2026 Pcss Math Prelim P2 QP

[Turn over PEICAI SECONDARY SCHOOL SECONDARY 4 EXPRESS / 5 NORMAL ACADEMIC PRELIMINARY EXAMINATION 2026 CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS 4052/02 Paper 2 19 August 2026 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 This document consists of 22 printed pages and 2 blank pages. Setter: Ms Novell Tham

[Turn over 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) Find all the prime numbers that satisfy the inequality 113 62 x−−   . Answer ………………………… [3] (b) Simplify 43 53 69 5 20 xy x z zy  . Answer ………………………… [2] (c) Simplify 1 34 12 927 r s −   . Answer ………………………… [2]

[Turn over 4 (d) Write as a single fraction in its simplest form 2 73 125 4 2 5xx −+−− . Answer ………………………… [4]

[Turn over 5 2 (a) In the diagram, ABCD is a square. The coordinates of A and D are (2, 3) and (5, 2) respectively. Find the area of square ABCD. Answer …………………………units2 [3] B C A 0 (2, 3) D (5, 2) y x

[Turn over 6 (b) The points M(0, 2k), N(1, k) and P(5, 6− ) lie on the same straight line. (i) Show that the value k is 2. Answer [2] (ii) Find the equation of MN. Answer ………………………… [2]

[Turn over 7 3 The diagram below shows a circle of radius 2 cm inscribed in a regular hexagon. (a) (i) Show that the length of one side of the hexagon is 2.31cm Answer [2] (ii) Find the area of the shaded region. Answer …………………………cm2 [3] 2cm m

[Turn over 8 (b) Two regular pentagons ABCDE and PQRST are joined together to form the shape shown below. Find angle AEC. Answer ………..………………..o [3]

[Turn over 9 (c) The sides CD and AB are produced to meet at Z. Show that triangle BZC is an isosceles triangle. Answer [3]

[Turn over 10 4 The table below shows the distribution of three types of apartments in three blocks of an Executive Condominium. This information can be represented by the matrix A= 25 20 60 35 45 30 30 50 10    . The areas of the 3-room, 4-room and 5-room apartments are 75 m², 95 m² and 120 m² respectively. (i) Represent the areas of the apartments in a 31 column matrix C. Answer C = [1] (ii) Evaluate the matrix M = AC Answer M = [2] (iii) State what the elements of M represent. Answer ………………………………………………………………………… ………………………………………………………………………… ……………………………………………………………………...[1] 3-room 4-room 5-room Block 1 25 20 60 Block 2 35 45 30 Block 3 30 50 10