CSEC Maths January2006 Paper 2

8/12/2019 CSEC Maths January2006 Paper 2

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TEST COE 01234020

FOR TP 2006017 ANA 2006

C A R IBB AN X A M INA T I O N C ONC IL

CONDARY DCATION CRTIFICAT XAMIATION

MATHMATIC

Pap 0 - Ga Pfcc

2 hs 4 mies

04 JANUARY 2006 a.m.))

INSTRUCTIONS TO CANDIDATS

1 Answer ALL questions in Section I and AN TWO in Section

2 Wrie your answers in the boolet provided

3 Al woring us b sown ceay

4. A is of fouae is provided on page 2 of this boolet

xamao Maa

Eeconic caculaor nonprogr aabe)Geoery seMaheaica tables provided)Graph _er provded)·

D OT R THIS PAG UNTIL YOU AR TOLD TO DO SO

Copyrgh© 20 Caibbe Exainaions Council®Al rights reserved

01234020/ANAR/F 26



1. a)

b)

SECTI I

Answer ALL the questions in this section

A working must be cearly s hown

Usg a calculator or otherwse calculate

)

)

the exact vlue of2

X _4 5

3 I

5 2

correct to 3 sgcat gures the value of 1875 (21

loa of $2 000 was borowed from a ba at % per aum.

Calculate

) the terest o the loa at the ed of the frst yea

) the total amout owg at the ed of the frst year

repaymet of $7 800 was made at the start of the secod year

Calculate

) the out stll outstadg at the start of the secod year

age 3

( 4 marks)

( 3 marks)

( 2 marks)

( 1 mark)

( 1 mark)

v) the terest o the oustadg amout at the e of the secod yea.( 1 mark)

Tota12 marks

GO ON O NEX GE01234020JAAYF 2006



2.

3

Page 4

(a) Given that =2 and = 4 calculate the value of (2 + )(2 ).'

( 2 marks)

(b) Solve the simultaneous equations

5 + 6 = 372- 3 = 4. ( 4 marks)

(c) Factorise completely

(i) 4 25 ( 2 marks)

(ii) 6 9 + 4 - 6 ( 2 marks)

(iii) 3 + 4 4

Totl12 marks

(a) Given the formula= �(u + v)t, express u in erms of v, s and t. ( 3 marks)

( On a certn day, 300 customers visitd a bery at sells bread and cakes

70 customers bought cakes only80 customers bought neither bread nor cakes

2customers bought bread only

customers bought both bread and cesu

(i) U represens the set of customers visiting the bkery on that day B represents theset of customers who bought bread, and represents he set of customers whobought ce. Copy and complee theVenn diagram to illustrate the information

( 3 marks)

(ii) Write an expression in to represent the TOT number of customers whovisited e bery on that day. ( 2 marks)

(iii) Calculate the number of customers who bought bread ONLY ( 3 marks)

Totl marks

G ON TO TH NEXT PAGE



4 (a){ The euato of the e s y 4 + 5.

) tate the graet of ay le that s parallel to l

Page 5

1 mrk)

() etee the euato of the le parallel to l that passes through the pot -. 3 mrks)

(b) An nswer s hee is provided for his ques ion

The agram above shows the postos of three ctes A Ba o the orth coastof Afrc The scale of the map s 1 : 0 0 000.

se your answer sheet when answering the following questions Show all lines andangles used in your alulations

()

iiMeasure an stat cetmees the legth of te le segmet B.

( 2 mrks)

Hece calculate klometres the actual shores stace om Cty B toCy ( 2 mrks)

sg a protractor eterme the bearng of B from A ( 4 mrks)

To12 mrks

GO O TO T XT PAGE0 1340/JAARY 006



Page 6

5. The curved srface are of a cylnder= where r s the rds and s the heght and thesufce e of sphere s 4 r2.

. .

. .

. : . . . :

· .

The dagram above not drawn to scale, shows a solid glass paperweght whch conssts of ahemsphere mounted on a cylnder.

