YTSS S4 Prelim 2024 P2 w Ans Key

NAME: ( ) CLASS: YISHUN TOWN SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS MATHEMATICS PAPER 2 (4052/02) DATE : 19 August 2024 DAY : Monday DURATION: 2 h 15 min MARKS: 90 READ THESE INSTRUCTIONS FIRST Do not turn over the cover page until you are told to do so. Write your name, class and class index number in the spaces at the top of this page. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the 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. 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, 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. MARKS OBTAINED FULL 1 6 2 5 3 12 4 7 5 7 6 9 7 10 8 12 9 12 10 10 TOTAL 90 This question paper consists of 22 printed pages. O

2 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4πr2 Volume of a cone = 1 3 πr2h Volume of a sphere = 4 3 πr3 Area of a triangle ABC = ab2 1 sin C 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 == 2 2 2 2 cosa b c bc A= + − Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) [Turn over Answer all the questions. 1 (a) The cash price of a car is $120 000. The hire purchase price of the car is $126 708. The hire purchase price is a deposit of 40% of the cash price plus 84 equal monthly payments. Calculate one monthly payment. Answer $ .................................... [3] (b) Jasice invests in an account that pays compound interest at 3.85% per year. She leaves the money in the account for 5 years. At the end of 5 years there is $11837.50 in the account. Calculate the amount of money Jasice invested, giving your answer to the nearest dollar. Answer $ .................................... [3]

4 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) 2 The diagram shows the points A (0, ‒1) and B (24, 11). (a) Find the equation of line AB. Answer ............................................ [2] (b) Point C (12, 0) lies on the x-axis. Find the area of triangle ABC. Answer ......................................units2 [2] x O y • A (0, ‒1) B • (24, 11) • C (12, 0)

5 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) [Turn over (c) Find the coordinates of D such that ABCD is a parallelogram. Answer (....................... , .......................) [1]

6 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) 3 (a) Simplify 1 29 3 33 4 64 .aa bb −  Answer ......................................... [3] (b) Given that 2 532 8 1, k= find the value of k. Answer k= .................................... [2]

7 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) [Turn over (c) (i) Express as a single fraction in its simplest form ( ) 2 2 2 15 .55 x x x xx −− + −− Answer .................................... [3] (ii) Hence solve the equation ( ) 2 2 2 15 5 .525 x x x x xxx − − + += −−− Answer x = .............. or .............. [4]

8 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) 4 The diagram shows a triangle ABC such that DF is parallel to BC and AC is parallel to DE. The points D, E and F lie on the line AB, BC and AC respectively. (a) Show that triangle ADF is similar to triangle ABC. Answer [2] 10 5 12 A D B C F E

9 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) [Turn over (b) In the triangle, DB = 5 cm, AD = 10 cm, BC = 12 cm and angle ABC = 120 . (i) Show that CF = 7.810 cm. Answer [3] (ii) Find angle DAF. Answer .......................................... [2]

10 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/02) 5 Machine X was used to pack chocolates into packets of 100 g. The masses, in grams, of 40 packets of chocolates packed by Machine X were recorded. The table below shows the data collected. Mass (in g) 85 90x 90 95x 95 100x 100 105x 105 110x Frequency 0 15 7 5 13 (a) Calculate (i) the mean mass, Answer .................................... g [1] (ii) the standard deviation. Answer .................................... g [1] Machine Y was also used to pack chocolates. The results are summarised in the table. Mass of chocolate packets from Machine Y (in g) Mean = 98.9 Standard deviation = 2.1 (b) Make two comments comparing the masses of the packets of chocolates packed by Machine X and Machine Y. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... [2]