ADSS Prelim 2025 P2 [QP]

ADMIRALTY SECONDARY SCHOOL SUBJECT : Elementary Mathematics CODE/PAPER : 4052/02 LEVEL/STREAM : Secondary 4 Express / 5 Normal (Academic) DATE : 28 August 2025 TIME : 0800h – 1015h DURATION : 2 hours 15 minutes Instructions to candidates: 1. Write your name, class and index number. 2. Answer ALL questions. 3. 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  . 4. Essential workings must be shown. Omission of essential workings and illegible handwriting will result in loss of marks. DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO. ______________________________________________________________ This question paper consists of 19 printed pages including this cover page. PRELIMINARY EXAMINATION 2025 NAME: NO: CLASS: 90

2 Mathematical Formulae Compound Interest Total amount = nrP    + 1001 Mensuration Curved surface area of a cone = lr  Surface area of a sphere = 2 4 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle ABC = Abc sin2 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

3 Answer all the questions. 1 1 (a) Simplify 2 2 5 20 5 5 10 x xx − +− . Answer ……..…..........………….. [2] (b) Simplify 2 3 4 12 21 7 a b a cc Answer …..…..………………….. [2]

4 (c) Simplify 1 12 3 9 27a b −   Answer …...…..…………………. [2] (d) Solve the equation 2 (1 ) 1 8 1 ( )33 yy y−+ = − − . Answer …..…..………………….. [4]

5 2 The stem -and-leaf diagram shows the time, in minutes taken by a group of 18 students to complete a survey. 2 1 1 2 3 4 5 7 3 0 3 4 7 8 4 2 6 7 5 1 9 6 4 Key: 2 1 means 21 minutes (a) Find the range of time taken. Answer …………………… min [1] (b) Find the median time taken. Answer …………………… min [1] (c) Calculate an estimate of the mean time taken. Answer …………………… min [1] (d) When the time taken to complete the survey by another 2 students was included, the mean time taken increased by 1.4%. If both students took the same amount of time to complete the survey, find the time that one of the students took to complete the survey, giving your answer to the nearest minutes. Answer …………………...… min [3]

6 3 Mr Lim and his family went to Genting Highland, which is 450 km from Singapore, for their family vacation. A friend drove them by his car to Genting Highland at a speed of x km/h. They took a coach back at a speed of (x − 20) km/h. (a) Write down an expression, in terms of x, for the time taken by car. Answer ……………………….. h [1] (b) Write down an expression, in terms of x, for the time taken by coach. Answer ……………………….. h [1] (c) If the difference in time was 40 mins, write down an equation in x and show that it reduces to 2 20 13500 0xx− − = . Answer [3] (d) Solve the equation 2 20 13500 0xx− − = , giving your answers correct to two decimal places. Answer x = ……..… or ……..… [4]

7 4 (a) A cake shop has two stores M and N. The following table shows the quantities of cakes in the two stores. Chocolate Strawberry Marble Store M 25 33 15 Store N 19 17 37 The selling prices of a chocolate cake, a strawberry cake and a marble cake are $45, $39 and $32 respectively. Their cost prices are $40, $34 and $26 respectively. (i) Evaluate the matrix A 25 33 15 19 17 37  =            32 39 45 . Answer …..……………………. [1] (ii) State what A represents. ……………………………………………………………………………………… [1] (iii) Using matrix multiplication, find a matrix B whose elements give the total costs for the three cakes of both stores respectively. Answer …………………………. [1]

8 (iv) Evaluate the matrix C = (1 1)(A – B). Answer …………………………. [1] (v) State what C represents. ……………………………………………………………………………………… [1] (b) In the diagram, PQRS is a quadrilateral. PQ=  a, PS =  b, 3QR PS=  and 2SR SM=  . The ratio of PT : TM is 2 : 3. (i) Express in terms of a and b, as simply as possible, (a) SR  , Answer ……………………….. [1] (b) SM  , Answer ……………………….. [1] P M T S R b a Q

9 (c) PM  , Answer ………………………… [1] (d) PT  . Answer ………………………… [1] (ii) Show that where is a constant to be determined.QT kTS k=  Answer [3]

10 5 Ann is waiting for a choir audition in a classroom with x boys and another y girls. In this audition, only two pupils will be chosen. (a) Complete the tree diagram to show the probabilities of the possible outcomes. 1st chosen pupil 2nd chosen pupil [3] (b) Find the probability that Ann is either the first or second candidate for the audition in terms of x and y. Express your answer in the simplest form. Answer ..………………………… [2] (c) If the probability that Ann is the first candidate for the audition is 15 1 and that the total number of boys is 6, calculate the total number of girls who participated in this audition. Answer ..………………………… [3] Ann Other pupils Ann Other pupils 1++ + yx yx …...… …...…