TESTCODE2014F4T2P2FORMTP2014F4T2P2 Term22013/14

NAPARIMACOLLEGEENDOFTERM2EXAMINATIONS

MATHEMATICSForm4Paper022hours

ExaminationMaterialsProvidedbycandidateElectroniccalculatornonprogrammableGeometrysetGraphpaper

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INSTRUCTIONSTOCANDIDATES1. ThistestconsistsofEIGHT8questions.2. AnswerALLquestions.3. Writeyouranswersonyourownpaper.4. Allworkingmustbeshownclearly

MARCH2013(a.m.)

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LISTOFFORMULAEVolumeofaprism , where A is the area of crosssection and is the

perpendicularlength.

Volumeofacylinder , where is the radius of the base and is is theperpendicularheight.

Volumeofarightpyramid , where is the area of the base and is is theperpendicularheight.

Circumference 2,where istheradiusofthecircle.

Areaofacircle ,where istheradiusofthecircle.

Areaofatrapezium ,where a andb are the lengths of the parallelsidesandhistheperpendiculardistancebetweentheparallelsides.

Rootsofquadraticequations If 0then

Trigonometricratios sin cos tan

Areaofatriangle Areaof ,wherebisthelengthofthebaseandhistheperpendicularheightAreaof sin Areaof where

Sinerule

Cosinerule 2 cos

OppositeHypotenuse

Adjacent

b

h

C

B A

a b

c

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SECTION1AnswerALLquestionsinthissection.Allworkingmustbeclearlyshown.

1. aUsingacalculator,orotherwise,calculate

i theexactvalueof

4

ii correctto3significantfigures,thevalueof18.75 2.11 3b Aloanof$12000wasborrowedfromabankat14%perannum.

Calculatei theinterestontheloanattheendofthefirstyear 2ii thetotalamountowingattheendofthefirstyear. 1

Arepaymentof$7800wasmadeatthestartofthesecondyear.Calculate

iii theamountstilloutstandingatthestartofthesecondyear 1iv theinterestontheoutstandingamountattheendofthesecondyear. 1

Total12marks2.aGiventhat 2and 4,calculatethevalueof2 2 . 2

b Solvethesimultaneousequations 45 6 372 3 4.

c Factorisecompletelyi 4 25 2ii 6 9 4 6 2iii 3 4 4 2

Total12marks3. aGiventheformula ,expressuintermsof,,and. 3b Onacertainday,300customersvisitedabakerythatsellsbreadandcakes.

70customersboughtcakesonly80customersboughtneitherbreadnorcakes2customersboughtbreadonlycustomersboughtbothbreadandcakes

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i Urepresentsthesetofcustomersvisitingthebakeryonthatday,Brepresentsthesetofcustomerswhoboughtbread,andCrepresentsthesetofcustomerswhoboughtcake.CopyandcompletetheVenndiagramtoillustratetheinformation.3

ii Write an expression in to represent the TOTAL number of customers whovisitedthebakeryonthatday. 2

iii CalculatethenumberofcustomerswhoboughtbreadONLY. 3Total11marks

4. aThearrowdiagramshownbelowrepresentstherelation: ,where 3, 4, 5, 6, 7, 8, 9, 10

Calculatethevalueofi 2ii 3 2iii when 95 2

b Avertical stickofheight1.8mcastsa shadowof length2mon thehorizontal asshowninthediagrambelow,notdrawntoscale.

Calculate,totheNEARESTdegree,theangleofelevationofthesun. 4c Theequationofthelineis 4 5.

i Statethegradientofanylinethatisparallelto. 1ii Determine the equation of the line parallel to that passes through the point

2, 6. 3Total14marks

5. Thedata beloware the lengths, to the nearest centimetre, of the right foot of the 25studentsinaclass.

14 15 16 16 1718 18 18 19 1920 20 21 22 2222 22 22 23 2324 25 25 26 27

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a Copyandcompletethefollowinggroupedfrequencytableforthedataabove.2LengthofRightFoot

cm Frequency1416 41719 ___2022 8________ 52628 2

b Astudent'srightfootmeasured16.8cm.Statetheclassintervalinwhichthislengthwouldlie. 1

c Calculateanestimateofthemeanlengthofastudent'srightfootusingthemidpointsoftheclassintervalsinaabove. 3

d Constructahistogramtorepresentthedatainaabove. 5Total11marks

6. Ananswersheetisprovidedforthisquestion.Theanswersheetshowsarectangle,A,ofarea20squareunitsandperimeter24units.

Usetheinformationbelowtocompletethetableontheanswersheet,whichshowsthelength,width,areaandperimeterofrectanglesB,C,DandE.a Onyouranswersheet,

i drawandlabela rectangleBofarea27squareunitsandperimeter24unitsb rectangleCofarea32squareunitsandperimeter24units.

4ii CompletethetabletoshowthedimensionsofrectanglesBandC,drawnatai

above. 2b RectangleDhasaperimeterof24cm,withlength,,andwidth,.Iftheareaofthe

rectangleDistobeaslargeaspossible,determinethevaluesofand.Inthetable,writethevaluesof,andtheareaofrectangleD. 2

c Rectangle E has a perimeter of 36 cm, length,, and width, . If the area of therectangleEistobeaslargeaspossible,determinethevaluesofand.Inthetable,writethevaluesof,andtheareaoftherectangleE. 2

Total10marks

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SECTION2AnswerALLquestionsinthissection.Allworkingmustbeclearlyshown.

7. AboatleavesadockatpointAandtravelsforadistanceof15kmtopointBonabearingof135.Theboatthenchangescourseandtravelsforadistanceof8kmtopointConabearingof060.a Illustratetheaboveinformationinaclearlylabelleddiagram. 2

Thediagramshouldshowthei northdirection 1ii bearings135and060 2iii distances8kmand15km. 2

b Calculatei thedistanceAC 3ii BCA 3iii thebearingofAfromC. 2

Total15marks8. aTherelationshipbetweenkineticenergy,,mass,,andvelocity,,foramoving

particleis 12

i Expressintermsofand. 3ii Determinethevalueofwhen45and13 2

b Given 3 8 2,i writeintheform ,where,and . 3ii solvetheequation 0,writingyouranswerscorrectto2decimal

places. 4iii Asketchofthegraphofisshownbelow.

Copythesketchandstatea thecoordinateofAb thecoordinateofCc theandcoordinatesofB. 3

Total15marksENDOFTEST

IFYOUFINISHBEFORETIMEISCALLED,CHECKYOURWORKONTHISTEST.

MARCH 2014

NAPARIMA COLLEGE

END OF TERM 2 EXAMINATIONS

MATHEMATICS

Paper 02 Answer Sheet for Question 6 Student Name ........................ ..........

:A

I

!

I Rectangle Length Width Area Perimeter

(square units) (units)

A 10 2 20 24

B 27 24

c 32 24

D 24

E 36

ATTACH THIS ANSWER SHEET TO YOUR ANSWER BOOKLET

Cover Sheet P2 MathsE2 Form 4 Term 2 2013-14Pages from CSEC Maths January2011 Paper 2