CXC Maths May 2007

8/13/2019 CXC Maths May 2007

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FORM TP 200710srEsrcoDE 1234020

MAY/JUNE 2OO7

CI L

LIST OF FORMT,JLAE

Volume of a prism

Volume of cylinder

Volume of a right pyramid

Circumference

Area of a circle

Area oftrapezium

Trigonometric ratios

Sine ule

Cosine ule

0r234020tF2007

CARIBBEAN EXAMINATIONS COUN

SECONDARYEDIJCATION CERTTFICATEEXAMINATION

MATHEMATICS

Paper02 - GeneralProficiency

2 hours 40 minutes

24MAY2fi)7(a.m.)

INSTRUCTIONS TO CAI{DIDATES

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

2. Write your answers in the booklet provided.

3. All working must be shown clearly.

4. A list offormulae is provided on page 2 ofthis booklet.

Examination Materials

Electronic calculator (non-programmable)

Geometry set

Mathematical tables (provided)

Graph paper (provided)

DO NOT TURN THIS PAGETJNTIL YOUARE TOLD TO DO SO.

Copyright @ 2005 Caribbean Examinations Council@.

All rights reserved.

Rootsofquadraticequations lf al + bx + c = 0,

then = -74:9Za

opposite side

sln u =--rtpotenus€

^ adiacent sidecos u =

Ttpotenrrse

oooosile sidehe = ili**Gia"

Area of triangle 6r.uo1 6=)bh

where b is the length of the base and h is the

perpendicular height

Areaof AABC = |atsinC

Areaof MBC = JsG - a)(s - D)(s * c)

wheres = a + b + c.,

V = Ah where A is the area of a cross-section and ft is the perpendicular

length.

V=nfhwhere r is the radius ofthe baseand & s the perpendicular height.

V = ), enwnerer{ is the area of the base and ft is the perpendicular height.

C =2nrwhere r is the radius of the circle.

A = nlwlrcre r is the radius of the circle.

A =|@

+ b) h where a and D are the lengths of the parallel sides and lr is

the perpendicular distance between the parallel sides.

bsinB

a2=b2+P-2bccosA

c

sin C

(t

sin A

Adjaccnt

<_t _-1

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Page3

SECTTON

Answer ALL the questions n this s€ction.

All working must be clearly shown.

'tlsing a calculator, r otherwise, eter mineheexact alueof (3.7)2 (6.24 * 1.3).( 3 marks)

A total of I 200students ttendTop View High School.

The ratio of teacherso students s l:30.

(a)

Page 4

The Venn Diagram below represents information on the type of games played by

members of a youth club. All members of the club play at least one game.

1. (a) ,

o)

(D How many tpachers are there at the school?

Two-fifths ofthe students own personal computers.

(iD How many students do NOT own personal computers?

( 2 marks)

( 2 marks)

( 4 marks)

Total 11 marks

4 marks)

2 marks)

5 marks)

11 marks

Thirty percent of the students who own personal computers also own play stations.

(iiD What fraction of the students in the school own play stations?

Exprcss your answer in its lowest terms,

S represents the set ofmembers who play squash.

T represents the set of members who play tennis.

H represents the set of members who play hockey.

Lro, Mia and Neil are three members of the youth club.

(D $tate what game(s) is/are playedby

a) I,eo

b) Mia

c) Neil

(iD Describe in words the members of the set lf n S. ( 5 marks)

(i) Using a pencil, a ruler and a pair of compassesonly.

a) Construct a triangle PQR in which QR = 8.5 cm, PO = 6 cm andPR = 7.5 cm.

Construct a ine PT such that PT is perpendicular to QR and meets QR at

T.

a) Measureand state hesizeof anglePQR.

b) Measurcand state he ength of PL ( 7 marks)

Total 12 marks

Giventhata*b=ab -

Evaluate

(D 4* 8

( i i ) 2*(4*8) (

Simplify, expressing our answer n its simplest orm

5P . 4p'

i * -n (

A stadium has two sections. A and B.

