GESS 2025 EM PRELIM P1

This document consists of 21 printed pages including the cover page. GAN ENG SENG SCHOOL Preliminary Exam 2025 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Sec 4 Express/ 5 Normal Academic 4052/01 28 Aug 2025 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft 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. Calculators should be used 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, unless the question requires the answer in terms of  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. For Examiner’s Use Total 90

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  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 2025 GESS SEC 4/5 PRELIM EM P1 NCT Answer all the questions. 1 (a) Calculate 1 3 3 33.17 55.2 ( 1) 647.9  − − + , giving your answer correct to 1 significant figure. Answer [1] (b) Convert 3 m/s to km/h. Answer km/h [1] 2 (a) If 10m = 2 and 10n = 11, find the value of 210 mn− . Answer [1] (b) Simplify 1 2 3 2 7 ( ) 7 mn mn m −  . Answer [2]

4 2025 GESS SEC 4/5 PRELIM EM P1 NCT 3 The period, T, of a pendulum is proportional to the square root of its length, L. If the period is increased by 25%, calculate the percentage change in the length. Answer [2] 4 The stem and leaf diagram below shows the times, in minutes, taken by a group of students in a school to assemble a toy car for a charity event. 1 0 2 4 5 5 8 8 9 2 1 1 3 3 4 5 6 6 6 7 7 8 9 3 0 0 0 1 1 3 7 Key: 2|0 represents 20 minutes (a) Find the time taken by the slowest student to assemble a toy car. Answer minutes [1] (b) 25% of the students took less than p minutes to assemble a toy car. Find the value of p. Answer p = [1]

5 2025 GESS SEC 4/5 PRELIM EM P1 NCT 5 Mdm Siti took a bank loan of $12 000 where the bank charges an annual compound interest of 7% compounded half-yearly. Find the interest earned at the end of 2 years. Answer $ [3] 6 Given that 2 2 xyz += , express x in terms of z and y. Answer x = [2]

6 2025 GESS SEC 4/5 PRELIM EM P1 NCT 7 (a) (i) Express 2 6 16xx−− in the form 2()x a b++ . Answer [2] (ii) Write down the coordinates of the turning point of the graph 2 6 16y x x= − − . Answer ( , ) [1] (iii) Write down the equation of line of symmetry. Answer [1] (b) Sketch the graph of 3( 1)( 5)y x x=− + − on the axes below . Indicate clearly the points where the graph crosses the axes and the turning point. Answer [2] y x 0

7 2025 GESS SEC 4/5 PRELIM EM P1 NCT 8 Three points A, B and C are shown below. (a) Construct the perpendicular bisector of BC. [1] (b) Construct the bisector of angle ABC. [1] (c) Mark clearly a possible point which is equidistant from B and C, and is nearer to AB than to BC. Label this point P. [1] (d) The point N is such that angle BCN = 85o and AN = 7 cm. Find the two possible positions of N and label them 𝑁1 and 𝑁2. [2] A B C

8 2025 GESS SEC 4/5 PRELIM EM P1 NCT 9 The sum of the first n terms of a sequence is (3 2).nn − (a) Find the first 3 terms of the sequence. Answer , , [2] (b) Find, in terms of n, and expression for the nth term of this sequence. Answer [1] 10 (a) The diagram below shows a pentagon with two of its interior angles as right angles, and the remaining interior angles are equal. Find the value of y x . Answer y x = [2] y◦ y◦ y◦

9 2025 GESS SEC 4/5 PRELIM EM P1 NCT (b) The diagram shows three regular polygons, A, B and C, joined together. Polygon A has 12 sides and polygon B has 4 sides. Find the number of sides in polygon C. Answer sides [2] A B C

10 2025 GESS SEC 4/5 PRELIM EM P1 NCT 11 Charles drew the bar graph below for his Element of Business Studies project. Explain how the bar graph may be misleading. Answer [1] 12 The position vector of C is 2 5 −  . The position vector of D is 3 1  − . (a) Find the vector that represents the translation from C to D. Answer [1] (b) E is a point on CD such that 2 61CE = , and the x-coordinate of C is greater than the x-coordinate of E. Find CE . Answer [2] 250 275 300 325 350 375 400 Monday Tuesday Wednesday Thursday Friday Saturday Sunday No. of customers Day Drastic increase in customers visiting Rebubu store