PLMGS(S) 4049 AM Prelim P1 2021 (w final ans)

[Turn over Name: ___________________________ ( ) Class: _______ Centre Number S Index Number ADDITIONAL MATHEMATICS 4049/01 Paper 1 27 August 2021 Candidates answer on the Question Paper. 2 hours 15 mintues No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Centre number, index number, name and class in the spaces at the top of this page. 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. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. 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 90. This document consists of 23 printed pages and 1 blank page. Paya Lebar Methodist Girls’ School (Secondary) Preliminary Examination 2021 Secondary 4 Express Calculator Model: (if applicable) For Examiner’s Use 90

2 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, a acbbx 2 42  Binomial Expansion ,21)( 221 nrrnnnnn bbar nbanbanaba                   where n is a positive integer and     ! 11 )!(! ! r rnnn rnr n r n        2. TRIGONOMETRY Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin(A  B) = sin A cos B  cos A sin B cos(A  B) = cos A cos B  sin A sin B BA BABA tantan1 tantan)tan(   sin 2A = 2 sin A cos A cos 2A = cos2 A  sin2 A = 2cos2 A  1 = 1  2sin2 A A AA 2tan1 tan22tan  Formulae for ABC C c B b A a sinsinsin  a2 = b2 + c2 – 2bc cos A Abc sin2 1

3 [Turn over 1 x is the principal value of 1 3tan 4   . Without using a calculator, find the value of (i) cos x , [1] (ii) sin 2 x . [2]

4 [Turn over 2 Solve the equation   02433283 12 22  xx . [4]

5 [Turn over 3 Find the set of values of the constant m for which the line 1y mx does not meet the curve 2 21 2 xxy x   . Express your answer in exact form. [5]

6 [Turn over 4 The diagram shows a circle passing through the points B, D, E and F. The straight line ABC is a tangent to the circle. CDE is a straight line and FD is parallel to AC. Prove that EB bisects angle DEF. [4] A B C D E F

7 [Turn over 5 The surface area of a spherical balloon is decreasing at the rate of 24 cm2/s. (i) If the radius of the balloon at time t seconds is r cm, find an expression, in terms of r, for the rate of change of the radius. [3] (ii) Find the rate of decrease in the volume of the balloon when the radius is 10 cm. [3]

8 [Turn over 6 A town has a population of 95 000. During a pandemic, the total number of people, N, infected t days after the virus has begun, is modelled by 06 95 000 2 498 .tN e  . (i) Find the number of people who were initially infected by the virus. [2] (ii) The authority decided to issue home quarantine orders when 8% of the population are infected. After how many days will the authority issue the order? [3]

9 [Turn over Continuation of working space for question 6(ii). (iii) Explain based on the model whether all 95 000 people will become infected after a long period of time. [2]

10 [Turn over 7 (a) (i) Write down and simplify the first four terms in the expansion, in ascending powers of x, of   5 23 x . [2] (ii) Hence find the coefficient of x3 in the expansion of    521 2 2 3xx . [2]