additional mathematics may 2012

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%. TEST CODE OI254O2OFORM TP 2012037 MAY/JUNE 2012CARIBBEAN EXAMINATIONS COUNCIL

SECONDARY EDUCATION CERTIFICATEEXAMINATION

ADDITIONAL MATHEMATICSPaper 02 - General Proficiency

2 hoars 40 minutes03 MAY 2012 (p.m.)

READ THE FOLLOWING INSTRUCTIONS CARE,FULLY.1- DO NOT open this examination paper until instructed to do so.2. This paper consists of FOUR sections. Answer ALL questions in Section I,Section U and Section [I].3. Answer ONE question in Section IV.4. Write your solutions with full working in the booklet provided.

Required Examination MaterialsElectronic Calculator (non programmable)Geometry SetMathematical Tables (provided)Graph Paper (provided)

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.=-----I

Copyright O 2011 Caribbean Examinations CouncilAll rights reserved.- 01254020/F 20t2

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tI,

3.

-3-SECTION TI

Answer BOTH questions.

(a) The equation of a circle is given by * + f - 4x * 6y: g7.(, Alinehas6quafi6nx+y* 1 :0. Showthatthis linepasses throughthe centre ofthe circle. (3 marks)Find the equation of the tangent to the circle at the point I (- 6, 3). (4 marks)-+Given OA: a,b)

(ii)

(D(ii)

f ot : [t.lheie":L;.Jandb: ItJ-+Write:P in terms of a and b.

Find lBPl.(2 marks)(3 marks)

Ttltd ill marks-+=- r

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(a).

-4-The diagram shows a sector of a circle centre O with an adjoining square.the circle is 4 m.

Prove the identity1 : l-sindcos 0ecd+tand

The radius of

(3 marks)

(4 marks)Total12 marks

If the sector AOC subtends an angle at O,calculate, giving your answer in terms oflt(i) the area of the shape OACMN(i1) the perimeter of the shape OAC\V. (5 marks)

(b) Given that sin +: +,"o, { : I andsin f : "o" : +,evaluate without usingcalculators, the exact value of cos f

(c)

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(a).

(b)

-5-SECTION III

Answer BOTH questions.

Differentiate the following expression with respect to x, simpliflring your answer.3x+4x-2

The point P (2,10) lies on the curvey :3f + 5x - 12. Find equations for(i) the tangent to the curve at P(ii) the normal to the curve at P.

(4 marks)

(5 marks)(c) The length of the side of a square is increasingatarate of 4 cms-l. Find the rate of increaseof the area when the length of the side is 5 cm. (5 marks)

Total14 marks

(4 marks). (a)

::::--. rft;'

'f2Evaluate J , {te -7x)3 dx.

(c)

(d)

dvThe'point 8'(4,8) [ies on a curve for which *:3x - 5. Determine the equation of thecurve. (3 marks)Calculate the area between the curvey:2 cos r * 3 sinx and the x-axis fromx : 0 to *.J

(3 marks)Calculate the volume of the solid formed when the area enclosed by the curve/ : f + 2and the r-axis, from x : 0 to x :3, is rotated through 360" about the x-axis.[Leave your solution in terms of z ]. (4 marks)

Total 14 marks

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(a).

-6-SECTION IV

Answer only ONE question.

A survey carried out in a town revealed that 25%o of the households surveyed owned alaptop computer andTlYo owned a desktop computer. In addition, it was found that l2ohowned both a laptop and a desktop computer.If a sample of households from the town is selected at random, determine the proportionthat own NEITHER a laptop NOR a desktop computer. (4 marks)

(b) A bag contains 4 red marbles, 3 black marbles and 3 blue marbles.drawn at random without replacement from the bag.Find the probability that the marbles(D drawn areALL of the SAME colour (3 marks)

(3 marks)iD contain EXACTLY 1 red marble.IThe probability of hirin g a taxi from garage A, B or C is 0.3, 0. 5 and 0.2 respectively. Theprobability that the taxi ordered will be late from A is O.O7, from B is 0.1 and from C is

0.2.(i) Illustrate this information on a fiee diagram showing the probabiliry on all branches.

(3 marks)A garage is chosen at random, determine the probability thata) the taxi will arrive lateb) the taxi will come from garage C given that it is late.

Three marbles are

(3 marks)(4 marks)

Total20 marks

(c)

(ii)

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v(a).

-7 -A car starting from rest at a point l, moves along a straight line reaching a velocity of24 ms' by u constant acceleration of 6 ms 2. The car maintains this constant velocityof 24 ms-1 for 5 seconds and is then brought to rest again by a constant accelerationof-3 ms-2.(i) Using the graph sheet provided, draw a velocity-time graph to illustrate themotion of the car. (3 marks)

(iD(iiD

Determine the TOTAL distance travelled by the car. (3 marks)

(5 marks)(5 marks)

Total20 marks

A second car, moving at a constant velocity of 32 ms-r drives past pointA,3 secondsafter the first car left pointl. Calculate the length of time after the first car startedthat this second car meets it.[Assume that the cars meet during the time when the first car is moving at aconstant velocity.l (4 marks)(b) Aparticle moves in a straight line with acceleration given by a: (51- 1) ms-2 at any time/ seconds. When t:2 seconds, the particle has velocity 4 ms-1 and is 8 m from a flxedpoint O. Determine

(i) its velocity when t: 4 ((ii) its displacement from O whet t :3.

END OF TEST

IF'YOU F'INISH BEFORE TIME IS CALLED, CHECK YOUR WORI( ON THIS TEST.

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FORM TP 2012037 TEST CODE OI254O2OMAY/.IT]NE 2OI2CARIBBEAN EXAMINATIONS COUNCILSECONDARY EDUCATION CERTIF'ICATEEXAMINATION

ADDITIONAL MATHEMATICSPaper 02 - General ProficiencyAnswer Sheet for Question 8. (a) (i) Candidate Number

6810121416Time (seconds)

ATTACH THIS ANSWBR SHEBT TO YOURANSWER BOOKLET

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additional mathematics may 2012

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