CSEC-MayJune2013-01234020.SPEC.pdf

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C A R I B B E A N E X A M I N A T I O N S C O U N C I L

CARIBBEAN SECONDARY EDUCATION CERTIFICATE

EXAMINATION

FILL IN ALL THE INFORMATION REQUESTED CLEARLY IN CAPITAL LETTERS.

TEST CODE

SUBJECT MATHEMATICS Paper 02

PROFICIENCY GENERAL

REGISTRATION NUMBER

SCHOOL/CENTRE NUMBER

NAME OF SCHOOL/CENTRE

CANDIDATES FULL NAME (FIRST, MIDDLE, LAST)

DATE OF BIRTH D D M M Y Y Y Y

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TEST CODE01234020

FORM TP 01234020/SPEC 2013

C A R I B B E A N E X A M I N A T I O N S C O U N C I L

CARIBBEAN SECONDARY EDUCATION CERTIFICATE

EXAMINATION

MATHEMATICS

SPECIMEN PAPER E-MARKING

Paper 02 General Prociency

2 hours 40 minutes

INSTRUCTIONS TO CANDIDATES

1. Answer ALL questions in Section I, and ANY TWO in Section II.

2. Draw diagrams in HB2 pencil, but use black or dark-blue ink pen for all other

writing.

3. You must answer the questions in the spaces provided. Answers written in the

margins or on blank pages will not be marked.

4. All working must be shown clearly.

5. A list of formulae is provided on page 2 of this booklet.

6. If you need to re-write any answer and there is not enough space to do so on the

original page, you must request extra lined pages from the invigilator. Remember

to draw a line through your original answer and correctly number your new

answer in the box provided.

7. If you use extra pages you MUST write your registration number and question

number clearly in the boxes provided at the top of EVERY extra page.

Required Examination Materials

Electronic calculator (non-programmable)

Geometry set

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

Copyright 2012 Caribbean Examinations Council.All rights reserved.

01234020/SPEC 2013/E-MARKING


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GO ON TO THE NEXT PAGE


Page 2

LIST OF FORMULAE

Volume of a prism V = AhwhereAis the area of a cross-section and his the perpendicular

length.

Volume of cylinder V= r2hwhere ris the radius of the base and his the perpendicular height.

Volume of a right pyramid V = AhwhereAis the area of the base and his the perpendicular height.

Circumference C= 2rwhere ris the radius of the circle.

Area of a circle A= r2 where ris the radius of the circle.

Area of trapezium A= (a+ b) hwhere aand bare the lengths of the parallel sides and his

the perpendicular distance between the parallel sides.

Roots of quadratic equations If ax2 + bx + c = 0,

then x =2

4

2

b b ac

a

+

Trigonometric ratios sin =

cos =

tan =

Area of triangle Area of = bhwhere b is the length of the base and his the

perpendicular height

Area of ABC = ab sinC

Area of ABC = ( ) ( )( )s s a s b s c

wheres =

Sine rule = =

Cosine rule a2 = b2 + c2 2bccosA

1

3

a

sinA

b

sinB

c

sin C

opposite side

hypotenuse

adjacent side

hypotenuse

opposite side

adjacent side

1

2

1

2

1

2

a+ b+ c

2

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Page 3

SECTION I

Answer ALL the questions in this section.

All working must be clearly shown.

1. (a) Determine the EXACT value of:

(i)

(3 marks)

(ii) 2.52

giving your answer to 2 signicant gures.

(3 marks)

1

4

1

22

5

2

5

3

4

2.89

17


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Page 4

(b) Mrs. Jack bought 150 T-shirts for $1 920 from a factory.

(i) Calculate the cost of ONE T-shirt.

(1 mark)

The T-shirts are sold at $19.99 each.

(ii) Calculate the amount of money Mrs. Jack received after selling ALL the T-shirts.

(1 mark)

(iii) Calculate the TOTAL prot made.

(1 mark)

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(iv) Calculate the prot made as a percentage of the cost price, giving your answer

correct to the nearest whole number.

(2 marks)

Total 11 marks

2. (a) Given thata= 1, b= 2 and c = 3, nd the value of:

(i) a + b+ c

(1 mark)

(ii) b2 c2

(1 mark)


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Page 6

(b) Write the following phrases as algebraic expressions:

(i) seven times the sum ofxandy

(1 mark)

(ii) the product of TWO consecutive numbers when the smaller number isy

(1 mark)

(c) Solve the pair of simultaneous equations:

2x+y= 7 and x 2y= 1

(3 marks)

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(d) Factorise completely:

(i) 4y2 z2

(1 mark)

(ii) 2ax 2ay bx + by

(2 marks)

(iii) 3x2 + 10x 8

(2 marks)

Total 12 marks


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Page 8

3. (a) A survey was conducted among 40 tourists. The results were:

28 visited Antigua (A)

30 visited Barbados (B)

3x visited both Antigua and Barbados x visited neither Antigua nor Barbados

(i) Complete the Venn diagram below to represent the information given above.

x

A B

U

(2 marks)

(ii) Write an expression, in x, to represent the TOTAL number of tourists in the

survey.

