2025 Fmss Prelims EM P1 QP with ans key

NAME: ____________________________ ( ) CLASS: _______ FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) MATHEMATICS 4052/01 Paper 1 Date: 25 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 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. For Examiner’s Use Table of Penalties Question Number Presentation  1  2 Rounding off  1 Parent’s/Guardian’s Signature Setter: Mdm Lee SP This question paper consists of 21 printed pages  90

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 2 Mathematics Paper 1 Mathematical Formulae Compound interest Total amount = P n r    + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard deviation = 22      −     f fx f fx

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 3 Mathematics Paper 1 Answer all the questions. 1 Expand and simplify ( )( )3 4 3 4x a a x+− . Answer ……………………………. [2] 2 (a) Express the ratio of 0.55 hours to 5 minutes and 30 seconds in its simplest form. Answer …………… : …………… [1] (b) Given that p = 3q and 2r = q, write down the ratio of p : q : r. Answer ………… : ………… : ………… [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 4 Mathematics Paper 1 3 A shopkeeper marked the price of a laptop so that he could make a profit of 25% on the cost price. During the Great Singapore Sale, he offered a 10% discount on the marked price and sold it at $1521. (a) Calculate the cost price of the laptop. Answer $ …………………………………… [2] (b) Calculate the profit made during the sale. Answer $ …………………………………… [1] 4 The figure below is made up of four congruent right-angled triangles, meeting at one common point, P. It is given that the length of the hypotenuse of the right-angled triangle is 12 cm and 3sin 5 = . Without solving for , calculate the perimeter of the figure. Answer ……………………………… cm [2]  P

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 5 Mathematics Paper 1 5 2 cm on a map of Singapore represents 5 km. (a) The scale can be written in the form 1 : n. Find the value of n. Answer n = …………………………… [1] (b) The distance on the map from Sentosa to Buona Vista is 4.72 cm. Calculate the actual distance, in kilometres, between these two places. Answer …………………………… km [1] (c) The area of Sentosa is 4.71 km2. Calculate the area, in square centimetres, of Sentosa on the map. Answer …………………………… cm2 [2] 6 The expression 2 8 13xx−+ can be written in the form ( ) 2 4xn−+ . (a) Find the value of n. Answer n = ……………………………. [1] (b) Explain why when x = 4, the expression 2 8 13xx−+ has its minimum value. …………………………………………………………………………………………. ……………………………………………………………………………...……..…. [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 6 Mathematics Paper 1 7 ABCD is a parallelogram. APQ, BRQ, CRS and DPS are straight lines which bisect angles A, B, C and D respectively. Show that triangle ADP and triangle CBR are congruent. Give a reason for each statement you make. Answer [3] A B D C S R Q P

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 7 Mathematics Paper 1 8 (a) Write 4991.2 10 − in the form 50010A − . Answer ……………………………… [1] (b) Work out ( ) ( ) 499 5001.2 10 4 10−   . Give your answer in standard form. Answer ……………………………… [1] 9 The force of attraction, F newtons, between two magnets is inversely proportional to the square of the distance, d metres, between the magnets. (a) Sketch the graph of F against d. Answer [1] (b) The force of attraction reduced by 75% of its original value. Calculate the percentage increase in the distance between the two magnets. Answer …………………………… % [2] F d 0

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 8 Mathematics Paper 1 10 (a) Convert 17  radians into degrees. Answer …………………………… [1] (b) sin y = 7 cos 85 Find the two possible values of y in the range 0 180y . Answer y = ……………… or y = ……………… [2] 11 In the diagram, A, B, C, D and E are points on a circle. AED and BCD are straight lines. DE is the diameter of the smaller circle. Explain why BE is the diameter of the larger circle. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ……………………………………………………………………………………………... [2] A B C D E

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 9 Mathematics Paper 1 12 Sketch the graph of ( )( )53y x x= − − on the axes below. Indicate clearly the coordinates of the points where the graph crosses the axes and the turning point on the curve. [3] 13 (a) The square root of x is equals to the cube root of 3610 3 n . Write x as the product of its prime factors. Answer x = ……………………………… [1] (b) Simplify 2 3 3 271 x − − . Give your answer in positive index form. Answer …………………………………… [2] y x O

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2025 10 Mathematics Paper 1 14 Written as a product of its prime factors, 10 32 5 11M =   . (a) The quotient of M and K is a perfect cube. Find the smallest possible integer value of K. Answer K = ………………………… [1] (b) The highest common factor of M and N