Serangoon Garden 4E5NA E Maths Prelim P2 2021 QP

SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP [Turn over CANDIDATE NAME CLASS REGISTER NUMBER ____________________________________________________________________ _ MATHEMATICS 4048/02 Paper 2 24 Aug 2021 Secondary 4 Express/ 5 Normal Academic 2 hours 30 minutes 0800 - 1030 Candidates answer on the Question Paper. ____________________________________________________________________ _ READ THESE INSTRUCTIONS FIRST Write your name, class and class register number 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, 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 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 100. This question paper consists of 19 printed pages and 1 blank page. Setter: Mr Poh WR Vetter: Ms Tay HY SERANGOON GARDEN SECONDARY SCHOOL Vision: Learners with Grit, Leaders with Heart Mission: Nurturing and empowering individuals to lead purposeful lives PRELIMINARY EXAMINATION 2021 FOR MARKER’S USE 100 __________________________ _______________ Name/Signature of Parent/Guardian Date

2 SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP Mathematical Formulae Compound interest Mensuration Trigonometry Statistics

3 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP

4 SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP Answer all the questions. 1 (a) Simplify , leaving your answer in positive index. Answer …………………………..…………. [2] (b) Solve the equation Answer …………………………..…………. [2] (c) Given that , express b in terms of a and x.

5 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP Answer b = ……………………..…………. [2] (d) Simplify . Answer …………………………..…………. [3] (e) Solve these simultaneous equations.

6 SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP Answer x = …………… , y = …………… [3] 2 A motorist cycled 55 km from Town A to Town B at an average speed of x km/h. He returned from Town B to Town A by the same route. His average speed for the return journey was 10 km/h less than the journey from Town A to Town B. (a) Write down an expression, in terms of x, for the number of hours taken to travel from Town A to Town B. Answer ……………………………… hours [1] (b) Write down an expression, in terms of x, for the number of hours taken to travel from Town B to Town A. Answer ……………………………… hours [1] (c) He took 1 hour 15 minutes more on the return journey than on the outward journey. (i) Write down an equation in x and show that it reduces to . Answer [3] (ii) Solve the equation . Answer x = …………… or …………… [3] (iii) Hence, find the total time he was cycling in hours and minutes, rounding your answer to the nearest minute.

7 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP Answer ……… hours …………… mins [2] 3 (a) Two spinners with numbers on them are shown below. They are divided equally into two sectors and three sectors respectively. (i) List all possible outcomes using a tree diagram when both spinners are spun. [2] Tree Diagram (ii) Find the probability that the sum of the two numbers where the pointers of the spinners land on is more than 5. Answer ………………………..…………. [2] (b) Dylan picked 2 balls from a bag containing 3 red balls and x green balls without replacement. If the probability of picking 1 red and 1 green ball is , find the possible number of green balls in the bag initially. Spinner 1 Spinner 2

8 SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP Answer ………………………..…………. [4] 4 The variables x and y are connected by the equation Some corresponding values of x and y are given in the table below. x 0 1 2 3 y 0.5 1 0 3 (a) On graph paper below, draw the graph of for . [3] y 3 2 1 0 3 2 1 x

9 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP (b) The equation has only 1 solution. Explain how this can be seen from your graph. Answer ------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------ [2] (c) By drawing a tangent, find the gradient of the curve at the point (2 , ). Answer …………………………..…………. [2] (d) (i) On the same grid, draw the line for . [2] (ii) Write down the x-coordinates of the points where this line intersects the curve. Answer x = ……………… or ……………… or ……………… [1] (iii) Show that the points of intersection of the line and the curve satisfy the equation Answer

10 SGS/Mathematics/4E5N/2021/Prelim/4048/P2/QP [2] (e) Using your graph, find the coordinates of another point on the curve with the same gradient as the answer in part (c). Answer (…………… , ……..……) [1] 5 A shop makes mini cakes and operates 7 days a week. The matrix, M, shows the number of cakes of different types that are made each day. Regular Deluxe Premium M (a) Evaluate the matrix P = 7M Answer P = …………………..…………. [1] (b) Regular cakes cost $1 each to make. Deluxe cakes cost $1.50 each to make. Premium cakes cost $2.50 each to make. By representing these amounts in a 3 × 1 column matrix N, evaluate the matrix T = PN. Answer T = …………………..…………. [2] (c) State what each of the elements of T represents.