CARIBBEAN EXAMINATIONS COUNCIL CARIBBEAN SECONDARY EDUCATION EXAMINATION ADDITIONAL MATHEMATICS. Paper 02 - General Proficiency

Size: px

Start display at page:

Download "CARIBBEAN EXAMINATIONS COUNCIL CARIBBEAN SECONDARY EDUCATION EXAMINATION ADDITIONAL MATHEMATICS. Paper 02 - General Proficiency"

Albert Bond
5 years ago
Views:

1 TEST CODE FORM TP MAY/JUNE 2015 CARIBBEAN EXAMINATIONS COUNCIL CARIBBEAN SECONDARY EDUCATION EXAMINATION ADDITIONAL MATHEMATICS Paper 02 - Geeral Proficiecy 2 hours 40 miutes ( 05 MAY 2015 (p.m.) ) READ THE FOLLOWING INSTRUCTIONS CAREFULLY. 1. This paper cosists of FOUR sectios. Aswer ALL questios i Sectio I, Sectio II ad Sectio III. 2. Aswer ONE questio i Sectio IV. 3. Write your solutios with full workig i the booklet provided. 4. A list of formulae is provided o page 2 of this booklet. Required Examiatio Materials Electroic Calculator (o-programmable) Geometry Set Mathematical Tables (provided) Graph Paper (provided) īiiiiiiiiii -== iiiiiiiiiii DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO. īiiiiiiiiii /F 2015 Copyright 2013 Caribbea Examiatios All rights reserved. Coucil

2 - 2- LIST OF FORMULAE Arithmetic Series S = 2 [2a + ( - 1)d] Geometric Series T =ar -J S a(/ - 1) r-l S = _a_ -1 < r < 1 or Irl < 1 co 1- r ' Circle 2 2 X + Y + 2ft + 2gy + c = (x +j) + (y + g) = r Vectors /\ V v=- cos e = aob lvl [a] x [b] Ivl =.,j (x 2 + /) where v = xi + yj Trigoometry si (A ± B) == si A cos B ± cos A si B cos (A ± B) == cos A cos B + si A si B ta (A ± B) == taa+tab 1 + ta A ta B Differetiatio d -i dx (ax + b) = a(ax + b) d. dx smx = cosx d. -cosx =-smx dx Statistics - i~i X Lx I = -- L/x i= 1 I I L(X._x)2 i = i~i 1 L/X2 i= 1 I I 2 - (x) Probability pea ub) = pea) + PCB) - pea (l B) Kiematics v = u + at 2 2 V =u +2as 1 2 S = ut+-at /F 2015

3 - 3 - SECTION I Aswer BOTH questios. ALL workig must be clearly show. 1. (a) The fuctios f ad g are defied by 2 f(x) =x + 5, g (x) = 4x - 3, x E R where R is the set of real umbers. Fid the value of g (((2)). (2 marks) (b) 3x+ 5 The fuctio h is defied by hex) = where x E R, x*- 2. x-2 Determie the iverse of hex). (c) Give that x - 2 is a factor of k(x) = 2x 3-5x 2 + X + 2, factorize k(x) completely. (d) Solve the followig equatios: (i) 16 x+2 = _1_ 4 (2 marks) (ii) log, (x + 2) + log, (x - 1) = log, (6x - 8) Total 14 marks F 2015

4 -4-2. (a) Give that/ex) = 3x 2-9x + 4: (i) Express r'(x) i the form a (x + b)2 + c, where a, bad c are real umbers. (ii) State the coordiates of the miimum poit of/ex). (l mark) (b) The equatio 3x 2-6x - 4 = 0 has roots a ad (3. Fid the value of -;- +t. (c) Determie the coordiates of the poits of itersectio of the curve 2x 2 - Y + 19 = 0 ad the lie y + llx = 4. (d) A employee ofa compay is offered a aual startig salary of$ which icreases by $2 400 per aum. Determie the aual salary that the employee should receive i the ith year. Total 14 marks o lF 2015

5 - 5 - SECTION II Aswer BOTH questios. ALL workig must be clearly show. 3. (a) The equatio of a circle is give by X2 +/ - 12x - 22y = O. (i) (ii) Determie the coordiates of the cetre of the circle. Fid the legth of the radius. (2 marks) (1 mark) (iii) Determie the equatio of the ormal to the circle at the poit (4, 10). (b) The positio vectors of two poits, A ad B, relative to a origi 0, are such that OA = 3i - 2j ad OB = 5i - 7j. Determie (i) the uit vector AB (ii) the acute agle AOB, i degrees, to oe decimal place. Total 12 marks /F 2015

