TKGS 2024 S4 Prelim Math P2 Question Paper (with answer key)

TANJONG KATONG GIRLS’ SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR EXPRESS CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/02 Paper 2 7 August 2024 2 hour 15 minutes Candidates answer on the Question Paper 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 a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE ON ANY BARCODES. Answer all questions. 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 total of the marks for this paper is 90. 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. Gives answers in degrees to one decimal place. For  , use either your calculator value or 3.142. This document consists of 23 printed pages and 1 blank page. For Examiner’s use

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 2 Mathematical Formulae Compound interest Total amount = nrP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cos a b c bc A= + − Statistics Mean = fx f   Standard deviation = 22 fx fx ff  −   

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 [Turn over] 3 TURN OVER FOR QUESTION 1

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 4 1 (a) Solve the equation ( )3 2 1 2173 x x− =− . Answer x= ……………………………………... [2] (b) Simplify (i) 22 2 25 9 15 10 6 9 ab a ab b b − − + − Answer …………………………………………… [3] (ii) 3 2 3 4 12 cc ab ab . Answer …………………………………………… [2]

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 [Turn over] 5 (c) (i) Solve the equation 2 790 2xx− + − = by completing the square . Give your solutions correct to two decimal places. Answer x= ………………. or ………………… [3] (ii) Explain why 2 79 18 2xx− + − = has no real solution. ……………………………………………………………………………….. ……………………………………………………………………………….. ……………………………………………………………………………….. ……………………………………………………………………………….. [2]

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 6 2 (a) In a particular month, 21 people took a driving test. One of the 21 people is selected at random. The probability that it is a man who passed the test is 1 7 . Two of the 21 people are selected at random. The probability that they are both women who failed the test is 1 10 . Complete the table of information about the 21 people who took the test on that particular month. Passed the test Failed the test Men 9 Women [4]

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 [Turn over] 7 (b) { : is a student in a class}xx = { : is a student who listens to pop music }A x x= { : is a student who listens to classical music}B x x= It is given that n( ) 35 = , n( ) 22,A = n( ) 14B = and n( ) 12AB = . (i) Describe in words the set AB  . ……………………………………………………………………………... ……………………………………………………………………………... [1] (ii) Find the number of students who listen to both pop and classical music. Answer …………………………………………...... [1] (iii) Find the number of students who listen to classical music only. Answer ……………………………………………... [1] (iv) Find the number of students who listen to neither pop nor classical music. Answer ……………………………………………... [1]

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 8 [3] 17.5 20 3 (a) Complete the table of values for 202 15yx x= + − . x 1 2.5 5 10 12.5 15 20 y 7 1− 7 11.6 16.3 26 [1] (b) On the grid, draw the graph of 202 15yx x= + − for 0 20x . 0 y 7.5 5 15 10 2.5 12.5 x 5 10 15 20 25 30 –5

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 [Turn over] 9 (c) Using the graph, state the range of values of x for which 202 22x x+ . Answer ……………………………………………… [2] (d) By drawing a tangent, find the gradient of the curve at the point where x = 4. Answer ……………………………………………… [2] (e) By drawing a suitable straight line on the grid, find the solutions of the equation 2 13 20 0xx− + = . Answer x= ……………….. or …………………. [2]

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 10 4 In the diagram, PQRS is a vertical rectangular wall of height 2.5 m and length 7.5 m. T is a point on level ground from the base of the wall RS. STR = 95 and SRT = 40. X is a point on ST such that SX : XT is 1 : 3. (a) Calculate the length of SX. Answer .………………………………………...... m [3] (b) Calculate the length of XR. Answer ………………………………………… m [3] T S R Q P X 7.5 m 2.5 m 40 95