kranji sec 4 mid term

8/10/2019 Kranji Sec 4 Mid Term

1/6

KRANJI

SE,CONDARY SCHOOL

ii'

.'

MID

YEAR

EXAMINATION

2OO8

ADDITIO

NAL

MATHEMATI

CS

40381r

'.

:..

".'

,-

r..'t.

.,

.,''''.'

I cvel

Scconrla

11 Four

Express

Duration

:

2

hour

Date : 7May2008

INSTRUCTIONS

TO

CANDIDATES

Write

your

name,

Centre

number

and candidate

number

in

the

spaces

provlded

on

the

answer

paper/answer

booklet.

Answer

all

the

questions-

Write

your

answers on the

separate answer

paper

provided-

lf

you

use

more

than one

sheet

of

paper,

fasten

all the

answer sheets

together-

All

working

must

be shown

clearly.

Give

non-exact

numerical answers

to

3 significant

figures,

or

1

decimal

place

in

the

case

of

angles

in degrees,

unless

a different

level

of accuracy

is

specified

in

the

{:luestion-

TNFORMATION

FOR

CANDIDATES

-Ihe

number

of

marks is

given

in

brackets

[ ]

at the end

of each

question

or

part question-

Ihe

total

number

of marks

for this

paper

is 80.

l'lilent

electronic

calculators

may

be

used

to evaluate

explicit

numericalexpressions

except

in

iilrestions

where tl-reir

use is

expressly

prohibited.

i\Itlrn

i\,'Iah/

N'lr'l-eh

YY

N:rmc

{llass

Secondary

fl-urn

over

fhis

qtrestit)n p..rlre r

consists

ot'

-5

ltrintccl

p:rges.


2/6

Binomiol

Theorem

(a

+

bl

:

a,

+{i)*,,.{i)"-*

where

n

is a

positive

inreger

and

/" )

:

,

n

,

-

'-'-"-

\,/

(n

-

r)rt"

Ouadratic

Equotion

Forthe

equation

ax'

+

bx +

c

:

A,

Identities

F-ornnrlae.for

\ABC

Matltematical

Formalae

I.

ALGEBRA

-[-r

.

.(:)"'-"b'

+...*

b'

,

2.

TRIGONOMETRY

sin2

A.*"or2

A:l

"""2

A:l+tzn2

A

cosec2A:l+cotZ

A

sin(rl

*

B):

sin

lcos,B

*

coslsin.B

"ot

(e

*

^A):

cos

I

cos

B+sin

Asin

B

tan(ArB)=

-

tanA*

B

'

I

+

tanAtanB

sinZA

-

2sin

Acos

A

coszA:

cos'

I

-sin'

A

:zcos,

A

-l:l

-

2sin2

tan2A

-

2tan

A

l-lernz

A

sin

,{

+

sin.B

:

zsin

(,{

+

r;cos}1

A

-

B)

2'

2

sinl

-sinB

:

z.or (A+

Bysin]1

A

-

B)

2'2

cosl

+

cosB:

z"orl{,1+

B)cos

lfn

-

ol

2'

2

cosl

-cosr

=

-2stur

lU

*B)sin

lU

-

ul

2'

2

sin

I

sin

B

sin

C'

az

:

b,'

+

c'

-

Zbccos

A.

I

A:

'

bcsin

A.

2


3/6

Given

that

calculator,

Ansrver

all

questions

J".t.fl

:-

I

,-,

rvhere

a and

i

are integers,

find

rvithoutusinga

2+J3

the value

of

a and

of

D.

2.

(a) llthe

line

y

--3x -t

cuts

the

curve

y:

kx(x-l)

at2 distinct

points,

find the

range

ofvalues ofk.

(b)

Fincl

the

range

of

values

ol

k fbr

',vhich

4xz

+ 5x

+

k is

alrrays

positive.

t4l

,)

Find

the

tlistance betrveen

the points

rlrclirrc

v:Lx+2.2

(h)

I)rtii,e rhc

itlenrity

1-:-::_.:

.scc'x+2tan

o['intcrsection

of

the

curve

y

:

a +9

x

and

t4l

r2l

L2l

t21

tll

i3l

tll

t6l

5

A

curve

has

the

equation

r :

3'*

18

,

x

*

4.

x+4

(i)

Obtain

an

expression

for

4

.

giring

your

ansrver

as a

single

fraction.

clx

rii)

Shorv

tttat

Q

is always

negative.

dx

(iii)

Find

the rate

of

change ofy

at

the

instant

when x:5,

if

x

is

decreasing at a

rate

of

2 units per

second"

4-

(i)

Solve

the

equationl2x

-

5l:4.

(ii)

Sketch the

graph

of

y

=lLr

-

5

|

for the range 0


4/6

(a)

cos(2x

-

36")

-

cos50"

:

0,

(b)

5+sinytar;

y:5cos/-

8.

(a)

Find

the

term

independent

of

x

in

the

expansion

"t

(i

-

r"-

)

(b)

In

the

expansion

of

(1+

3-r)"

where

r

is an

integer,

the

surn

of coeflicients

oI.

and

xz

is

630- Evaluate

n.

9.

(a)

Given

that

log,

o:

p,

express

logr(Z4Ulau)

in

terms

ofp.

(b)

Solve the

following equations

(i)

lg(8x2

-l9x

+

20)

:

I

+

lg(.r

-

1)'

,

(ii)

e"

+4e-2':4"

[31

t4l

trl

t rl

L*l

i4l

l0-

A

rectangular

garden

ABCD

is

said

to

be

laid

out

as

shorvn

in

the

diagram

belog.

The

garden

consists

of

a

rectangular lawn

PQRS

surrounded

by

flower

beds.

T'hc

garden

ABCD has

an area

of 1200

m2- The

flower

beds

are

3m

wicle

along

the

sides

pS

and

QR

and 2m along

the

sides

SR

and

PQ.

The

lengths

PQ

andpR

are

x

m

and

y

nr

respectively.

D

{.

(i)

Expressy

in

terms

of

x and

shorv llrat

the zrrea,{

ln2,

of

the

lau,n

IrQRS

is

givcn

bv A:

ll76x

-

4x2

x+6

i4i

(ii)

Given

thatx

vzuies,

tind the

stationan'r,nltre

of ,4

and

deternrinc vvhethcr

this

rs

a

rnaxullllrn

or

nlrnlrnurn

vzrlue-

i7t


5/6

The

table

belorv

shows

experimental

values,

corrected

to one

decimal

place.

of

two

quantities

x

and

ywhich

are

related

by the

equation

I:2

*

t-

:1,

wherep

and g

are

pzq

constants-

It is

believed

that

one

of

the

values

ofy

is

subjected

to an

abnormally

large

error.

(i)

(i

i)

(iii)

Using a

single

sheet

of

graph

paper,

ploty2

against

x

1-

Z.

Use

tlie

graph

tcr

identily

the

abnomral

reading

and

estimate

the

correct

value

ofy,

estimate

the

value

ofp

and q.

End

ofPaner

t3l

[2)

t3l

x

2

J

4

5

v

2.6

3.0

3.5

3_6

3_9


6/6

Secondary

4

Express

Mid

Year

Exam

2008

Paper

I

Answer Key:

-1

--1

i

--1

I

i

-l

I

I

_j

I

r.)

a:175. b

:

100

7a\

x

=

43o

,

173"

,223" ,

353'

2a\

-L

kranji sec 4 mid term

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