3. 2026 NCHS Prelim Math 2 QP with Ans Keys

Name: Register Number: Class: _______________________________________________________________________________________________________________________________________________________________________________ PRELIMINARY EXAMINATION 2026 SECONDARY FOUR EXPRESS MATHEMATICS 4052/02 Paper 2 Candidates answer on the Question Paper. 24 August 2026, Monday 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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. ______________________________________________________________________ This document consists of 24 printed pages and 2 blank pages. For Marker’s Use 90 Lack annotation/ units/ incorrect properties’ name −1 Accuracy −1 Final answer −1 Use of Pencil for essential working −1

2 Mathematical Formulae Compound interest Total amount = 𝑃 (1 + 𝑟 100) 𝑛 Mensuration Curved surface area of a cone = Surface area of a sphere = 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 − 2𝑏𝑐 cos 𝐴 Statistics Mean = Standard deviation = rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == f fx   22        −  f fx f fx

3 Answer all questions. 1 (a) Solve 8 2−3𝑥 = 7. Answer …………………………… [2] (b) Factorise completely 10𝑎 − 4𝑏𝑎 − 15𝑐 + 6𝑏𝑐. Answer …………………………… [2] (c) Solve the simultaneous equations. 3𝑥 + 5𝑦 = 2 5𝑥 − 4𝑦 = −6 You must show your working. Answer x =…………, y =…………… [3]

4 (d) Write as a single fraction in its simplest form 3𝑥−20 𝑥2−49 + 5 7−𝑥. Answer …………………………… [3]

5 2 (a) The cumulative frequency diagram shows the travelling time of 60 adults travelling to work by MRT on Monday. (i) Use the diagram to estimate (a) the median travelling time, Answer …………………minutes [1] (b) the interquartile range of the travelling time, Answer …………………minutes [2] (c) the 80th percentile of travelling time. Answer …………………minutes [1] Cumulative Frequency Travelling Time (minutes)

6 (b) Another 60 adults travelled to work by MRT on Tuesday. The box-and-whisker diagram illustrates the distribution of the time taken. Travelling Time (minutes) Make two comparisons between the travelling times of the adults on Monday and on Tuesday. Answer ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. [2] (c) In 2025, the total number of MRT trips by commuters is 3.49 millions. This represents a 2.29% increase from 2024. Calculate the total number of MRT trips in 2024. Give your answer in standard form. Answer …………………………… [2]

7 3 (a) A recreational club organized three different groups to visit the zoo. Group A had 12 adults and 5 children. Group B had 20 adults and 6 children. Group C had 16 adults and 3 children. The information can be represented by the matrix 𝐋 = ( 12 5 20 6 16 3 ) (i) The entrance fee for an adult and a child is $49 and $34 respectively. Represent the entrance fees in a 2× 1 column matrix M. Answer M =…………….……… [1] (ii) Evaluate the matrix 𝐂 = LM. Answer 𝐂 =…………….……… [1] (iii) Evaluate 𝐏 = (1 1 1)𝐂. State what the elements of P represents. Answer ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [1] (b) A map is drawn to a scale of 1 : 250 000. (i) The Mandai Boardwalk is 3.3 km. Calculate the distance, in centimetres, of the Mandai Broadwalk on the map. Answer …………………… cm [2]

8 (ii) A lake is represented by an area of 8 cm2on the map. Calculate the actual area, in square kilometres, of the lake. Answer …………………… km2 [2] (c) Given that E is 130% of D and 2 3 𝐸 = 1 2 𝐹. Express the ratio of 𝐷: 𝐸: 𝐹 in its simplest form. Answer ……………………….. [3]

9 4 The diagram shows a triangle ABC. D is a point on AB and E is a point on AC such that DE is parallel to BC and DE = 10 cm. (a) (i) Show that the triangles ADE and ABC are similar. Give a reason for each statement you make. Answer ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. [2] (ii) The ratio area of triangle ADE : area of triangle ABC is 4 : 25. If the area of triangle ABC is 200 cm2, find the height of the trapezium DECB. Answer ……………………. cm [3] D B C A 10 cm E

10 (b) The diagram shows a square , ABFG, a regular pentagon, BCDEF, and two sides of a third regular polygon, GF and FE. Find the number of sides for the third regular polygon. Answer …………………………… [3]