2026 GMS P2 QP

[Turn Over Candidate Name Class Index Number MATHEMATICS 4052/02 Paper 2 4 Express 5 Normal (Academic) Candidates answer on the Question Paper. 2 hours 15 minutes Setter: Ms Desiree Ho Wednesday, 19 August 2026 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 π , use either your calculator value or 3.142. This document consists of 24 printed pages. For Examiner’s Use Geylang Methodist School (Secondary) Preliminary Examination 2026 90

2 GMS(S)/Math/P2/Prelim2026/4E5N Mathematical Formulae Compound interest Total amount = Mensuration Curved Surface Area of a cone = πrl Surface Area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = n rP      + 1001 Cabsin21 r  2 2 1 r  C c B b A a sinsinsin == Abccba cos2222 −+=   f fx 22 −  ffxffx

3 GMS(S)/Math/P2/Prelim2026/4E5N [Turn Over TURN OVER TO QUESTION 1

4 GMS(S)/Math/P2/Prelim2026/4E5N 1 (a) (i) Solve the inequalities 321 1 5 4x−−  +  . Answer [3] (ii) Hence, find the smallest positive value of 221x + . Answer [2]

5 GMS(S)/Math/P2/Prelim2026/4E5N [Turn Over (b) Simplify 0 3 26 12 7 21 a b bc ca  . Answer [2] (c) Simplify 1 69 3 327 pq r − −   . Answer [2] (d) Write as a single fraction in its simplest form 733 21 xxx+− −− . Answer [3]

6 GMS(S)/Math/P2/Prelim2026/4E5N 2 Penny is a property agent. She handles the sale of landed homes (L), private condominiums (C) and HDB flats (F) in the east and central parts of Singapore. The matrix T shows the number of transactions of each property type that Penny handled in a particular month. L C F 4 8 East 5 2 9 Central x=T The commission earned for each property type is $13 000 for landed home s, $8000 for private condominiums and $4000 for HDB flats. (a) Represent the commission in a 31 matrix C. Answer C = [1] (b) Find, in terms of x, the matrix P = TC. Answer P = [2] (c) State what the first element of matrix P represents. [1]

7 GMS(S)/Math/P2/Prelim2026/4E5N [Turn Over (d) Penny earns $15 000 more from selling the properties in the east than those in the central area. Find the value of x. Answer x = [1] (e) Penny decreases her commission for properties in the east by 20% and increases it for properties in the central area by 15%, Calculate the percentage change in her total commission earned. Give your answer to 1 decimal place. Answer [2]

8 GMS(S)/Math/P2/Prelim2026/4E5N 3 (a) ( )4.5,0A and ( )0,9B are points on a straight line. (i) Find the equation of the straight line, AB. Answer [2] (ii) M is a point on AB such that it is equidistant from the x-axis and the y-axis. Show that coordinates of M are ( )3,3 . Answer [2] O x x x y

9 GMS(S)/Math/P2/Prelim2026/4E5N [Turn Over (iii) 0 3NM =  . Prove that triangle ANM is similar to triangle AOB. [4] (b) The ratio of the height of two square pyramids is 1 : 4. The ratio of the length of their square bases is 2 : 3. Find the ratio of the volume of the smaller pyramid to that of the larger pyramid. Answer : [2]

10 GMS(S)/Math/P2/Prelim2026/4E5N 4 The diagram shows a container made up of a triangular prism and a cuboid with dimensions ( )5 x− cm by ( )5 x− cm by x cm. The height of the triangular prism is 2x cm. The volume of the solid, y cm3 is given by 322 20 50y x x x= − + . (a) Explain why 05 x . [2] (b) Complete the table of values for 322 20 50y x x x= − + . x 0.5 1 1.5 2 2.5 3 3.5 4 4.5 y 20.25 32 36.75 36 31.25 24 8 2.25 [1] (c) On the opposite grid, draw the graph of 322 20 50y x x x= − + for 0.5 4.5x . [3] (d) Use your graph to find the smallest value of x when the volume of the solid is 28 cm3. Answer x = [1]