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Total maExam co This paper Section 1 –Questions Attempt Section II Attempt Table of S

on 1

arks – 70 onsists of 1

r consists of

– Page 2-4 1-10 t Question 1

– Pages 5-t questions

Standard In

10 pages.

f TWO secti

(10 marks

1-10

-9 (60 mar 11-14

ntegrals is o

ions.

s)

rks)

on page 10

2

Section I - 10 marks Use the multiple choice answer sheet for question 1-10

1. Thevalueof lim

→

sin 73

is

A 2

B

C 0

D 1

2. Whatistheacuteangle,tothenearestdegree, betweenthelines 7 4 and2 3 6 0.

A 26°

B 48°

C 70°

D 75°

3. Let , and betherootsof2 4 9 0.

Whatisthevalueof

A

B

C

D

4.

5.

6.

7.

Whicho

A

B

C

D

ThecooFindthe

A 2,

B 1

C 3

D 4,

Thenumandend

A

B

C !

!

D !

Theinv

A

B

C

D

ofthefollow

2

2

ordinatesoecoordinat

1 ,

3,2

2

mberofdifdwiththel

!

!

!

!

!

!

versefuncti

3

wingcould

2

2

fthepointstesof tha

fferentarraetterRis:

onof

8

8

bethepoly

s and aatdividesth

angements

where

3

ynomial

are 1,1 aheinterval

ofthelette

√3

and 3, 1 extern

ersofthew

8 is

respectiveallyinther

wordREGI

ely.ratio1: 3.

ISTERwhhichbegin

8.

9.

10

Apossib

A

B

C

D

Themid

A 81

B 216

C 384

D 96

0. If s

A

B √

C

D

bleequatio

1 cos

1 cos 2

cos 2

1 cos 2

ddletermi

6

4

6

in 2 ,t

onforthecu

2

1

ntheexpan

then e

urvedrawn

nsion 2

equals

4

nis:‐

4 is

End of Secction 1

Se AtAnEaAl

Qu

a)

b)

c)

d)

e)

f)

g)

ection II –

ttempt quesnswer eachach piece ofll necessary

uestion 11

Solvefo

Itisgive

Find i

ii

Thegra

Determ

Formthequatio

Solvesi

The radiwhich th

– Extende

stions 11-1h question of paper muy working s

(15 mark

or

enthat

theampli

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minetheval

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n 2 cos

ius of a sphhe volume o

ed Respon

6. on a SEPARust show yoshould be s

ks)

2 cos 3

itude.

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uesof , ,

nequation

0for

erical balloof the balloo

nse

RATE PAGour numberhown in ev

21

, 0

TwocmeetIf

2 1 i

and

byelimina

3 tan

0 2

on is increaon is increas

End o

5

GE. Clearlr. very questio

11

1

2

chordsat .

7cm,

sshown.

atingthepa

n 2

.

asing at the sing when t

of Question

ly indicate

on.

and of

3cm,

arameter,

2 sec

rate of 2cmthe radius is

11

question nu

acircleare

5cmfi

,fromthes

m/sec. Find ts 10cm (in t

umber.

eextended

find .

separamet

the rate at terms of

Mar

3

1

1

to 1

2

tric 2

3

. 2

rks

2

2

2

Qu

a)

b)

c)

d)

e)

uestion 12

Evaluat

Byusing

Twopa

i Cii P

iii P

i Er

ii A

S

Thecoe

Showth

(15 mark

te 2 sin

gthesubst

ralleltange

Copyortra

ProveΔ

Provethat

Expressradians.

Aparticlem2 cos 3

Showthatt

efficientsof

hat 2

ks)

titution

entstoacir

acethediag

≡ Δ

∠ 9

2 cos 3

movesina3 5 sin 3theparticle

f and

0,where

√ ,evalu

rcle,centre

gramintoy

90°.

5 sin 3 i

straightlin3 .eismoving

intheexp

e and ar

End o

6

uate

√

e ,arecut

yoursolutio

ntheform

neanditsp

ginsimple

pansionof

repositive

of Question

byathird

onbooklet.

cos

positionatt

harmonicm

integers.

12

tangentat

.

3 ,w

time isgiv

motion.

arethesa

and .

where isin

venby

ame.

Mar

2

3

2

2

n 2

1

3

rks

2

2

2

2

7

Question 13 (15 marks)

a) In how many ways can a committee of 5 people be formed from a group of 9 people, if 2 people, Harry and Archie, refuse to serve together on the same committee.

2

b) i Showbyasketch,withoutusingcalculus,thattheequation 4 5 0hasonlyoneroot.

ii Showthatthisrootliesbetween0and1.

iii Bytaking 0.5asafirstapproximation,useoneapplicationofNewton’smethodtofindabetterapproximationofthisroottotwodecimalplaces.

1

1

2

c) Aparticlemovesinastraightlinewithvelocity m/sec andaccelerationgivenby2 ,where isthedisplacementfrom .

Theinitialvelocityis 2m/secattheorigin.

i Provethat 4 .

ii Hencefindthedisplacementintermsof .

2

3

d) Whenabodyfalls,therateofchangeofitsvelocity, , isgivenby 500

where isaconstant.

i Showthat 500 500 isapossiblesolutiontothisequation.

ii Thevelocityafter5secondsis21m/sec,findthevalueof to3significantfigures.

iii Findthevelocityafter20seconds.

iv Explaintheeffectonthevelocityas becomeslarge.

1

1

1

1

End of Question 13

Qu

a)

b)

uestion 14

Apartichorizon

i H

ii W

Twopo

i I

ii S

(15 mark

cleisprojecntal.Theeq

30√

Howhighi

Whatisthe

ints and

If hascoo

Showthatt

ks)

ctedwithaquationsof

√2 an

sthepartic

ehorizonta

Qmoveon

ordinates

thelocuso

Q

aninitialvemotionare

d 3

cleafterith

alrangeoft

ntheparabo

, ,sho

22

f isanoth

uestion 14

8

elocityof60e:

30√2 5

hastravelle

theparticle

ola 4

owthatthe

,2 2

herparabo

continues o

0m/sec ata

5 Dono

ed120mho

e?

sothatt

midpoint,

28

la.

on page 6

anangleof

otproveth

orizontally

their valu

,of is

f 45°tothe

hese

y?

uesdifferb

Mar

2

1

y .

2

2

rks

2

2

2

Qu

c)

uestion14

i P

ii T

T

I

iii G

continued

Provebym

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If isthe

Giventhataxisis li

mathematic

rectanglesa

areaofthe

theareabom → , f

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9

on14

anddivideetedasshow

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1

thecurve,e for usi

End of Exam

1

dinto intwn.

hat

1

betweening the resu

m

tervalsbetw

0 andult in part

ween0and

1,andthi .

d1.

he

3

3

2

2

10

STANDARD INTEGRALS

dxx n ,1

1 1

nx

n ;1n ,0x if 0n

dxx

1 ,ln x 0x

dxe ax ,1 axea

0a

axdxcos ,sin1

axa

0a

axdxsin ,cos1

axa

0a

axdx2sec ,tan1

axa

0a

axdxax tansec ,sec1

axa

0a

dx

xa 22

1 ,tan

1 1

a

x

a 0a

dxxa 22

1 ,sin 1

a

x ,0a axa

dxax 22

1 ),ln( 22 axx 0 ax

dxax 22

1 )ln( 22 axx

NOTE: ,logln xx e 0x