2021 SASS AMath Prelims P2 w Ans

Index Class Number Candidate Name ST ANDREWS SECONDARYSCHOOL PRELIMINARYEXAMINATION2021 SECONDARY 4 EXPRESSST ANDREW'SSCHOOLST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLSTANDREW'S SCHOOL ST ANDREWS SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW S SCHOOLST ANDREW 'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLST ANDREW'S SCHOOL ST ANDREWw'SSCHOOL ST ANDREW'S SCHOOL ST ANDREW 'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLST ANDREW'SSCHOOLST ANDREW'S SCH0OL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLST ANDREW 'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'SSCHOOLST ANDREW 'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ST ANDREW's SCHOOL ST ANDREW'S SCHOOL ST ANDREW'S SCHOOL ADDITIONAL MATHEMATICS 4049/02 Paper2 (golutions) FRIDAY 20 AUGUST 2021 2 hours 15 minutesCandidates answeron the Question Paper. READ THESE INSTRUCTIONS FIRST Writeyour name,classand index number in the spaces at the top of this page. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correctionfluid. Answerall the questions.Give non-exactnumericalanswers correct to 3 significant igures,or 1 decimal place in the case of angles in degrees, unless a differentlevel of accuracy is specifiedin the question.The use of an approvedscientificcalculatoris 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 numberof marksis givenin brackets [ ]at the end of each question or part question. The totalnumberof marksfor this paper is 90. This question paper consists of 0 printed pages. [Turn over AMATHS7015LSTSAS 2021

3 1 Simplify2+2 (3] 42-1 -2/-3 a) - ) ) ) Turn over

A 2 i) The equation of a curveis= n 2x. Find the coordinatesof the turning point in terms (3] of e. For having powMA d CogdiuaRun t Hence, determinethe natureof this turning point. [21 ( dn

6 The population M, of monkeys in a forestwas recorded from 1960 to 2010 and the resultsare 4 shown in the table below. Year 1960 1975 1990 2010 M 5.22 15.4558.20 380 It is given that M = 2+ ab where t is the time measured in years from January 1955 and a and b are constants. ) On the grid below, draw a straightline graphto illustrate this data. 3] M +o 5o | 35 55 M-9 ab 14 m-1) 1 ab M-2) laa la b IA LM-) tl> *1g 4 3.5 *** ***** -5 ****** 0S 10 0

i) Use your graphto estimate (a) the value of a and of b, [3] .8-0.h ATadevet b0 0 0.04i+ b 10 10 lb 0.0417, iteCopt 0.5 A 10 [2 b) the year in whichthe populationwill reach 600. Uo0-)> 3-18 tbu how ph) G5 b0 2015,

8 (a) A curve has the equationy=ir-+12r+3. Determine whethery is an 5 2 4) increasing or decreasing function of x. Dt -So)+1 Hen y a iks Sine ,0 (-+ (b) Show that the x-axis is not a tangent to the curve. A70 l MAnS S ro no rhig pont.

9 6 The volumeof a solid right cylinder of radius r cm is 2507 cm () Show that the total surface area, S cm, of the cylinderis given by C33 S= 2724 300 V Tw'h V T [Turnover

Calculatethe value of r for which S has a stationary value. 3 T dr t DOTO (iii) Determine whetherthis valueof r makes S a maximum or a minimum, and find the corresponding height of the cylinder. [3] Y all o dr Hr+ l000 T MALS aminlum 10M ITurn over

11 (a) Sin A Prove the identity cosecA-- 4 = cot A. 1+cos A LHS toSA t osh- SnA(3ínP) SiMA CIt osn) tpsn-inA It oA-(1- w'A) CinA CIt oSh) Sint Cit loSH) Co sh 1tLosR) SiMA Cl+ osh) oA TnA [Turn over

12 sin A (b) Hencesolvethe equationcosecA-= tan 24 for 0° A S 180°. [3]| 1+cosA +AnH_ tAn A tan At an'A - \ 0 tav'h anA A 30 o sin A c) Show that thereare no solutions to the equationcosecA- = -tan 2A for 1+cos A 0s AS360°. 12] tan 20 -HnA A tAnA tan A 1aA AnA no SolnttoM