MSHS Prelim P1 EM Markers Report 2025

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− + − . 𝑥3 − 𝑥(𝑥 + 2)(𝑥 − 2) = 𝑥3 − 𝑥(𝑥2 − 4) = 𝑥3 − 𝑥3 + 4𝑥 = 4𝑥 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 23 x−   Markers Report Well done but a few expanded wrongly Markers Report Well done but some did not draw final number line (shading alone not accepted)

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 . ( )( ) 150000 90000 60000 1090 5 12 65400 Interest 65400 60000 5400 60000 55400 100 1.8 x x −=   = =− = = = Answer x = ........................................ [4] (b) Calculate the extra cost of using hire purchase as a percentage of the cash price. 5400 100% 3.6%150000= Answer ....................................... % [1] Markers Report A handle used percentage change formula resulting in 9% (wrong concept) Markers Report Generally well done

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 Markers Report Generally well done but some students have missing arcs.

6 5 (a) An interior angle of a regular n-sided polygon is 1.5 times larger than its exterior angle. Find n. 1.5 180 2.5 180 72 360 72 5 xx x x n n + =  = = =  = Answer n = ................................ [3] (b) What is the name of the n-sided polygon given in part (a) ? Pentagon Answer ........................................ [1] Markers Report Generally well done, other methods accepted. Markers Report Generally well done.

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. 1: 200000 1 cm: 2 km 6 cm: 12 km 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. 22 2 22 2 1: 250000 1cm : 2.5km 1cm : 6.25km 3.6 6.25 22.5km 1cm : 4km 22.5 5.625cm4  = = Answer .................................... 2cm [2] Markers Report Generally well done. Markers Report Generally well done.

8 7 Factorise (a) 22 5 3xx+− , ( )( ) 22 5 3 3 1 2 xx xx +− = + − + Answer ............................................. [2] (b) 23 24 4 18x y x xy− + − . ( ) ( ) ( )( ) 23 24 4 18 3 4 6 4 3 6 3 4 x y x xy x x y x x y x − + − = + − + = − + 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. ( ) 1 23 n− Answer ............................................. [1] (b) Explain why the number 98415 is not a term of the sequence. Because the number if not even. ....................................................................................................................................... ....................................................................................................................................... [1] Markers Report Generally well done, accept other forms eg. ( )( )3 1 2xx− + − , ( )( )3 1 2xx− − − Markers Report Generally well done Markers Report Not well done, many cannot deduce the general term. Accept other simplified expressions. Markers Report Not well done. Accept actual finding of n and explain that n is not whole number. No ecf if n is found from wrong expression in part (a).

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 Markers Report - In general, well done - Students forget to reduce fractions 2 7   51 20 4  = 7 10   15 3 20 4  = 63 20 10  = 15 5 21 7  =

10 (b) Find the probability that (i) both marbles drawn are blue. 2 1 1 7 4 14= Answer ............................................. [1] (ii) at most one of the marbles drawn is red. 571 7 10 1 2 5 3 2 3 2 1 7 10 7 4 7 4 1 2 or − =       +  +            = Answer ............................................. [2] Markers Report - (b)(i) In general, well done - (b) (ii) Students did not interpret correctly and included the case where both are red.