2020 SNGS MA Prelim P2 Question Paper w Ans Key

Name: _________________________ ( ) Class:_____________ PRELIMINARY EXAMINATION GENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL MATHEMATICS 4048/02 Paper 2 Friday 21 August 2020 2 hours 30 minutes Candidates answer on the Question Paper. ______________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name, class, and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use paper clips, highlighters, 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 . 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 marks for this paper is 100. Paper 1 / 80 Q1 Q4 Q7 Q10 Paper 2 /100 Q2 Q5 Q8 Q3 Q6 Q9 Total / 100 ________________________________________________________________________________ This document consists of 23 printed pages and 1 blank page [Turn Over

2 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 Mathematical Formulae Compound interest Total amount n rP      += 1001 Mensuration Curved surface area of a cone lr= Surface area of a sphere 24 r= V olume of a cone hr 2 3 1= V olume of a sphere 3 3 4 r= Area of a triangle ABC Cba 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 == Acbcba cos2222 −+= Statistics Mean  = f xf Standard deviation 22       −=     f xf f xf

3 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 [Turn Over 1 (a) Write as a single fraction in its simplest form 2 25 7 10 3 6 xx x x x −− ++ + + . Answer …………………………………. [3] (b) Simplify 22 2 16 9 12 9 xy x xy − − . Answer …………………………………. [2] (c) Solve the equation 12 ( 1)( 2) 8x x x =+ − − . Answer x = ………………………………. [4]

4 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 2 (a) (i) Paul sold a painting for $15680. He made a profit of 12% in the sale. How much did he pay for the painting? Answer $ …………………………………. [1] (ii) Paul saved $15680 in a bank at 2.05% per year compound interest. What was the value of his savings after 3 years? Give your answer correct to the nearest dollar. Answer $ …………………………………. [2] (iii) Which was greater, the profit he made on the painting or the interest he received in 3 years from the bank? Calculate the difference between the two. Answer ………………………………………..…………………………………………….. ………………………………………………………………………………………….... [3]

5 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 [Turn Over (b) Paul bought an apartment at the end of 2006. The price of the apartment at the end of 2006 was 9% higher than at the end of 2005. The price of the apartment at the end of 2007 was 6% higher than at the end of 2006. (i) Express the price of the apartment at the end of 2007 as a percentage of the price at the end of 2005. Answer …………………………………. % [1] (ii) Given that the increase in the price from 2006 to 2007 was $63000, calculate the increase in the price of the apartment from 2005 to 2006. Give your answer correct to the nearest hundred dollars. Answer $…………………………………. [3]

6 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 3 A Thai restaurant sells 3 different types of dinner sets. Each dinner set contains packets of 4 different types of food items: fried rice, stir fried vegetables, sambal toufu and mango sticky rice. Matrix T shows the breakdown of the number of packets of each type of food item within the 3 different sets. T = 2 4 7 1 2 3 1 1 2 234 `       (a) On average, the restaurant sells 5 Set A, 3 Set B and 6 Set C per day. Represent this as a 3  1 column matrix R. Answer …………………………………. [1] (b) Evaluate the matrix N = 7R. Answer …………………………………. [1] (c) Evaluate M = TN. Answer …………………………………. [2] Set A B C Fried Rice Stir Fried Vegetables Sambal Toufu Mango Sticky Rice

7 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 [Turn Over (d) State what each of the element(s) of M represent. Answer …………………….………………………………………………………………….. ………………………………………………………………………………………………[1] (e) (i) If the restaurant sells Set A at $24, Set B at $43 and Set C at $70, calculate the total sales from the dinner sets. Answer $ …………………………………. [1] (ii) Instead of buying the dinner sets where the combination of food items is fixed, the food items can also be bought individually (this is known as à la carte). For à la carte purchase, a packet of fried rice costs $4, mixed vegetable $6.50, sambal toufu $5 and mango sticky rice $5. In order to boost business, the restaurant also extends a discount of 10% for all à la carte purchases. Calculate the percentage loss in sales when the restaurant sells dinner sets instead of à la carte. Answer …………………………………. % [3]

8 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 4 (a) The nth term of a sequence is given by ( 3) 2 n nnT += . (i) Use the formula to find 16T . Answer 16T = ………………………………. [1] (ii) Which term in the sequence has a value of 54? Answer …………………………………. [2] (iii) Find, in its simplest form, the expression for 1nnTT+ + , leaving your answer in terms of n. Answer …………………………………. [2] (iv) Explain why the sum of two consecutive terms of this sequence will never be a perfect square. [2]

9 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 [Turn Over (b) The first four terms of a sequence are 6, 10, 14 and 18. (i) Write down the 7th term in this sequence. Answer …………………………………. [1] (ii) Find, an expression, in terms of n, for the nth term of this sequence. Answer …………………………………. [1]

10 CHIJ SNGS Preliminary Examinations 2020 - Mathematics 4048/02 5 A man was driving his truck from point A to point C in a remote part of a country. After he has travelled for 80 km, at a constant speed of x km/h, he reached point B, where his truck broke down. (a) Write down an expression, in terms of x, for the time in hours, taken for him to drive from A to B. Answer …………………………………. h [1] He then walks the remaining 6 km from B to C at a constant speed of (x − 60) km/h. (b) Write down an expression, in terms of x, for the time in hours, taken for him to walk from B to C. Answer …………………………………. h [1] (c) The man took 4 hours to travel from A to