Crest Sec 4NA Prelim Question Paper 2

CREST SECONDARY SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION NA Name: ( ) Class: MATHEMATICS (SYLLABUS A) Paper 2 Candidates answer on the Question Paper. 4045/02 Thursday 15 August 2024 2 hours 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. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Section A Answer all the questions. Section B Answer one question. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown in the space below the question. Omission of essential working will result in loss of marks. The total number of marks for this paper is 70. 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. This document consists of 19 printed pages and 1 blank page. Setter: Ms Liew Jia Meng [Turn over For Examiner’s use 70

2 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 Measurement 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 = Cabsin2 1 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= + − Statistic Mean = fx f   Standard deviation = 22f x f x ff  −  

3 Section A (62 marks) Answer all the questions in this section. 1 Calculate the value of ( ) 2 34 3 2 5 − +  . Answer ……….………………… [1] 2 Simplify 2 2 3 12 14 7 mn m n nn . Answer ……….………………… [2] 3 Factorise. (a) 16x2 – 49 Answer ……….………………… [1] (b) 12ab – 16bc + 3a – 4c Answer ……….………………… [2] [Turn over

4 4 The height of Mount Everest is 8 848m. On a particular day, the temperature at Mount Everest base camp was 5  C and the temperature at the summit was – 20  C. (a) Find the difference in temperature between the base camp and summit within a day. Answer ……….………………  C [1] (b) What is the rate of temperature change? Answer ……….……………  C/m [2] 5 Stacey operates a home-based bakery, specialising in madeleines. She recorded the number of madeleines sold each day in the month of January. The results are shown in the table. Number of madeleines sold, x Frequency 0 20x 2 20 30x 11 30 40x 9 40 50x 6 50 80x 3 (a) Calculate an estimate for the mean and the standard deviation. (i) Mean Answer Mean = ……………………………… [1] (ii) Standard Deviation Answer Standard deviation = ………………… [2] (b) Stacey forgot to include a corporate order in her table. The order was for 60 madeleines. She expected the estimated mean to increase after she updated the table to include this order. Explain whether Stacey is correct. Answer ……………………………………………………………………… ……………………………………………………………………… [1]

5 6 These are the first five terms of a sequence. 28 24 20 16 12 (a) Find the next two terms of the sequence. Answer …………… , …………… [1] (b) Write an expression, in terms of n, for the nth term of this sequence. Answer ……….………………… [1] (c) Donovan says that – 42 is a term in this sequence. Is he correct? Show your working. Answer [2] [Turn over

6 7 There are 12 pink, 7 purple and 1 white ball in a bag. 2 balls are drawn at random, without replacement. Find the probability that (a) the 2 pink balls are drawn, Answer ……….………………… [1] (b) exactly 1 purple ball is drawn, Answer ……….………………… [2] (c) none of them is white. Answer ……….………………… [2]

7 8 AB is parallel to CD. E is on BC such that BE = 5 cm, CE = 2 cm, and DE = 3 cm. (a) Name a pair of similar triangles and explain your reasons for the similarity. Answer Triangles ………………… and ………………… are similar because ……………………………………………………………………… ……………………………………………………………………… ……………………………………………………………………… ……………………………………………………………………… ……………………………………………………………………… [2] (b) Find the length of AD. Answer ……….……………… cm [3] [Turn over C A B E D

8 9 A, B, C, D and E lie on a circle, centre O. Angle AED = 123  . Find (a) Angle ABD Answer Angle ABD = ……………………………… Reason …………… ……………………………………………………………………………… [2] (b) Angle CBD Answer Angle CBD = ……………………………… Reason …………… ……………………………………………………………………………… [2] (c) Angle CAD Answer Angle CAD = ……………………………… Reason …………… ……………………………………………………………………………… [2] 123 A B C D O E

9 10 The table below is for 2xy= . x – 1.5 – 1 – 0.5 0 0.5 1 1.5 2 y 0.35 0.71 1 1.41 2 2.83 4 (a) Complete the table. [1] (b) Draw the graph of 2xy= for 1.5 2 x−   , on the graph provided behind. [2] (c) Is it possible to find a value of x when y = 0? Explain your answer. Answer ……………………………………………………………………… ……………………………………………………………………… ……………………………………………………………………… [1] (d) Use your graph to find the value of x when y = 3.5. Answer x = ……….……………… [1] (e) By drawing a suitable tangent, find the gradient of the curve when x = – 0.5. Answer ……….………………… [2] [Turn over

10 – 1.5 – 1 – 0.5 0.5 1 1.5 2 x y 0.5 1 1.5 2 2.5 3 3.5 4 0