2023 CCHY 4NA Prelim EM P2 QP

* [Turn_over 2023 Preliminary Examination Secondary Four Normal Academic CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS SYLLABUS A 4045/02 Paper 2 31 July 2023 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on 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 paper clips, glue or correction fluid. Section A Answer all 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 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 π , use either your calculator value or 3.142. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. Question Number Marks Marks Obtained 1 3 2 4 3 5 4 6 5 7 6 7 7 6 8 7 9 9 10 8 11 8 12 8 TOTAL 70 This document consists of 17 printed pages and 1 blank page. CHUNG CHENG HIGH SCHOOL (YISHUN)

2 [Turn_over Mathematical Formulae Compound Interest Total amount 1 100 n rP= + Measurement Curved surface area of a cone πrl= 2Surface area of a sphere 4 πr= 21Volume of a cone 3 πr h= 34Volume of a sphere 3 πr= 1Area of triangle sin 2ABC ab C= , where is in radiansArc length rθθ= 2 , where is in radians1Sector area 2 r θθ= Trigonometry sin sin sin abc ABC= = 2 22 2 cos Aa c bcb += − Statistics Mean fx f= ∑ ∑ 22 Standard deviation fx fx ff  = −  ∑∑ ∑∑

3 [Turn_over Section A (62 marks) Answer all the questions in this section. 1 (a) Evaluate 1.8056 8.1349 13.8321+ . Write down all the figures shown on your calculator as the answer. (b) Give your answer to part (a) correct to (i) 3 significant figures, (ii) 2 decimal places. Answer (a) ……………………………………… [1] (b)(i) …………………………………… [1] (b)(ii) …………………………………… [1] 2 As of 31 May 2023, the number of COVID -19 cases reported in Singapore and Bhutan ar e 2 459 457 and 62 671 respectively. Source : WHO Coronavirus (COVID-19) Dashboard | WHO Coronavirus (COVID-19) Dashboard With Vaccination Data (a) Find the difference in the number of cases reported between Singapore and Bhutan. Give your answer in standard form correct to 3 significant figures. Answer ……………………………… [2] (b) Find the number of times the number of cases reported in Singapore as compared to Bhutan. Give your answer correct to the nearest 10. Answer ……………………………… [2]

4 [Turn_over 3 (a) The coordinates of P and Q are (– 4, 3) and (2, 15) respectively. Find the equation of the line PQ. Answer ……………………………… [3] (b) The line CD is parallel to the line PQ. R(7, 11) is a point on the line CD. Work out the equation of the line CD. Answer ……………………………… [2]

5 [Turn_over 4 (a) Solve the simultaneous equations. 3x + y = 12 x – 2y = 11 Answer x = …………………………………… ..... y = …………………………………… [3] (b) The diagram shows a regular octagon. Find the value of x. Answer ……………………………… [3] x°

6 [Turn_over 5 (a) Factorise 12m – 3m3 completely. Answer ……………………………… [2] (b) Solve the equation 63 27xx+ = . Answer x = …………………………… [2] (c) Solve the equation 23 4 90xx+ −= . Give your answers correct to 2 decimal places. Answer x = ……………… or x = ……………… [3]

7 [Turn_over 6 (a) y is directly proportional to the positive square root of x. When x = 9, y = 54. (i) Find an equation connecting x and y. Answer y = …………………………… [2] (ii) Find the value of x when y = 72. Answer x = …………………………… [2] (b) Observe the following pattern. first pattern : 1 3× = 22 – 1 second pattern : 3 5× = 42 – 1 third pattern : 5 7× = 62 – 1 (i) Write down the fourth pattern. Answer ……………………………… [1] (ii) Hence, write down an expression for the nth pattern. Answer ……………………………… [2]

8 [Turn_over 7 (a) In the diagram, AB is parallel to CD. AEB, AFH and EFG are straight lines. Find the value of x and of y. Answer x = …………………………………… [1] y = …………………………………… [2] (b) The value of a car decreases over time. Its value decreases by 10% every year. The original price of the car is $168 000. Work out the total percentage decrease at the end of the 2nd year. Answer …………………………… % [3] E F G A B C D H 65° 42° x° y°

9 [Turn_over 8 (a) The scale of a map is 1 : 25 000. The area of a park is 10 cm2 on the map. Find the actual area in square kilometres. Answer …………………………… 2km [3] (b) An empty fuel tank is filled using a cylindrical pipe with diameter 8 cm. Fuel flows along this pipe at a rate of 2 metres per second. It takes 24 minutes to fill the tank. Calculate the capacity of the tank. Give your answer to the nearest litres. Answer …………………………… litres [4]

10 [Turn_over 9 (a) Complete the table of values for 3211 232y x xx= − −+ . Give your answers correct to 1 decimal place. [2] (b) On the grid, plot the graph of 3211 232y x xx= − −+ for –2 ≤ x ≤ 3. [3] (c) By drawing a suitable tangent, find the gradient of the curve when x = 2.5. Answer ……………………………… [2] x –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 2.5 3 y –0.7 1.3 2.2 2 0.8 0.5 0.7 1.6 3.5 4 3 2 1 0 –1 y x –2 –1 1 2 3 4