent the solution set of the simultaneous inequalities 3x and 26 x−   on the number line below. Answer [1] 0 2 1 4 3 6 5 7 2 x

4 3 The cash price for a car was $150000 . Sally paid a downpayment of $90000 and paid the remaining amount by monthly instalments for 5 years. A simple interest of %x per annum was charged and that her monthly instalment was $1090 . (a) Find the value of x . Answer x = ........................................ [4] (b) Calculate the extra cost of using hire purchase as a percentage of the cash price. Answer ....................................... % [1]

5 4 The diagram shows a segment of a circle, PQR. (a) A point X on the perimeter of the segment is such that PX = RX. Find and label the position of X. [1] (b) On the diagram, construct the angle bisector of angle XPR. [1] (c) On the diagram, shade a region inside PQR that is closer to PR than PX, and closer to P than R. [1] P Q R

6 5 (a) An interior angle of a regular n-sided polygon is 1.5 times its exterior angle . Find the value of n. Answer n = ................................ [3] (b) What is the name of the n-sided polygon given in part (a) ? Answer ........................................ [1]

7 6 The scale of Map A is given as 1: 200 000. (a) The length of a road on the map is 6 cm. Calculate the actual distance, in kilometres, of the road. Answer ....................................... km [2] (b) The scale of Map B is 1: 250 000 and the size of an island on Map B is 3.6 2cm . Calculate the area of the same island, in square centimetres, on Map A. Answer .................................... 2cm [2]

8 7 Factorise (a) 22 5 3xx+− , Answer ............................................. [2] (b) 23 24 4 18x y x xy− + − . Answer ............................................. [2] 8 The first four terms in a sequence are 2, 6, 18, 54. (a) Find an expression, in terms of n, for the nth term of the sequence. Answer ............................................. [1] (b) Explain why the number 98415 is not a term of the sequence. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... [1]

9 9 A bag contains 21 marbles, of which 6 are blue and 15 are red. Two marbles are drawn at random, one after the other, from the box without replacement. (a) Complete the tree diagram below. [2] First marble drawn Second marble drawn Blue Blue Red Blue Red Red (b) Find the probability that (i) both marbles drawn are blue, Answer ............................................. [1] (ii) at most one of the marbles drawn is red. Answer ............................................. [2] 2 7     7 10        

10 10 In the diagram, PXR is a straight line, 290 , 17 cm, 8 cm and area of 36 cm .PRQ PQ QR PXQ =  = =  = Calculate (a) RX, Answer ....................................... cm [3] (b) cos QXP . Answer ............................................. [2] 8 cm 17 cm Q R X P