add maths form 5 paper 1 midterm 2012

8/11/2019 Add Maths Form 5 Paper 1 Midterm 2012

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STUDENTS NAME: __________________________ CLASS:

MID YEAR EXAMINATION

2012

ADDITIONAL MATHEMATICS

PAPER 1

SENIOR 5

TWO HOURS

Instructions to candidate:

DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO

1. This question paper consists of 25 questions.

2. Answer ALL questions.

3. Show your working. It may help you to get marks.

4. The diagrams in the question are not drawn to scale unless stated.

5. You may use a nonprogrammable scientific calculator.

SEKOLAH SERI

CAHAYA(Kayangan Heights)

Lot 5, Jalan Merah Saga, U9/5,

40250 Shah Alam, Selangor.

Tel: +603 7846 3985

Fax: +603 7846 3980

Careline: 1-300-88-REAL(7325)www.real.edu.my

This question paper consists of 15 printed pages.


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The following formulae may be helpful in answering the questions. The symbols given are the onescommonly used.

ALGEBRA

1

24

2

b b ac

x a

2 am an= a m + n

3 am an= a m - n

4 (am)

n=a

nm

5 logamn= log am + logan

6 logan

m = log am - logan

7 log amn = nlog am

8 logab =a

b

c

c

log

log

9 Tn= a + (n-1)d

10 Sn= ])1(2[2

dnan

11 Tn= arn-1

12 Sn=r

ra

r

ra nn

1

)1(

1

)1(, (r 1)

13

r

aS

1

, r


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STATISTICS

1 x =N

x

2 x =

f

fx

3 =N

xx 2)(=

2_2

xN

x

4 =

f

xxf 2)(=

22

xf

fx

5 m = Cf

FN

Lm

2

1

6 1

0

100Q

IQ

71

11

w

IwI

8)!(

!

rn

nPrn

9!)!(

!

rrn

nCr

n

10 P (AB) = P (A) +P (B) - P (AB)

11 P (X= r) = rnr

r

n qpC , p + q = 1

12 Mean= np

13 npq

14 z =

x

TRIGONOMETRY

1 Arc length,s= r

2 Area of sector ,L= 21

2r

3 sin 2A+ cos 2A= 1

4 sec2A= 1 + tan2A

5 cosec2A= 1 + cot2A

6 sin 2A= 2 sinAcosA

7 cos 2A= cos2Asin2A

= 2 cos2A- 1

= 1 - 2 sin2A

8 tan 2A=A

A2tan1

tan2

9 sin (A B) = sinAcosB cosAsinB

10 cos (A B) = cosAcosB sinAsinB

11 tan (A B) =BA

BA

tantan1

tantan

12C

c

B

b

A

a

sinsinsin

13 a2= b2+ c2 - 2bccosA

14 Area of triangle = Cabsin2

1


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Answer allquestions.

1. Diagram 1 shows the functionf.

(a)State the codomain of the functionf.

(b)Determine the value of m.[3marks]

Answer: (a) ..

(b) ...

2. The following information above refers to the functions gand2.g

2

: 2 ,

: 9,

g x x k

g x hx

where hand kare constants.

Find the value of hand k.

[4marks]

Answer: h = ..

k = ...

4

2

For

examiners

use only

3

1


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3. Given the function ( ) 2 3h x x and ( ) 15,k x px find

(a) 1(7),h

(b)the value ofpsuch that (4) 13.kh

[4 marks]

Answer: (a) ..

(b) ...

4. It is given that -2 andpare the roots of the quadratic equation 2 3 0x x k . Statethe value ofpand of k.

[4marks]

Answer:p= ..

k=...

5.

The quadratic equation

2

7 16 0,px qx p where p and q are constants has equalroots. Ifpand qare positive, find the ratiop:qin the simplest form.[3 marks]

Answer: ..

Forxaminers

use only

3

5

4

4

4

3


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6. Diagram 2 shows the graph of the function ( ) 3 2 ,f x x for the domain 0 4.x

Diagram 2

State

(a) the value of k,

(b)the range of ( )f x corresponding to the given domain.

[3 marks]

Answer: (a) ..

(b) ...

7. Find the range of valuesxfor which 2 1 4 18.x x

[3 marks]

Answer: ..................................

3

6

3

7

For

examiners

use only


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8. Diagram 3 shows the graph of a quadratic function 2( ) 4 ( 2) ,f x a x where a is a

constant.