Tickets for Section A cost $a each.Tickets for Section B cost $b each.

Johanna paid $105 for 5 Section A tickets and 3 Section B tickets.

Raiyah paid $63 for 4 Section A tickets and I Section B ticket.

(i) Write two equationsin a and D to represent the information above.

(ii) Calculate the values of a md b. (

TotaI

a

o)

(c)

(b)

b)

(ii)

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(a). The diagram below shows a map of a golf course drawn on a grid

The scale of the map is l:4{XX).

Page 5

of I cm squares.

Using the map of the golf course, find

(i) the distance, to the nerest rn, from South Gate to East Gate

(iD the distance, to the nearest m, from North Gate to South Gate

(iii) the area on the ground represented by I cm2 on the map

(iv) the actual area ofthe golfcourse, giving the answer in square metres( 6 marks)

The diagrarn below, not drawn to scale, shows a prism of volume 960 cm3. The

cross-s€ction ABCD is a square. The length of the prism is 15 cm.

Calculate

(i) the length of the edge AB, in cm

(iD the total surface area of the prism, in cm2. ( 5 marks)

Total 11 marks

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Page 6

Two variables x and y are related such that 'y varies inversely as the square of.r' .

(a) Write an equation inx,y and&to describe the inverse variation, where &is the constant

of variation. ( 2 marks)

Using the information in the table above, calculate the value

(i) Ic, he constant ofvariation

(ii) r

(i iD f.(6marks)

Deterrninehe equationof the line which is parallelto the ine y = 2x + 3 andpasses

throughthecoordinab(4,7), ( 4marks)

Total 12 marks

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(b)

of

(c)

(b)

Gtte

So

Grrthfe

EastGate

x 3 1. 8 f

v ) r 8

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(a),

Page 7

An answer sheet is pnovided for this question.

Ijluf N' isthe image of LMN under an enlargement.

(i) Write on your answer sheet

a) the scale factor for the enlargement

b) the coordinates ofthe c entre ofthe en largement.

U M" N" is tIre image of 1-ll4Nunder a reflection in the line y = -L

(ii) Draw andlabel thetriangle UM"N" onyouranswer sheet. ( 5rnarks)

Three towns, P, Q and R are such that the bearing ofP from Q is 070'. R is 10 km due

east of Q and PO = 5 km.

(0 Calculate, correct to one decimal place, the distance PR.

(iD Giventhat ZQPR = 142", state the bearing of R from P. ( 6 marks)

Total 11 marks

Page 8

A class of 32 students participated in running a 400 m race in preparation for their sports day.The time, in seconds, taken by each student is recorded below.

83 51 56 58 62 65 61

72 7t 54 62 81 80 78

7r 55 70 54 82 59 7r

83 63 65 72 78 ',13 68

Copy andcomplete he frequency able o representhis data.

Time in seconds Frequency

50-54 J

55-59

60-6/ 6

65 -69

70 74

75 79

80-84

Using the raw scoies, determine the range for the data.

( 2 marks)

( 2 marks)

Using a scale of 2 cm to represent 5 seconds on the horizontal axis and ascale of I cm

to represent I student on the vertical axis, draw a frequency polygon to represent the

data.

NOTE: An empty interval must be shown at each end of the distribution and thepolygon closed. ( 6 marks)

To qualify for the finals, a student must complete the race in less than 60 seconds.

What is the probability that a student rom this class will qualify for the finals?

( 2 marks)

Total 12 marks

64

77

62

75

II

(a)

(b)

(b)

(c)

(d)

t

l

.tv4I

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Paee 9

Rectangle WXYZbelow represents one whole unit which has been divided into seven smaller

parts. These parts are labelled A, B, C, D, E, F and G.

Copy and complete the following table, stating what fraction of t}re rectangle eachpa4 represents.

Write the parts in order of the size of their perimeters.

