r % TEST CODE OI254O2O-lMAY/JUNE 20I6FORM TP 2016037
CARIBBEAN EXAMINATIONS COUNCIL
CARIBBEAN SECONDARY EDUCATION CERTIFICATE@EXAMINATION
ADDITIONAL MATHEMATICS
Paper 02 - General Proficiency
2 hours 40 minutes
Reouired Examination Materials
Electronic calculator (non programmable)Geometry setMathematical tables (provided)Graph paper (provided)
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.
1
READ THE FOLLOWING INSTRUCTIONS CAREFULLY.
This paper consists of FOUR sections. Answer ALL questions in Section I,Section II and Section III.
Answer ONE question in Section IV.
Write your answers in the spaces provided in this booklet
Do NOT write in the margins.
A list of formulae is provided on page 4 of this booklet.
If you need to rewrite any answer and there is not enough space to do so on theoriginal page, you must use the extra page(s) provided at the back of this booklet.Remember to draw a line through your original answer.
If you use the extra page(s) you MUST write the question number clearly inthe box provided at the top of the extra page(s) and, where relevant, includethe question part beside the answer.
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Copyright O 2013 Caribbean Examinations CouncilAll rights reserved.
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LIST OF FORMULAE
Arithmetic Series
Geometric Series
Circle
Vectors
Trigonometry
Differentiation
Statistics
Probability
Kinematics
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T,:a+(n-l)d S,:+f\a+(n-l)dl
a(f - 1) S,:#, -l <r< I or lrl < Ir-
x'+f+2fx+29+c:0 (x +J)'+ O + g)': f
l"l (x'+ f) where v: xi+ li0:I cosd: a'blvl lal x lbl
fr fr. + b)' : an(ax + S)n r
sin (l + B)= sinl cosB* cos Asin B
cos (l + B) =cosl cos BT sin A sin B
tan(A+ B) tanA + tan B1T tan Atan B
n
dd.x
d
dx
sln.I:cosx
cos, : -sln.x
n
f,x, Ir, 7)' Zr,n
xx
n, 5P- (r)'i :-n nn
T f, Z=,'f
P(A w B): P(A) + P(B) - P(A a B)
v:u*At v2:U2i2AS
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JL 0125402004
2
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SECTION I
Answer BOTH questions.
ALL working must be clearly shown.
The domain for the function/(x):2x - 5 is {-2, -1, 0, I }
(i) Determine the range of the function.
(ii) Find / '(x)
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(2 marks)
(1 mark)
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l. (a)
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JL 0125402005
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(iii) Sketch the graphs of f (x) andfa (x) on the same axes.
(iv) Comment on the relationship between the two graphs
(b) Solve the equation 22t+t + 5 (2')- 3:0
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(2 marks)
(1 mark)
(4 marks)
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IL 0125402006
-7 -
rh)l;l(c) (i) Given that T: k p r, make c the subject of the formula.
(ii) Solve the equation
log (x + 1) + log (x- l) : 2 log (x + 2).
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(2 marks)
(2 marks)
Total 14 marks
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2. (a) (i) Determine the nature of the roots of the quadratic equation 2f + 3x - 9:0
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(1 mark)
(ii) Given thatf (x) :2f -r 3x - 9, sketch the graph of the quadratic function, clearlyindicating the minimum value.
(5 marks)
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JL 0125402008
t- -9 -
25
(b) Evaluate ZZ'.
(3 marks)
(c) A man invested $x in a company in January 2010, on which he earns quarterly dividends.At the end of the second, third and fourth quarter in 201 l, he earned $100, $1 l5 and $130respectively" Calculate the total dividends on his investment by the end of 2016.
(5 marks)
Total 14 marks
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JL 0125402009
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SECTION II
Answer BOTH questions.
ALL working must be clearly shown.
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3. (a)
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(i) The points M (3,2) and N(-1, 4) are the ends of a diameter of circle C. Determinethe equation of circle C.