(2 marks)

(iii) Calculate the value ofx.

(2 marks)

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Page 9

(b) The diagram below,not drawn to scale, shows a wooden toy in the shape of a prism,

with cross sectionABCDE. Fis the midpoint ofEC,and BAE= CBA= 90.

A B

CE F

D

6 cm

5 cm 5 cm

5 cm

10 cm

Calculate

(i) the length ofEF

(1 mark)

(ii) the length ofDF

(2 marks)

(iii) the area of the faceABCDE.

(3 marks)

Total 12 marks


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Page 10


01234029/PT 2012

4. (a) Wheny varies directly as the square ofx, the variation equation is writteny= kx2, where

kis a constant.

(i) Given thaty= 50 whenx= 10, nd the value of k.

(2 marks)

(ii) Calculate the value ofywhenx= 30.

(2 marks)

(b) (i) Using a ruler, a pencil and a pair of compasses, construct triangleEFGwith

EG= 6 cm, FEG= 60 andEGF= 90. Draw the triangle on the followingpage. (5 marks)

(ii) Measure and state

a) the length ofEF

(1 mark)

b) the size of EFG

(1 mark)

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Page 11


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5. (a) The diagram below shows the graph ofy=x2+ 2x 3 for the domain 4 x 2.

-4 -3 -2 -1

-1

1

2

3

4

5

y

x

-2

-3

-4

0 1 2

y= x2+ 2x- 3

Use the graph to determine

(i) the scale used on thexaxis

(1 mark)

(ii) the value ofyfor whichx= 1.5

(2 marks)

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(iii) the values ofxfor whichy= 0

(2 marks)

(iv) the range of values ofy, giving your answers in the form ay b, where aand

bare real numbers.

(2 marks)


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Page 14

(b) The functionsfandgare dened asf(x) = 2x 5 andg(x) =x2+ 3.

(i) Calculate the value of

a) f(4)

(1 mark)

b) gf(4)

(2 marks)

c) Findf 1(x).

(2 marks)

Total 12 marks

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6. (a) The diagram below,not drawn to scale, shows two straight lines,PQ andRS, intersecting

a pair of parallel lines, TUand VW.

115

54

x

y

T

R P

U

W

S

V

Q

Determine, giving a reason for EACH of your answers, the value of

(i) x

(2 marks)

(ii) y.

(2 marks)


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(b) The diagram below shows triangleLMN, and its image, triangleLMN, after undergoing

a rotation.

-3 -2 -1

3

2

1

0 1 2 3

y

L

MN

x

M

N

L

(i) Describe the rotation FULLY by stating

a) the centre

(1 mark)

b) the angle

(1 mark)

c) the direction.

(1 mark)

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(ii) State TWO geometric relationships between triangleLMNand its image, triangle

LMN.

(2 marks)

(iii) TriangleLMNis translated by the vector1

-2

.

Determine the coordinates of the image of the pointL under this transformation.

(2 marks)

Total 11 marks


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Page 18

7. A class of 24 students threw the cricket ball at sports. The distance thrown by each student was

measured to the nearest metre. The results are shown below.

22 50 35 52 47 30

48 34 45 23 43 40

55 29 46 56 43 59

36 63 54 32 49 60

(a) Complete the frequency table for the data shown above.

Distance (m) Frequency

20 29 3

30 39 5

(3 marks)

(b) State the lower boundary for the class interval 20 29.

(1 mark)

(c) Determine the probability that a student, chosen at random, threw the ball a distance

recorded as 50 metres or more.

(2 marks)

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(d) Using a scale of 1 cm on thex-axis to represent 5 metres, and a scale of 1 cm on the

y-axis to represent 1 student, draw a histogram to illustrate the data.

(5 marks)

Total 11 marks


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Page 20

8. The diagram below shows the rst three gures in a sequence of gures. Each gure is made

up of squares of side 1 cm.

Fig. 1 Fig. 2 Fig. 3

(a) On the grid below, draw the FOURTH gure (Fig. 4) in the sequence.

(2 marks)

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(b) Study the patterns in the table shown below, and complete the table by inserting the

appropriate values in the rows numbered (i), (ii), (iii) and (iv).

