EXAMINATION MATHEMATICS - Online CXC CSEC Maths Class ...
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JANUARY 2OI8
CARIBBEAN EXAMINATIONS COUNCIL
CARIBBEAN SECONDARY EDUCATION CERTIFICATE@ EXAMINATION
MATHEMATICS
Paper 02 - General Prcficiency
2 hours 40 minutes
READ THE FOLLOWING INSTRUCTIONS CAREFULLY.
1. This paper consists of TWO sections: I and II.
2. Section I has EIGHT questions and Section II has THREE questions.
3. AnswerALL questions in Section I and any TWO questions from Section II.
4. Write your answers in the booklet provided.
5. Do NOT write in the margins.
6. All working MUST be clearly shown.
7. A list of formulae is provided on page 4 of this booklet.
8. If you need to rewrite any answer and there is not enough space to do so on the
original page, you must use the extra page(s) provided at the back of this booklet. Remember to draw a line through your original answer.
9. If you use the extra page(s) you MUST write the question number clearly in the
box provided at the top of the extra page(s) and, where relevant, include the question part beside the answer.
Required Examination Materials
Electronic calculator Geometry set
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.
Copyright @ 2017 Caribbean Examinations Council
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LIST OF FORMULAE Volume of a prism
Volume of a cylinder Volume of a right pyramid Circumference
Pas;l
I :V Ah where is the area of a cross-section and ft is the perpendicular
length.
V = nf hwhere r is the radius of the base and & is the perpendicular height.
f :
I
]-,lhwttere
,,{ is the
area of the base and
& is the
perpendicular
height.
C = Znr where r is the radius of the circle.
Arc length
Area of a circle Area of a sector
t: *- x 2nr where 0 is the angle subtended by the arc, measured in
degrees.
:A nf where r is the radius of the circle.
n: #x nl where 0 is the angle of the sector, measured in degtees.
Areaof atrapezium
A=+@+ b)ft where aandbare the lengths of theparallel sides and ft
is the perpendicular distance between the parallel sides.
Roots of quadratic equations lf axz + bx -r c: 0,
Trigonometric ratios
th-en l- = -b +,{b? 4a; ----u-
: stn 0
length of opposite side
I#gtfm$Foienuse
cos0 = length ofadjacent side
length ofhypotenuse
tanO: length of
side
length ofadjacent side
0 Adjacent
Opposite
Area of a triangle Sine rule
Areaof A= ) bhwhereb is the length of the base and ft is the perpendicular
height.
Area of A ABC = |- ab sin C Area of A ABC : s(s-a)(s-b)(s-c)
where s - a+b*c
2
sam_7b-c silT silU
c
B
a
c
A b
Cosine rule
a2 = b2. i c2 - 2bc cos A
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Pas"I
SECTION I
Answer ALL questions in this section. All working must be clearly shown.
1. (a) Using a calculator, or otherwise, calculate
(i) t* * ,1 * tf , eivinc your answer as a fraction in its lowest terms
(ii) 165 x 0.382, giving your answer as an EXACT value.
(2 marks)
(1 mark)
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(b) Write your answer in (a) (ii) correct to (i) two decimal places
(iD three significant figures
(iii) the nearest whole number.
Pas"7l
(1 mark) (1 mark) (1 mark)
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(c)
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MrAdams invested $5 000 at the credit union and received S5 810, inclusive of simple interest, after 3 years. Determine
(i) the simple interest earned
(ii) the annual interest rate paid by the credit union
(1 mark)
(2 marks)
(iii) the length of time it will take for MrAdams' investment to be doubled, at the same
rate of interest.
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2. J;4b (a) Given that a * b means
, where the positive root is taken, determine
(i) the value of I * 2
(2 marks)
(ii) whether the operation denoted by * is commutative. Justifu your answer.
(3 marks)
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(b)
(D Solve the inequality 3 -Zx> 5
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(ii) Represent your answer in (b) (i) on the number line shown below.
(2 marks)
-4 -3 -2 -1 0 1 2 3 4
(l mark)
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(c)
rase {
Statement one: Two adult tickets and three children tickets cost $43.00. Statement two: One adult ticket and one ticket for a child cost $18.50.
(i) Let x represent the cost of an adult ticket andy the cost of a ticket for a child. Write
TWO equations in x andy to represent the information above.
(iD Solve the equations to determine the cost of an adult ticket.
(2 marks)
(2 marks) Total 12 marks
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