(Bedok South) AM4 P2 (2025) Students

1 BEDOK SOUTH SECONDARY SCHOOL PRELIMINARY EXAMINATION 2025 4E5N CANDIDATE NAME CLASS REGISTER NUMBER ADDITIONAL MATHEMATICS Paper 2 4049 / 02 2 hours 15 minutes 90 Answer all the questions. 1 (a) Solve the equation 232(4 ) 8 11(2 ) 2x x x +− = − , giving your answer correct to 3 significant figures. [5] (b) Show that the solution from part (a) may be written in the form lognmp− where m, n and p are integers to be determined. [2] 2 The mass, M grams, of a radioactive substance, present at time t years after first being observed, is given by the formula 200 ktMe −= , where k is a constant. The mass of the substance was 123.7 g after being observed for 2 years. (a) (i) State the initial mass of the substance. [1] (ii) Show that k is approximately 0.240, correct to 3 significant figures. [1] (iii) Find the mass of the substance when t = 5, [1] (iv) Find the value of t when the mass of the substance is 15% of its initial mass. Give your answers correct to three significant figures. [2] (b) Explain, with clear working, why the mass of the substance can never be more than 200 grams. [1] (c) Sketch the graph of M against t. [2] 3 (a) It is given that 2 25yx x= − , where 𝑥 ≥ ℎ. Show that d( 25 2) d yx x kx x − − = , where k is an integer and determine the value of h and of k. [4] (b) Hence evaluate   7 3 10 ( 2 2 ) 6 d . 5 x x x x − − + [4] 4 (a) (i) Factorise completely 3 64x + . [2] (ii) Hence, express 2 3 3 64 x x + in partial fractions. [5] (b) Using the results in part (a), or otherwise, find 32 3 2 3 128 d64 xx xx ++ + . [3]

2 5 A particle moves in a straight line so that, at time t seconds after passing a fixed point O, its velocity is v m/s, where 4 8cos 2vt=+ . Find (a) the velocity of the particle at the instant it passes O, [1] (b) the least value of the particle’s acceleration, [1] (c) the values of t, in terms of π, when the particle is at rest for 03 t , [4] (d) the distance travelled in the first 2 seconds. [4] 6 The diagram shows right angled trapezium OCDF inside a semicircle with centre O and radius 10 cm such that angle BOC is θ radians, and angle CDF and angle OFD are right angles. (a) Show that the perimeter, P cm, of trapezium OCDF is given by 10 30 cos 10 sinP = + + [2] (b) Find the value of R when 10 sin 30 cos+ is expressed as cos( )R − , where R and α are constants, and hence state the maximum perimeter of the trapezium. [3] (c) Show that the area, A cm2, of trapezium OCDF is given by 75 sin 2A = [2] (d) The area of the trapezium varies with the value of θ. Find the value of θ for which the area has a stationary value and determine whether this area is a maximum or a minimum. [4] 7 Solutions to this question b