CHIJ SJC 4048 02 QP

Index Number Class Name Calculator Model CHIJ ST JOSEPH’S CONVENT PRELIMINARY EXAMINATION O. MATHEMATICS Paper 2 Secondary 4 Express / 4 Normal Academic (O Level) / 5 Normal Academic O. 4048/02 25 August 2021 2 hours 30 minutes Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of the marks for this paper is 100. This document consists of 33 printed pages. Setter: Ms Ong Suat King & Mrs Margaret Ng [Turn over Mathematical Formulae FOR EXAMINER’S USE 100

2 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 CsinabABC 2 1= Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry Acosbccba Csin c Bsin b Asin a 2222 −+= == Statistics Mean f fx  = Standard deviation 22        − = f fx f fx

3 Answer all the questions 1 (a) Simplify 22 23 6 5 6 xy x xy y − −− . Answer ……………………………….. [2] (b) Express as a single fraction in its simplest form 224 3 2 1 yx x xy − +−− . Answer ……………………………….. [3]

4 (c) Given that yxxy )1(23 1 −= , express y in terms of x. Answer y = ………………………….. [3]

5 2 Mr Lee paid $100 for his water bills in January when the rate was $x per cubic metres. In December, the price of water was increased by 5 cents per cubic metres. By cutting down on usage, Mr Lee still managed to pay $100 for his water bill in December. (a) Write down an expression, in terms of x, for the amount of water used by Mr Lee in January. Answer ……………………………….. [1] (b) Write down an expression, in te rms of x, for the amount of water used by Mr Lee in December. Answer ……………………………….. [1] (c) If the amount of water used in December was 2 m3 less than the amount used in January, form an equation in x and show that it reduces to 220 50 0xx+ − = . Answer ……………………………….. [3] (in answer space)

6 (d) Solve the equation and find the price of water per cubic metres in January. Answer $ …………………………/ m3 [3] (e) Using your result obtained in part (d), calculate ho w much water Mr Lee used in December leaving your answer correct to 2 decimal places. Answer …………………………… m3 [2]

7 3 The diagram below shows a series of pattern formed by dots and squares of side of 1 cm. The total number of dots and number of small squares of each figure is shown in the table below. By considering the diagrams above and the pattern developed, (a) find the values of a, b and c, Answer a = …………………………….. [1] Answer b = …………………………….. [1] Answer c = …………………………….. [3] Figure Total number of small squares (S) Total number of dots (D) Number of match sticks used (M) 1 1 4 4 2 4 9 12 3 9 16 24 4 16 25 40 5 a b c n x y z Figure 1 Figure 2 Figure 3 Figure 4

8 (b) find the total number of dots needed to form Figure 25, Answer ……………………………….. [1] (c) express y in terms of n, Answer y = ………………………….. [1] (d) express z in terms of n , Answer z = ………………………….. [1] (e) find the value of D when M = 5100. Answer D = …………….………….. [2]

9 4 The workers of a company can take public transport to travel from the company to the nearest Mass Rapid Transit (MRT) station. They can travel by basic bus, Light Rail Transit (LRT) or express bus. When paying with a fare card, the fares are $0.7 0 for basic bus, $0.80 for LRT and $1.40 for express bus. This information can be represented by the matrix 0.70 0.80 1.40 F  = . When paying by cash, the fares for basic bus and LRT increase by 85% and the fare for express bus increases by 60% . (a) The elements of the matrix S, where 00 00 00 a S b F c  = , represents the fares for basic bus, LRT and express bus when paid by cash. (i) Find the values of a, b and c. Answer a = …………………………….. [1] Answer b = …………………………….. [1] Answer c = …………………………….. [1]

10 (ii) Hence evaluate S. Answer S = …………………………….. [2] (b) The workers work in three shifts. The table below shows the mode of transport they chose to travel to the MRT station after completing their shifts each day. Basic bus LRT Express bus Shift 1 25 14 0 Shift 2 18 20 19 Shift 3 13 20 7