2025 Fmss Prelims EM P2 QP with ans key

NAME: ____________________________ ( ) CLASS: _______ MATHEMATICS 4052/02 Paper 2 Date: 26 August 2025 Duration: 2 hours 15 minutes Candidates answer on the Question Paper. ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name, index 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 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 i s 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. For Examiner’s Use Table of Penalties Question Number 90 Presentation  1  2 Parent’s / Guardian’s Signature Rounding off  1 Setter: Ms Lee CP This question paper consists of 24 printed pages.  FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 2 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = P Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of a triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = n r      + 1001 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 == Abccba cos2222 −+=   f fx 22       −     f fx f fx

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 3 Mathematics Paper 2 Answer all the questions. 1 (a) Solve the equation 3 56 164 16 x x + −= . Answer x = …..…………………………… [2] (b) Write as a single fraction in its simplest form 2 3 13 2 3 6 5 6x x x−− + − . Answer …………………………………… [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 4 Mathematics Paper 2 1 (c) Given that 2 1a bc=− , express c in terms of a and b. Answer ………………….…………….…… [2] (d) (i) Solve the inequality 22 25 232 xx x++  −  . Answer ………………….…………….…… [2] (ii) Hence, find the prime numbers that satisfy the inequality in (i). Answer ………………….…………….…… [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 5 Mathematics Paper 2 2 (a) In a game, two six-sided dice are used. Die P has 2 blue faces and 4 yellow faces. Die Q has 4 blue faces and 2 yellow faces. Two dice are thrown together. (i) Find the probability that both dice show a blue face on top, leaving your answer as a fraction in the simplest form. Answer ………..……………………… [1] If both dice show blue, the player wins a prize. If just one die shows blue, the player throws both dice again. The player wins a prize if both dice show blue this time. (ii) Calculate the probability, that the player wins a prize on either the first throw or the second throw, leaving your answer as a fraction in the simplest form. Answer ………..……………………… [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 6 Mathematics Paper 2 2 (b) The cumulative frequency curve below shows the distribution of length of 200 leaves from tree A. (i) Use the curve to find the (a) median length, Answer ………..……………….…mm [1] (b) interquartile range. Answer ………..……………….…mm [1] (ii) The above data is shown in a pie chart. What is the angle representing the sector for the range of length of leaves between 40 mm and 50 mm? Answer ………..……………….……° [1] 0 20 40 60 80 100 120 140 160 180 200 30 35 40 45 50 55 60 65 70 75 80 Length (x mm) Cumulative frequency

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 7 Mathematics Paper 2 2 (b) (iii) It was found that the lengths were measured wrongly. The correct length of each leaf is 4 mm more than recorded. Explain how the median and interquartile range have been affected. Answer ….…………………………………………………………………………….. …………………………………………………………………………………………. ……...……………………………………………………………………………….[2] (iv) With reference to the cumulative frequency curve, Alex said: “The range of length of the 200 leaves is 76 – 30 = 46.” Explain why this statement is not true. Answer ….…………………………………………………………………………….. ……...……………………………………………………………………………….[1] (v) With reference to the cumulative frequency curve, Charlie said: “60% of the leaves has a length of at least 53.5 mm.” Is Charlie correct? Justify your answer with clear calculations. Answer ….…………………………………………………………………………….. …………………………………………………………………………………………. ……...……………………………………………………………………………….[2] (vi) The box-and-whisker plot below shows the lengths of leaves distribution from tree B. Make two comparisons for the distribution of length of leaves between the two trees. Answer 1 ……….………………………………………………………………………….….. …………………………………………………………………………………………. 2 ………………………………………………………………………………………. …………………………………………………...………………………………….[2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 8 Mathematics Paper 2 3 (a) Anna currently takes 80 seconds to swim a 50 m lap. In a year from now, she aims to increase her swimming speed by 20%. Calculate the time Anna will take to complete 50 m in a year from now, leave your answer to the nearest second. Answer ………………………………....s [2] (b) Brad and Jude train by swimming a 50 m lap. Brad swam at an average speed of x m/s and completed 28 laps. Jude swam at an average speed of 1 5 m/s slower than Brad and he completed 30 laps. Brad started swimming 13 3 minutes later than Jude but they stopped at exactly the same time. (i) Write down an expression, in terms of x, for the time taken by Brad to complete 28 laps. Answer ………………………………..s [1] (ii) Write down an equation in x to represent the information given and show that it reduces to 10x2 – 7x – 14 = 0. Answer [3]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 9 Mathematics Paper 2 3 (b) (iii) Solve the equation 10x2 – 7x – 14 = 0, giving your answer correct to 2 decimal places. Answer x = ……………… or x = ……………….. [3] (iv) Find the average of the times taken by Brad and Jude to swim one lap on Monday. Answer ………………………………..s [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Ac