2023 S4NA Prelim MA P2 QP

Name: Register Number: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4045/02 PAPER 2 1 August 2023 Tuesday 2 hours PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERI AN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2023 SECONDARY FOUR NORMAL (ACADEMIC) PRELIMINARY EXAMINATION DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. INSTRUCTIONS TO CANDIDATES: Write your nam e, index number and class on the spaces provided abov e. Write in dark blue or black pen. You may use a n HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Section A Answer all questions. Section B Answer one 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 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. Note that all the diagrams in this paper are not drawn to scale. 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 70. For Examiner’s Use Qn 1 2 3 4 5 6 7 8 9 10 11 12 Marks Deducted Marks Category Accuracy Symbols Others Question No. Setter: Mrs Joyce Yeo Vetter: Mr Tan Chee Wee This paper consists of 17 printed pages (including this cover page) and 1 blank page. TOTAL MARKS 70

2 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 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 Section A (62 marks) Answer all the questions in this section. 1 (a) Work out (i) 2212 ( 9) ( 6)− − − − , Answer ……………………… [1] (ii) 292.195.17 2031.0 3 + . Answer ……………………… [1] (b) (i) Write 29.951 correct to 3 significant figures. Answer ……………………… [1] (ii) Write 4.523 million to the nearest ten thousand. Answer ……………………… [1] 2 (a) Given that 1 3 43 81 3 m= , find the value of m. Answer m =…………………… [2] (b) Simplify 7 3 9a a . Answer ……………………… [2]

4 3 (a) p is directly proportional to q3. Given that p = 24 when q = 2, find (i) the formula connecting p and q, Answer ……………………… [2] (ii) the value of q when p = 192. Answer ……………………… [1] (b) 5 men can paint a house in 6 days. The house was painted in n days. Write down an expression, in terms of n, for the number of men needed to paint the house. Answer ……………………… [2]

5 4 (a) Find 130% of 2 litres in millilitres. Answer …………………ml [1] (b) A map is drawn to a scale of 1 : 50000. (i) The perimeter of a reservoir on the map is 22.8 cm. Find the actual perimeter, in kilometres, of the reservoir. Answer …………………km [2] (ii) The actual area of a plantation is 46 km2. Calculate the area, in square centimetres, of the plantation on the map. Answer …………………cm2 [2]

6 5 The diagram shows the speed-time graph of a particle over a period of 60 seconds. (a) Describe what is happening between t = 20 and t = 60. Answer …………………………………………………………………………………… …………………………………………………………………………………[1] (b) Calculate the acceleration of the particle in the first 20 seconds. Answer ……………………m/s2 [1] (c) Calculate the speed of the particle at t = 45. Answer ……………………m/s [2] (d) The area under the graph represents the total distance travelled. Calculate the total distance travelled by the particle. Answer ………………………m [2] Speed (v) in m/s Time (t) in seconds 0 16 24 20 60

7 6 In the diagram, angle AEC = angle ACB = angle CAD = 90  . Angle EAC = 55 , AC = 4.1 cm and CD = 5.4 cm. Calculate (a) the length of AD, Answer ……………………cm [2] (b) the length of AB, Answer ……………………cm [2] (c) the angle ADC. Answer ………………………o [2] D A E C 4.1 5.4 B

8 7 The table shows the number of times students of a class were late for school in a month. Number of times 0 1 2 3 4 Number of students 6 12 3 8 p (a) State the largest value of p if the mode is 1. Answer …………………… [1] (b) Find the value of p if the probability of choosing a student who was late more than 2 times is 0.5. Answer ……………………[2] (c) It is given that p = 11. (i) Find the mean. Answer ……………………[2] (ii) A student’s record was left out of the table. This student was late 3 times in a month. The table is now updated to include this student’s record. Without calculation, explain how the mean will be affected. Answer …………………………………………………………………………… …………………………………………………………………………… ……………………………………………………………………………[1]

9 8 (a) Lightning strikes the earth approximately 1.4 billion times per year. (i) Write 1.4 billion in standard form. Answer ……………………[1] (ii) Calculate the average number of times the lightning strikes the earth in a day, assuming there are 365 days in a year. Write your answer in standard form. Answer ……………………[2] (b) Solve the simultaneous equations. 5 2 16 37 xy xy −= + =− Answer x = …………………… y = …………………… [3] (c) Solve 0153 2 =−− xx . Give your answers correct to 2 decimal places. Answer x = ….……… or ………… [3]

10 9 (a) Complete the table of values for 3 9y x x=− . [2] x –3 –2 –1.5 –1 0 1 1.5 2 3 4 y 0 10 8 0 –8 –10.125 0 28 (b) On the grid provided, plot the graph of 3 9y x x=− for 34 x−   . [3] Answer on next page. (c) Use your graph to find the values of x when y = 5. Answer x =…………, …………, ………… [2] (d) By drawing a tangent, find the gradient of the curve 3 9y x x=− when x = 2.5. Answer ……………………[2]