The radus of the hemsphere s 3 cm the radus of the cylnder s 3 cm an ts heght s 8 cm.

(a) Calculate usng = 314,

( b}

() the curved surface area of the cylnder ( 2 marks)

() the surface ea of the hemsphere ( 2 marks)

() the TOT surface area of the solid paperweight ( 2 marks)

Usng a ruler a pencl d a par of compasses consuct the parlelogram KMN, nwhch K = 8 cm KN = 6 cm and L KN = 60° ( 5 marks)

Total marks

GO O TO E EX PAGE01234020/JANARY/F 2006



Page 7

6. A as wer s heet s rovded for ts questo

The diaram below shows quadrlateral QRS, and ts mage, quadrilateral 'Q R'S' aer thas been rotated.

(a

) (b

c

tate he cordates of the ponts R and ' 2 marks

Descbe the otaton completely 3 marks

On he answer sheet povded dr� a d lael drlat 1 QS"whch s themage oQKS after ha been reected•n t x-as 3 marks

( ) Descrbe completely the sngle tansfomaton that mas quadrlateral QRS onto Q R S 2 marks

Tota tO marks

GO ON O HE XT AGE0234020YF 2006



Page 8

7 The data beow e the engths to the neaest centimee, o e ight ft of he 5 students ina cass

14

1516161

18

18 18

19

19

0

01

3

4

25 5627

(a) Copy d compete te foowing gouped equency tabe fo the data aboe

gh of gh Foo Fucy(cm)

14 - 16 4

17 - 19

0 - 8

5

6 - 8

( 2 mak)

State the owe bounday of te cass intea 4 16. ( 1 mak)

(c) Sate the wid of e cass inea 0 - ( 1 mak)

(d) A students igt foot measued 68 cm State the cass inte in wich this ength

(e)

woud ie ( 1 mak )

A student was chosen at do om e goup d e ength of is ight foot wasmeasue Ccuate pobabiit at the ength was GREATER o EQUto 0 cm ( 2 mak)

State e mod ength of a studen s ight foot ( 1mak)•

Cacuate estimate of the mean ength of a students ight foot using the idpoints ofthe cass inas in (a) aboe ( 3 mak)

Toal mak

GO ON TO EXT PAGE013400/JY/ 6



Page

8 The path of a ba thrown in the air is gien by the equation = 20 - 5 where is theertica distance aboe the ground in mees) and is the time in seconds) after the ba wasthrown

The tabe beow shos some aues of and the cresponding aues of correct to 1 decima pace

a)

0 0.5 1 15 2 25 3 3.5

h 00 88 15 188 18.8 88 00

Copy d compete e tabe of aues ( 2 maks)

Draw te graph of 20 - 5 for 0 � � 4 You may proceed as foows

i) Using a sce of 2 cm to represent 05 seconds draw the horizonta axis for0 � � 4 ( 1 mak )

ii) Using a scae of 1 cm to represen 1 mee draw the ertica axis for

iii)

i)

00 � � 210 ( 1 mak)

Pot the points from your tabe of aues on the axes awn ( 2 maks)

Join the points with a smooth cure ( 1 mak )

_c) Using your graph cacuate estimates o

i) te EATEST height aboe the groun reached by the b ( 1 mak)

ii) the number of seconds for which the b was MOE than 12 mees aboe the

iii)

ground ( 2 maks)

the inra of time during which the a was moing upwrds ( 1 mak)

Tol maks

GO ON TO T PAGE01234020/JAY/F 26



9. (a)

SECTION II

Answer TWO questions in this section

ALEBRA AND REAONS, FUNCTINSAND GAPHS

Solve th air o simultaneous equations

2 + y =7 x2 - = 6.

