TKGS 2026 S4 A Math WA2

TANJONG KATONG GIRLS’ SCHOOL WEIGHTED ASSESSMENT TWO SECONDARY FOUR CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049 4 May 2026 40 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your 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 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 marks for this paper is 30. This document consists of 9 printed pages and 1 blank page. For Examiner’s use

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0+ +=ax bx c , 2 4 2 b b acx a −± −= Binomial expansion 1 22( ) ... ... ,12 n n n n nr r nnn nab a ab a b a b b r −− −  + = + + ++ ++     where n is a positive integer and ! ( 1)...( 1) !( )! ! n n nn n r r rn r r  − −+= = − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA= + 22 cos ec 1 cotAA= + sin( ) sin cos cos sinAB A B A B±= ± cos( ) cos cos sin sinAB A B A B±=  tan tantan( ) 1 tan tan ABAB AB ±±=  sin 2 2sin cosA AA= 22 2 2cos2 cos sin 2cos 1 1 2sinA AA A A= − = −=− 2 2tantan2 1 tan AA A= − Formula for ∆ABC sin sin sin abc ABC= = 222 2 cosa b c bc A=+− 1 2 sinbc A∆=

Tanjong Katong Girls’ School [Turn over 3 4049/S4WA2/2026 1 (a) Find 23d sin( ) cos tand x xxx  ++ . [3] (b) Integrate 5 2 23xx x − with respect to x. [2]

Tanjong Katong Girls’ School 4 4049/S4WA2/2026 2 (a) Given that 2 2ln 34 xy x −= + , show that d d y x at the point 4x= is 1 26 . [3] (b) It is also given that y is decreasing at a constant rate of 5 units per second. Using the answer from part (a), find the rate of change of x with respect to time when 4x= [2]

Tanjong Katong Girls’ School [Turn over 5 4049/S4WA2/2026 3 The function f is given by 2f( ) 1 xex x − = + . Explain with mathematical working, why f( )x is a decreasing function, for all real values of x and 1x≠− . [4]

Tanjong Katong Girls’ School 6 4049/S4WA2/2026 4 The equation of a curve is 1by ax x= +− , where a and b are constants. The normal to the curve at the point S (1, 3) is parallel to the line 2 10xy+= . This normal meets the curve again at point T. (a) Show that 3a= and 1b= . [5]

Tanjong Katong Girls’ School [Turn over 7 4049/S4WA2/2026 (b) Find the coordinates of point T. [4]

Tanjong Katong Girls’ School 8 4049/S4WA2/2026 5 The diagram shows a piece of wire of length 64 m which is bent to form a semicircle of radius 4r m and a rectangle of length 2x m. (a) Express x in terms of r and π. [1] (b) Hence, show that the area, A m2, of the figure is 22256 32 8rr r π−− . [2] 2x m 4r m

Tanjong Katong Girls’ School [Turn over 9 4049/S4WA2/2026 (c) Given that r can vary, find the value of r which gives a stationary value of A. Give your answer correct to 2 decimal places. Determine whether this value of r gives a maximum or minimum value for A. [4]

Tanjong Katong Girls’ School 10 4049/S4WA2/2026 Blank Page