( 5 marks)

( 2 marks)

The area of G is 2 square units. E, F and G are rearranged to form a trapezium.

(i) What i s the area of the trapezium in square units?

(ii) Sketch the trapezium clearly showing the outline ofeach ofthe three parts.

( 3 marks)

Total 10 marks

Page 0

SECTION II

Answer TWO questions n this section.

RELATIONS. FT,]NCTIONSAND GRAPHS

(a) Given that g(r) = andf l. r)=1a4.

(i) Calculate the value ofg (-2).

(iD Write an expression for g(.r) in its simplest form.

(iii) Find the inverse tunction g-l(.t). ( 7 marks)

The length of the rectangle below is (2x - l) cm and its width is ("r+ 3) cm.

Write an expression in the form ar2 + bx + c for the area of the rectangle.

Given that the area ofthe rectangle is 294 cm2, determine the value ofx.

Hence, state the dimensions of the rectangle, in centimetres. ( 8 marks)

Total 15 marks

2x+l:

f

(b)(a)

(i )

(ii)

(iiD

o)(c)

(2r- r)

Part Fraction

A

B

CI

%

D

E

F

GI

18

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(a)2.

Page 13

The figurebelow, notdrawn to scale, s aregularorstagonwith centreX, andXf = 6 cm.

Calculate

(D tlrcsizeof angleYXZ

(ii) the areaofthe triangle .

(iiD the areaofthe octagon.

lXZ, expressing your answer conect to one decimal place

Page 14

VECTORS AND MATRICFS

4.

OK andOM xe positionvectorssuch hat OK = &andOM = a.

(a) Sketch he diagramabove.Show he approximate ositionsof pointsR andSsuch hat

R is the mid-point of OK

S s apoint on oM such h"t A =+

oi.

(b) Write down, n termsof &and41 hevectors

+(D MK

)(ii) RM

--+(iii) rs

--)(iv) RS.

( 2 msrks)

( I marks)

L is the mid-point of RM. Usinga vector method, prove hat RS s parallel o Kr.( 5 narks)

Total 15 marks

13.

(b)

( 6 marks)

thepoint,T.n the diagram below, not drawn to scale, ZM is a tangent to the circle atO is the centre of the circle and ar,leleAvITS = 23" .

Calculdte the size of each of the following angles, giving reasons for your answer

a) mgleTPQ

b) angle MTQ

c) angleTQS

d) angle,SRQ.

(c)

( 9marks)

Total 15 marks

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,) /s s\ /r+ o\ |,J '"=[, z) 'MC=l-o s) ' I4.

(aA, B and Carethree 2 x 2matices such hat A = I

tc

Describe in words, the geometric transformations

a) "/which mapsEFGfl onlo EFG'E

b) Kwhich maps EFG E onto YI{G"H'.

Write the matrix which represents the transformation described above as

a) J

b) K

The point P (Q, 2) is mapped onto P by the transformation J. State theco-ordinates of P'.

The point Q 6, -4) is mapped o to g by the transformation K. State the

co-ordinates of Q'. ( Emarks)

Total 15 marksENDOFTEST

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rESrcoDE 1234020

FORMTP 2007105 MAY/JUNE2OO7

CARIBBEAN EXAMINATIONS COUNCIL

SECONDARY EDUCATION CERTIFICATE

EXAMINATION

MATHEMATICS

Paper02 - GeneralProficiencY

Answer Sheet for Question 6 (a) Candidate Number .....................'-.........

(a) (D Scale actor for the enlargement

Co-ordinates of the centre of the enlargement

ATTACH THIS ANSWERSHEETTO YOURANSWER BOOKLET

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Page 15

( 7 marks)

its imagesafter undergoingb)

Find

(i) 34

(ii) Fl

(iii) 3A + Ft

( iv) thevalueof a,b,.canddgiventhat3,4 +Ft =C .

The diagram below shows a parallelogram EFGH and

two successive transformations.

(i)

(ii)

(iii)

(iv)

. t

CXC Maths May 2007

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