Diagram 3

The curve ( )y f x has a maximum point of (2, ),q where qis a constant.

State,

(a) the value of q,

(b)the value of a,

(c) the equation of the axis of symmetry.

[3 marks]

Answer : ..................................

9. Given that and are the roots of the quadratic equation 22 5 0,x x k where kis

a constant.

Find

(a) the value of ,

(b)the value of ksuch that 3.

[3 marks]

Answer: (a) ..

(b) ...3

9

3

8

Forxaminers

use only


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10.Solve the equation:

1 41

2 5 (10 )100

x x x

[3 marks]

Answer: ..

11.Given that 2 2log ( 2 ) 3 log ( ),x y x y findyin terms ofx.

[3 marks]

Answer:

12.Given log 4m p and log 3m t . Express 64

log3

mm

in terms ofpand t.

[3marks]

Answer: ........................

3

10

3

11

Forexaminers

use only

3

12


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13.Given that 2 8,3 1p p and 8p are the first three terms of an arithmetic

progression.

Find,

(a) the value ofp,

(b)the nthterm.[3 marks]

Answer: (a) ..

(b) ...

14.

The sum to infinity of a geometric progression with a first term of 5 is 25. Find

(a) the common ratio,

(b)the sum of the first three terms of the progression.

[3 marks]

Answer(a) ...................................

(b)....

Forxaminers

use only

3

13

3

14


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15. The variablesxandyare related by the equation 100 ,xy p wherepis a constant.

Diagram 4 shows the straight graph obtained by plotting10log y againstx.

Diagram 4

(a) Express the equation 100 xy p in its linear form used to obtain the straight line

graph shown in diagram.

(b) Find the value ofp.

[4 marks]

Answer: (a).....................................

(b).....................................

16.Point Qdivides internally the straight line joining pointP(10,8) and point S(2,4)

such that PQ: QS = 3:1

Find the coordinates of Q.

[3 marks]

Answer: ......................................

Forexaminers

use only

4

15

3

16


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17.A pointPmoves such that its distance from the pointsA(1,4) andB(5,-1) are in the

ratio of 2:3.

Find the equation of the locus of pointP.

[3 marks]

Answer: .........

18. Diagram 5shows a vectorOR drawn on a Cartesian plane.

Diagram 5

(a)Find the magnitude of vector .OR

(b)Write the unit vector in the direction of .OR [4 marks]

Answer(a) .........

(b)..........................................

For

xaminers

use only

3

17

4

18


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19. Diagram 6 shows a triangle LMN. It is given that K is the midpoint of MN,

6 2LN x y and 4 .LM y

Diagram 6

Find in terms of x and .y

(a) ,MN

(b) .LK

[3 marks]

Answer: ............

20.Solve the equation 24cos 4sin 5 0x x for o o0 360 .x

[3 marks]

Answer:.............

3

19

3

20

For

examiners

use only


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21.Diagram shows a triangle ROQ and semicircle PQS with centre O. The line QR is a

tangent to the semicircle at point Q.

Diagram 7

Given that the o30ORQ and the radius of the semicircle is 6cm.

Find

(a) ,ROQ in radian,

(b)the area of shaded region.

[3 marks]

Answer: (a).

(b)..

22.The curve ( )y f x is such that 2 9,dy

kxdx

wherekis a constant, has a turning

point at 3x . Find the value of k. [3marks]

Answer: .

3

22

For

examiners

use only

3

21


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23.Given that 2 3 2y x x ,

(a) Find the valuedy

dxof when 4,x

(b) Express the approximate change in x, in terms of p, when y changes from 6 to 6+p,

wherepis a small value.

[3marks]

Answer: ....

24.Table 1 shows the distribution for the ages of 80 members of a Sport Club.

Age 11-20 21-30 31-40 41-50 51-60 61-70

Number of

members4 11 17 25 15 6

Table 1

Calculate the median age of the Sport Club members.

[3 marks]

Answer: ....

3

23

For

examiners

use only

3

24


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25.Given that2

( )1

d xf x

dx x

find the value of

4

0( )x f x dx

[3 marks]

Answer: ....

END OF QUESTION PAPER

Prepared by: Checked by: Verified by: Received by:

.. .. .

Mr. Thiyaku Mr. Mahadevan Mdm. Tee Exam Unit

(Subject Teacher) (Subject Teacher) (HOD Mathematics)

3

25


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add maths form 5 paper 1 midterm 2012

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