Page 10

6 marks)

(b) Express 4x2 12 3 in the orm a x + ) 2 + k, wher , d k e real numbers

(c) Using your answer rom (b) above, or oherwise caculate

(i) he minimum value o 4x2 12 - 3

ii) he value of x or wich he minimum occurs

( 3 mrk)

( mark)

( 1 mark)

(iii) the values o x for which 4x2 12 3 = 0 expressing your answers to 3signican gures 4 marks)

otal marks



10 (a)

)

Page 11

A shop stocks x ix and Zent adios It ha shel space fo up to 20 adios

(i) Wite a inequaliy to epesent this infomation ( 1 mark)

The owne of the shop spends $150 to puchase each onix adio and $300 fo eachZent adio she has $4 500 to spend on the puchase of these adios

(ii) Wite an inequality to epesent this infomation ( 1 mark)

The owne of the shop decides to stock at least 6 onix and at least 6 Zent adios

(iii) Wite TWO inequalities to epesent this infomation ( 2 marks)

(i) Using a sce of 2 cm to epesent 5 nix adios and 2 cm to epesent5 Zent adios daw the hoizontal axis fo 0 : x : 30 and the veical axis

fo 0 : : 25. ( 1 mark)

(ii) On these axes, daw he fou bound lines fo the fou inequalities witen in(a) (i) (ii) and (iii) above ( 4 marks)

(iii) hade the egion on you gaph that satisies fou of the inequalities witten

(iv)

in (a) (i (ii ad (iii) above ( 1 mark)

tate the coodinates of the vetices of the shaded egion ( 2 marks)

(c) The owne of the shop sells the adios to make a pot of $80 on ach onix and $00

on each Zent adio

(i) Expess the TOT pot in tems of x and . ( 1 mark)

(ii) Calculate the MIMUM pot ( 2 maks)

Totl s�



11.

age 12

GEOMERY AN RIGONOMERY

B

In the diagram above no drawn o scale, 0 is the centre of the circle, L O = 130°L DE = 30°, and EC and ED are chords of the circe

·

(a) Calculate the size of EACH of the following anges, giving reaons for EACH step ofyour answers.

(i) L C ( 2 marks)

(ii) CD ( 2 m arks)

(iii) L ED ( 2 marks)

) Show that MCE and DE are similr ( 3 marks)

(c) Give that CE = 6 cm E= 9.1 cm and DE= 5cm,

(i) calcuate the ength of E 3 marks)

(ii) calcuate correct to 1 decim pace the rea of ED ( 3 marks)

Total IS ma rks

GO ON TO T X PAGE 01234020/JAARY/F 2006



Page 14

VECTORS AN MATRICES

13. The points (1 2) B (5, 2) C (6, 4) and D (2, 4) are the vertices of a quadriateral BCD

(a) Express in the form (�) �

(i) the position vectors O, B OC and OD where 0 is the origin (0 0)

(ii)

the vectos B and DC.

( 2 marks)

( 2 marks)

( Calclate j.jand hence deteine the nit vector in the direction ofd

(c) Using the answers in (a) (ii)

( 2 marks)

(i) state TWO geometrica relationships btween the line segments B and DC

( 2 marks)

(ii) explain why BCD is a paralelogam. ( 2 marks)

(d) Using a vector method determine the position tor of G, te midpoint of the line C.

Hence state the coordinates of the point of intersection of the diagonals C and BD

of paallelogram BCD ( 5 marks)

Totl IS marks

GO ON TO E XT PAE01234020/JAARY/F 26



14 (a The matrix = (� �) .(i Calclate, in terms of the determinant of .

(ii Calclate the values of given that is singl.

Page 5

3 mark)

The matrix M = ( ! ) .

(i Find �, the inverse o M.

(ii Hence, calculate the vlue o x ad of y or which M ( ) = ( )

( 6 mark)

c The image (' y', of any point, (, y, nde a ansformation is given by the equation

Clculate

i e iage, ' , of (3 - undrN 3 mark)

(ii the coordinates of the point, , y which is apped by onto ( 4).·

3 mark)

TolS mark

E OF TET

CSEC Maths January2006 Paper 2

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