(5 marks)
(ii) Find the equation of the tangent to the circle C at the point P (-1,6)
(3 marks)
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(b) The position vector of two points A and.B, relative to a fixed origin, O, are a and b
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respecrivery, where ,:l:1. "ro
,: [;] . p ties onissuch that rt: +Ii---+
Find the coordinates of OP.
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(4 marks)
Total 12 marks
L 0125402011
r -12- -lThe following diagram (not drawn to scale) shows two sectors, AOB and DOC. OB and
OC are x cm and (x + 2) cm respectively and angle AOB : 0.
D
4. (a)
A
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2tr_Trf 0: radians, calculate the area of the shaded region in terms of x,
(4 marks)
(b) Given that cos 30" and sin 45o:fr , without the use of a calculator, evaluate2
cos 105o, in surd form, giving your answer in the simplest terms
(5 marks)
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012540201F 2016
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JL 0125402012
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(3 marks)
Total 12 marks
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SECTION III
Answer BOTH questions.
ALLworking must be clearly shown.
5. (a) nina $ given thaty : 'l-5f 4,simplifying your answer.
(4 marks)
(b) The point P (1, 8) lies on the curve with equati on y:2x (x + I )2. Determine the equation
of the normal to the curve at the point P.
(5 marks)
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Obtain the equation for EACH of the two tangents drawn to the curve)/: f at the pointswhere y: 16.
(5 marks)
Total 14 marks
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(c)
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J6. (a) (i) Find (3cos0-5sin0)d0
3
(3 marks)
(4 marks)
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(ii) Evaluate I l+ -3 +2r)dx
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JL 0125402016
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The following figure shows the finite region R bounded by the lines x : l, x: 2 and thearc of the curve / : (x - 2)2 + 5 .
y-axis
(b)
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(0,9)
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Calculate the area of the region R
(4 marks)
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The point P (1 ,2) lies on the curve which has a gradient function given byFind the equation of the curve.
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-l(c)
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9-:3x2 - 6x.dx
(3 marks)
Total 14 marks
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SECTION IV
Answer only ONE question.
ALL working must be clearly shown
7. (a) Use the data set provided below to answer the questions which follow.
t5 16 l8 t8 20 2l 22 22
22 25 28 30 30 32 35 40
41 52 54 59 60 65 68 75
(i) Construct a stem-and-leaf diagram to represent the given data.
(3 marks)
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(ii) State an advantage of using the stem-and-leaf diagram to represent the given data.
(l mark)
(iii) Determine the mode
(l mark)
(iv) Determine the median.
(2 marks)
(v) Determine the interquartile range.
(3 marks)
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Two events, A and B, are such that P(A):0.5, P(B): 0.8 and P(A w B) : 0.9
(i) Determine P(A a B'1.
(ii) Determine P(A I B\
(iii) State, giving a reason, whether or not A and.B are independent events.
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-l(b)
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(2 marks)
(2 marks)
(2 marks)
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A bag contains 3 red balls, 4 black balls and 3 yellow balls. Three balls are drawn at
random with replacement from the bag. Find the probability that the balls drawn are allof the same colour.
(4 marks)
Total20 marks
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-l(c)
01254020/F 2016
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A motorist starts from a point, X, and travels 100 m due North to a point, Y, at a constantspeed of 5 m s-r. He stays atYfor 40 seconds and then travels at a constant speed ofl0 m s-' for 200 m due South to a point, Z.
(i) On the following grid, draw a displacement-time graph to display this information.
(5 marks)
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-l8. (a)
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q)
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(ii) Calculate the average speed for the whole journey
(iii) Calculate the average velocity of the whole journey.
(3 marks)
(3 marks)
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r -25 -
(b) A particle starting from rest, travels in a straight line with an acceleration, a, given bya : cos / where r is the time in seconds.
(i) Find the velocity of the particle in terms of r
(3 marks)
(ii) Calculate the displacement of the particle in the interval of time t : r to t : 2r.
(6 marks)
Total20 marks
END OF TEST
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS TEST.
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EXTRA SPACE
If you use this extra page, you MUST write the question number clearly in the box provided.
Question No.
01254020/F 2016
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