YTSS S4 Prelim 2024 P1 w Ans Key

NAME: ( ) CLASS: YISHUN TOWN SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS MATHEMATICS PAPER 1 (4052/01) DATE : 16 August 2024 DAY : Friday 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 1 2 2 3 2 4 2 5 2 6 2 7 2 8 3 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 5 23 5 24 5 25 7 TOTAL 90 This question paper consists of 25 printed pages and 1 blank page. O

2 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) Mathematical Formulae Compound interest Total amount = n rP      + 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 triangle ABC = Cab 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 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) [Turn over Answer all the questions. 1 Calculate 3 390.1 32.02 0.731+ , giving your answer correct to 2 significant figures. Answer ........................................ [1] 2 The sine of an angle is 0.6310. Give two possible values for the angle in radians. Answer ............... or ............... rad [2] 3 The cost of a meal at a restaurant is $20.60 before service charge and Goods and Services Tax (GST). Find the total cost of the meal inclusive of a 10% service charge and 9% GST. Answer $ .................................. [2]

4 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) 4 The graph shows the number of students who were late for school in Term 1. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. Answer …………………………………………………………………………………………………... …………………………………………………………………………………………………................. …………………………………………………………………………………………………………… ………………………………………………………………………………………...……................ [2] 40 45 50 55 60 65 70 75 80 85 90 Secondary 1 Secondary 2 Secondary 3 Secondary 4/5 Late coming by Level

5 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) [Turn over 5 The Mathematics scores of 380 students are represented in the box-and-whisker-plot. Find (a) the median score, Answer ........................................ [1] (b) the interquartile range of the scores. Answer ........................................ [1] 6 (a) Express 2 36xx−+ in the form 2()x a b++ . Answer ........................................ [1] (b) Hence explain why 2 3 6 0xx− + = has no real solution. Answer …………………………………………………………………………………………… ………………………………………………………………………………………………...... [1]

6 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) 7 At a carnival, the ratio of adults to children is 5 : 18. The ratio of girls to boys is 7 : 2. Given that the ratio of women to girls is 1 : 7, find the ratio of men to boys. Answer .................. : .................. [2]

7 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) [Turn over 8 ABCDE is part of a regular n-sided polygon with an interior angle of 156o. CPQD is a rhombus such that angle 80 .PCD= Find (a) angle QDE, Answer ........................................ [1] (b) the number of sides of the polygon. Answer ........................................ [2] A P Q E D B C

8 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) 9 A microchip is made up of transistors printed on one side. Each transistor is a flat square of side 51 nanometres. (a) Express 51 nanometres in metres, in standard form. (1 nanometre = 10-9 metres) Answer ...................................... m [1] (b) Find the surface area of each transistor in square metres, in standard form. Answer ..................................... m2 [1] (c) The microchip is in the shape of a square of length 0.102 cm. Assuming that the surface of the microchip is completely filled with transistors, calculate the total number of transistors on the microchip, leaving your answer in standard form. Answer ........................................ [2]

9 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) [Turn over 10 (a) Solve the inequality 4145 2 xx +− . Answer ........................................ [2] (b) Represent your solution in (a) on a number line. [1] (c) Write down the largest integer, x, which satisfies the inequality 4145 2 xx +− . Answer x = ................................... [1]

10 2024 YTSS Preliminary Exam Secondary 4 Mathematics EXP (4052/01) 11 In the diagram, A, B, C, D and E are points on the circle with centre O. Angle OAC = 35  and angle ACB = 28  . EOB is a diameter of the circle. Find, giving a reason for each statement you make, (a) angle ECA, Answer ........................................ [1] (b) angle EOA, Answer ........................................ [1] (c) angle EDC. Answer ........................................ [2] 28° 35° O B C D E A