2024 GSS 4E5N Prelim Paper 2 (as on 5 Aug)

[Turn over This paper consists of 23 printed pages, including this cover page. GREENRIDGE SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) CANDIDATE NAME CLASS - INDEX NUMBER MATHEMATICS 4052/02 Paper 2 23 August 2024 Setter: Mrs Li Geok Eng 2 hour 15 minutes Candidates answer on the Question Paper. Additional Materials: Nil 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. Answer all 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. For Examiner’s Use Total 90

2 Mathematical Formulae Compound interest Total amount = n rP       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 [Turn over Answer all the questions. 1 (a) Simplify 3 2 52 64 a ab b a b . Answer …………...………………… [1] (b) Solve 50 8 x x . Answer x = ….……… or ………….. [2] (c) Simplify 241 2 10 5 v pv p v     . Answer …………...………………… [3]

4 (d) Solve 22 3(3 1)xx . Give your solutions correct to two decimal places. Answer Answer x = ……….… or …………. [4]

5 [Turn over 2 (a) Hamid borrowed a sum of money for 3 years at an interest rate of 3.5% per annum simple interest to pay for his car. If the total interest Hamid paid on the loan was $10 374, find the sum of money that he borrowed. Answer $ ………...………………… [2] (b) The table shows information collected by Hamid about his driving in 2023. Total distance driven in 2023 16 992 km Average price paid for petrol $2.72 per litre Average petrol consumption of his car 6.7 litres per 100 km Calculate the total amount Hamid paid for petrol in 2023. Answer $ ………...………………… [2]

6 (c) At the start of 2020, Hamid bought his car at a cash price of $120 500. Each year the value of the car decreases by 5% of its value at the start of the year. At the end of 2023, Hamid decided to sell his car. (i) Explain why the percentage reduction at the end of three years is not 15% of $120 500. …………………………………………………………………………………... …………………………………………………………………………………... [1] (ii) Calculate the value of his car at the end of 2023. Give your answer correct to the nearest dollar. Answer $ ……...…………………… [3]

7 [Turn over 3 (a) { : is an integer, 2 14}x x x    { : is a prime number}A x x { : is a multiple of 3}B x x (i) List the elements in  'AB . Answer …………...………………… [1] (ii) List the elements in AB . Answer …………...………………… [1] (iii) Given that CA , n( ) 3C  and BC  , list the elements of a possible set C. Answer …………...………………… [1]

8 3 (b) (i) The diagram shows a cone P of height 24 cm. The volume of the liquid in the cone is half the volume of the cone. Calculate the depth, d cm, of the liquid. Answer ……...……………..…… cm [2] (ii) The volume of cone P is v cm3. Cone T has radius which is double that of the cone P and its height is one-third that of the cone P. Express the volume of cone T in terms of v. Answer ……...………………… cm3 [2] d cm 24 cm

9 [Turn over (c) A, B and C are points on the circumference of a circle. Angle CAB = angle CBA. DA and DB are tangents to the circle from the point D. Prove that triangle ACD and triangle BCD are congruent. Answer [3] D A O B C

10 4 The diagram shows the cross section of a cylinder, centre O, radius r, lying on its side. The cylinder contains water to a depth of 18 cm. The width, AB, of the surface of the water is 24 cm. (a) Use algebraic method to show that r = 13 cm. Answer [2] (b) Show that angle AOB is 134.76o correct to 2 decimal places. Answer [2] A O B O O P O 24 cm 18 cm r O r O