6 (a) The followig diagram shows a circle of radius r = 4 em, with cetre 0 ad sector AOB which subteds a agle, e = -%- radias at the cetre. If the area of the triagle AOB =+/ si e, the calculate the area of the shaded regio. (b) Solve the followig equatio, givig your aswer correct to oe decimal place. 8 si 2 e = 5-10 cos e, where 0 0 :s e:s 3900 (c) Prove the idetity si e + si 2e 1 + cos e + cos 2e == ta e. Total 12 marks o F 2015

7 -7 - SECTION III Aswer ALL workig BOTH questios. must be clearly show. 5. (a) Differetiate the followig expressio with respect to x, simplifyig your aswer. (2/ + 3) si 5x (b) (i) Fid the coordiates of all the statioary poits of the curve y = x 3-5x 2 + 3x + 1. (ii) Determie the ature of EACH poit i (i) above. (2 marks) =+ (c) A spherical balloo of volume V 1[ / is beig filled with air at the rate of 200 cm 3 s-i. Calculate, i terms of 1t, the rate at which the radius is icreasig whe the radius of the balloo is 10 em. ' (5 marks) Total 14 marks o F 2015

8 -8-6. (a) Evaluate f ~cos 3e de. 6 (b) A curve has a equatio which satisfies ~ = kx(x - 1) where k is a costat. Give that the value of the gradiet of the curve at the poit (2,3) is 14, determie (i) the value of k (2 marks) (ii) the equatio of the curve. (c) Calculate, i terms of 1, the volume of the solid formed whe the area eclosed by the curve y = X2 + 1 ad the x-axis, from x = 0 to x = 1, is rotated through about the x-axis. Total 14 marks o lF 2015

9 -9 - SECTION IV Aswer ALL workig oly ONE questio. must be clearly show. 7. (a) There are three traffic lights that a motorist must pass o the way to work. The probability that the motorist has to stop at the first traffic light is 0.2, ad that for the secod ad third traffic lights are 0.5 ad 0.8 respectively. Fid the probability that the motorist has to stop at (i) ONLY ONE oe traffic light (ii) AT LEAST TWO traffic lights. (b) Use the data i the followig table to estimate the mea of x. x f (c) Research i a tow shows that if it rais o ayoe day the the probability that it will rai the followig day is 25%. If it does ot rai oe day the the probability that it will rai the followig day is 12%. Startig o a Moday ad give that it rais o that Moday: (i) Draw a probability tree diagram to illustrate the iformatio, ad show the probability o ALL of the braches. (ii) Determie the probability that it will rai o the Wedesday of that week. Total 20 marks lF 2015

10 (a) A particle movig i a straight lie has a velocity of 3 m S-I at t = 0 ad 4 secods later its velocity is 9 m S-I. (i) O the aswer graph sheet, provided as a isert, draw a velocity-time graph to represet the motio of the particle. (ii) Calculate the acceleratio of the particle. (iii) Determie the icrease i displacemet over the iterval t = 0 to t = 4. (b) A particle moves i a straight lie so that t secods after passig through a fixed poit 0, its acceleratio, a, is give by a = (3t - l)m S-2. The particle has a velocity, v, of 4 m s -I whe t = 2 ad its displacemet, s, from 0 is 6 metres whe t = 2. Fid (i) the velocity whe t = 4 (5 marks) (ii) the displacemet of the particle from 0 whe t = 3. (5 marks) Total 20 marks END OF TEST IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS TEST. o F 2015

= TEST CODE FORM TP 2015037 MAY/JUNE 2015 CARIBBEAN CARIBBEAN EXAMINATIONS COUNCIL SECONDARY EDUCATION EXAMINATION CERTIFICATE ADDITIONAL MATHEMATICS

11 = TEST CODE FORM TP MAY/JUNE 2015 CARIBBEAN CARIBBEAN EXAMINATIONS COUNCIL SECONDARY EDUCATION EXAMINATION CERTIFICATE ADDITIONAL MATHEMATICS Paper 02 - Geeral Proficiecy Aswer Sheet for Questio 8. (a) (i) Cadidate Number ATTACH THIS ANSWER SHEET TO YOUR ANSWER BOOKLET o /P

Additional Mathematics

Additional Mathematics Additioal Mathematics CSEC PAST PAPERS Macmilla Educatio 4 Cria Street, Lodo, N1 9XW A divisio of Macmilla Publishers Limited Compaies ad represetatives throughout the world www.macmilla-caribbea.com ISBN