2026 Riverside E-Math Paper 2

This document consists of 22 printed pages including1 blank page. RIVERSIDE SECONDARY SCHOOL SUBJECT : MATHEMATICS SUBJECT CODE /PAPER : 4052/02 LEVEL/STREAM : Sec 4 Express & 5 Normal (Academic) DURATION : 2 hours 15 minutes Write your class, index number and name in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 1 decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . At the end of the examination fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. Submit Part A and Part B separately. NAME: NO: CLASS: PRELIMINARY EXAMINATION 2026 www.KiasuExamPaper.com 302 www.KiasuExamPaper.com 302

2 Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = 4 2 Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry a2 = b2 + c2 bc cos A Statistics Mean = Standard deviation = www.KiasuExamPaper.com 303 www.KiasuExamPaper.com 303

Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 [Turn Over 3 Part A Answer all the questions. 1 (a) Simplify . Answer ......................................... [2] (b) Simplify and write your answer in positive index notation. Answer ......................................... [2] (c) Given that , find x. Answer x =.................................... [2] www.KiasuExamPaper.com 304 www.KiasuExamPaper.com 304

4 Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 (d) Write as a single fraction in its simplest form . Answer ......................................... [4] (e) Explain why, for all integer values of n, is always even. Answer ................................................................................................................ ................................................................................................................ ................................................................................................................ [2] www.KiasuExamPaper.com 305 www.KiasuExamPaper.com 305

Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 [Turn Over 5 2 (a) A quadratic equation has solutions and , where p is a positive integer. Write the equation in the form , where b and c are expressed in terms of p. Answer ......................................... [2] (b) A quadratic curve intersects the x-axis at and . Find the equation of its line of symmetry. Answer ......................................... [1] (c) (i) A straight line passes through and . Find the column vector . Answer =................................ [2] (ii) Write down another column vector that is parallel to . Answer ......................................... [1] www.KiasuExamPaper.com 306 www.KiasuExamPaper.com 306

6 Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 3 (a) During the World Cup, merchandise such as jerseys and caps are sold. Game 1 sold 12 000 jerseys and 4000 caps. Game 2 sold 9000 jerseys and 5600 caps. Game 3 sold 11800 jerseys and 3000 caps. The number sold, in thousands, are shown in the matrix A jersey is priced at $80 and a cap at $30. (i) Represent the price of the merchandise in a column matrix P. Answer P = [1] (ii) Evaluate the matrix . Answer T = [2] (iii) Explain what the elements in T represent. Answer ...................................................................................................... .................................................................................................................... [1] www.KiasuExamPaper.com 307 www.KiasuExamPaper.com 307

Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 [Turn Over 7 (b) The remaining stock consists of 7000 jerseys and 8000 caps. After a storewide discount was applied, the sale of the remaining stock is represented by the matrix equation , where d is a constant. Find the percentage discount given by the store. Answer .............................% [4] www.KiasuExamPaper.com 308 www.KiasuExamPaper.com 308

8 Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 4 (a) (i) Complete the table of values below for . x 0 1 2 3 y 0 2 0 0 5 [1] (ii) On the grid, draw the graph of for . [3] www.KiasuExamPaper.com 309 www.KiasuExamPaper.com 309

Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 [Turn Over 9 (iii) The water quality level of a pond over a 3-week period is modelled by the curve , where x represents the time in weeks. The minimum safe level for fish to survive is given by the line . On the same grid, draw the line . [1] (iv) From the graph, write down the value(s) of x where the water quality equals the minimum safe level. Answer x =...................................................... [2] (v) The fish are safe when the water quality is above the minimum safe level. Use your graph to find the range of values of x for which the fish are safe. Answer ....................................................... [1] (b) The graph of , where k and a are positive integers, passes through the points and . Find the value of k and of a. Answer k =......................................... [2] a =......................................... [1] www.KiasuExamPaper.com 310 www.KiasuExamPaper.com 310

10 Riverside Secondary School 2026/PRELIMS/4E/5N/EM/4052/02 P Q R O A C 1 rad 6 B 5 The diagram shows a circle with centre O and radius 6 cm. A, Q, B and C lie on the circle. PA and PB are tangents to the circle at A and B respectively. O, R, Q and P lie on a straight line. Angle ACB = 1 radian. (a) Show that triangle AOP is congruent to triangle BOP. Give a reason for each statement you make. Answer ........................................................................................................................... .............................................................................................................................. .............................................................................................................................. .............................................................................................................................. ....................................................................................................................................[3] (b) State the value of angle AOB in radians. Give