Area of Perimeter Figure Figure of Figure

(cm2) (cm)

1 1 1 6 2 = 4

2 4 2 6 2 = 10

3 9 3 6 2 = 16

(i) 4

(ii) 5

(iii) 15

(iv) n

(8 marks)

Total 10 marks


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Page 22

SECTION II

Answer TWO questions in this section.

ALGEBRA AND RELATIONS, FUNCTIONS AND GRAPHS

9. (a) The diagram below shows the speed-time graph of the motion of an athlete during a

race.

(i) Using the graph, determine

a) the MAXIMUMspeed

(1 mark)

b) the number of seconds for which the speed was constant

(1 mark)

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Time in seconds

Speed

in m/s

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c) the TOTAL distance covered by the athlete during the race.

(2 marks)

(ii) During which time-period of the race was

a) the speed of the athlete increasing

(1 mark)

b) the speed of the athlete decreasing

(1 mark)

c) the acceleration of the athlete zero?

(1 mark)


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Page 24

(b) A farmer supplies his neighbours withxpumpkins andymelons daily, using the following

conditions:

First condition : y 3

Second condition : yx Third condition : the total number of pumpkins and melons must not exceed 12.

(i) Write an inequality to represent the THIRD condition.

(1 mark)

(ii) Using a scale of 1 cm to represent one pumpkin on thex-axis and 1 cm to

represent one melonon they-axis, draw the graphs of the lines associated with

the THREE inequalities. Use the graph paper on the following page.

(4 marks)

(iii) Identify, by shading, the region on your graph which satises the THREE

inequalities. (1 mark)

(iv) Determine, from your graph, the minimumvalues ofxandywhich satisfy the

conditions.

(2 marks)

Total 15 marks

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MEASUREMENT, GEOMETRY AND TRIGONOMETRY

10. (a) In the diagram below, not drawn to scale,PQis a tangent to the circlePTSR, so that

angleRPQ= 46

angleRQP= 32 and TRQis a straight line.

4632

T

P

R

Q

S

Calculate, giving a reason for EACH step to your answer,

(i) anglePTR

(2 marks)

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Page 27

(ii) angle TPR

(3 marks)

(iii) angle TSR

(2 marks)


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(b) The diagram below, not drawn to scale, shows a vertical agpole, FT, with its foot,

F, on the horizontal plane EFG. ET and GT are wires which support the agpole

in its position. The angle of elevation of Tfrom G is 55,EF = 8 m,FG = 6 m and

EFG= 120.

E G

F

T

8 m 6 m

120

55

Calculate, giving your answer correct to 3 signicant gures

(i) the height,FT, of the agpole

(2 marks)

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(ii) the length ofEG

(3 marks)

(iii) the angle of elevation ofTfromE.

(3 marks)

Total 15 marks


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Page 30

VECTORS AND MATRICES

11. (a) A and Bare two 2 2 matrices such that

A = 1 22 5

and B = 5 22 1

(i) Find AB.

(2 marks)

(ii) Determine B 1, the inverse of B.

(1 mark)

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(iii) Given that

25 2

2 1 3

x

y

=

,

writex

y

as the product of TWO matrices.

(2 marks)

(iv) Hence, calculate the values ofxandy.

(2 marks)


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Page 32

(b) The diagram below, not drawn to scale, shows triangleJKL.

J

K

L

MandN are points onJK andJL respectively, such that

JM = JK and JN = JL.

(i) On the diagram above show the pointsMandN.

(2 marks)

(ii) Given thatJM = u andJN =v,

write, in terms ofuandv,an expression for

a) JK

(1 mark)

b) MN

(1 mark)

c) KL

(2 marks)

1

3

1

3

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(iii) Using your ndings in (b) (ii), deduce TWO geometrical relationships between

KLandMN.

(2 marks)

Total 15 marks

END OF TEST


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CANDIDATES RECEIPT

INSTRUCTIONS TO CANDIDATE:

1. Fill in all the information requested clearly in capital letters.

TEST CODE: 0 1 2 3 4 0 2 0

SUBJECT: MATHEMATICS Paper 02

PROFICIENCY: GENERAL

REGISTRATION NUMBER:

FULL NAME: ________________________________________________________________

(BLOCK LETTERS)

Signature: ____________________________________________________________________

Date: ________________________________________________________________________

2. Ensure that this slip is detached by the Supervisor or Invigilator and given to you when you

hand in this booklet.

3. Keep it in a safe place until you have received your results.

INSTRUCTION TO SUPERVISOR/INVIGILATOR:

Sign the declaration below, detach this slip and hand it to the candidate as his/her receipt for this booklet

collected by you.

I hereby acknowledge receipt of the candidates booklet for the examination stated above.

Signature: _____________________________

Supervisor/Invigilator

Date: _________________________________

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