2007 MidTerm F5 Johor (Addmath_P1)

8/14/2019 2007 MidTerm F5 Johor (Addmath_P1)

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SULIT 3472/1

PEJABAT PELAJARAN DAERAH JOHOR BAHRU

PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 5 2007

Kertas soalan ini mengandungi 14 halaman bercetak

[ Lihat sebelah

3472/1 SULIT

For examiners use only

QuestionTotal

Marks

Marks

Obtained

1 2

2 4

3 3

4 4

5 3

6 3

7 3

8 3

9 4

10 4

11 3

12 3

13 2

14 2

15 4

16 4

17 4

18 3

19 2

20 3

21 4

22 4

23 3

24 4

25 2

TOTAL 80

MATEMATIK TAMBAHAN

Kertas 1

Dua jam

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1 This question paper consists of 25 questions.

2. Answerall questions.

3. Give only one answer for each question.4. Write your answers clearly in the spaces provided in

the question paper.

5. Show your working. It may help you to get marks.6. If you wish to change your answer, cross out the work

that you have done. Then write down the new

answer.

7. The diagrams in the questions provided are notdrawn to scale unless stated.

8. The marks allocated for each question and sub-partof a question are shown in brackets.

9. A list of formulae is provided on pages 2 to 3.10. A booklet of four-figure mathematical tables is

provided.

.11 You may use a non-programmable scientific

calculator.

12 This question paper must be handed in at the end of

the examination .

Name : ..

Form : ..

3472/1

Matematik Tambahan

Kertas 1

Mei 2007

2 hours


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SULIT 3472/2

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

ALGEBRA

1 2 4

2

b b acx

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 = n log 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)

13r

aS

1, r


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SULIT 3 3472/1

STATISTICS

[ Lihat sebelah

3472/1 SULIT

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 sinA cosA

7 cos 2A = cos2A sin2A= 2 cos2A - 1

= 1 - 2 sin2A

8 tan 2A =A

A2tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosBsinA sinB

11 tan (A B) =BA

BA

tantan1

tantan

12C

c

B

b

A

a

sinsinsin==

13 a2 = b2 + c2 - 2bc cosA

14 Area of triangle = Cabsin2

1

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

61

0

100Q

IQ

=

71

11

w

IwI

=

8)!(

!rn

nPrn

=

9!)!(

!

rrn

nCr

n

=

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

11 P (X= r) =rnr

r

nqpC , p + q = 1

12 Mean = np

13 npq=

14 z =

x


4/14

Answer all questions. 1.

Based on the above information, the relation between A and B is defined by the set of

ordered pairs { (2,3) , (3,4), (3,5) , (4,6) }.

State

(a) the image of 3,

(b) the type of relation

[ 2 marks ]

Answer: (a) ..

(b) ...

2. Given 2:2 xxf and 63: + xxg . Find

(a) )2(1g ,

(b) )(xfg .

[ 4 marks]

Answer: (a) ..

(b) ...

4

2

2

1

A = { 2, 3, 4 }

B = { 3, 4, 5 , 6 }


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SULIT 3 3472/1

3. Diagram 1 shows the graph of quadratic functiony = f(x).y

DIAGRAM 1

Given that the curve qpxxf ++=2)()( , where p and q are constants cuts x-axis

at x = 1 and x = 3

Find

(a) the value of p and q.

(b) the coordinates of the minimum point.

[3 marks]

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

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

4 A quadratic equation 2x( x 3 ) = kx 2 , has two distinct roots.

Find the range of values of k .

[4 marks ]

Answer: .........

[ Lihat sebelah

3472/1 SULIT

For examinersuse only

3

4

3

3

1 O 3 x


6/14

5 Find the range of the values of x for 6)73( +xx .

[3 marks]

Answer: ..

6 Solve the equation32

1)2(64 12 =+ xx

[3 marks]

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

7 Solve the equation )5log(1)62log( +=+ xx

[3 marks]

Answer: ...

8 Given that NMN 42 log23log = , express Min terms ofN [3 marks]

For examiners

use only


3

7

3

6

2

5


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SULIT 3 3472/1

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

9. The second and ninth term of an arithmetic progression are 19 and 33respectively.

Find the sum of the first twenty terms.

[4 marks]

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

10 The second and fifth term of a geometric term are 112 and 14 respectively. Find

(a) the first term and the common ration

(b) the sum to infinity of the geometric progression

[4 marks]

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

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

11 Diagram 2 , shows a straight line graph oflg y against lg(x+2)

[ Lihat sebelah

3472/1 SULIT

4

9

4

10

3

8


lg y


8/14

DIAGRAM 2

Express y in terms of x.

[3 marks]

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

12 The point ( )12, +nmQ internally divides the line segment that connects the point

),2( aaP and ( )nmR 3,2 in the ratio 1:3 .

Express m in terms of n.

[3 marks]

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

13. Diagram 3 shows a triangle ABC.

y

3

11

lg(x+2)O

)2,1(

( )3,6


3

12


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SULIT 3 3472/1

Given that the coordinates point A , B and C are (2,5), (3,1) and ( 3,2) respectively.

Find the area of the triangle ABC.

[2 marks]

Answer:........

14. Given v = ji 34 and w = i6 j5 , find the vector v2 w3 [2 marks]

Answer: .

15 Given that )0,0(O , )5,1(P , )2,3(Q and )0,(aR , find

(a) PQ in terms of of the unit vectors , i and j

[ Lihat sebelah

3472/1 SULIT

r examiners

use only

2

13

A(2,5)

B(3,1)

C(3,2)

O x

DIAGRAM 3

2

14


10/14

(b) the value ofa such that

PQ +QR =

i9 j5

[ 4 marks ]

.

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

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

16 Diagram 4 shows ORS and OPQ are two concentric sectors with centre O.

DIAGRAM 4

Given that POQ = 0.82 radian and OP=3PR. Find the area of shaded region.[4 marks]

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

17 Given that ( )23 = xxy , calculate

(a) the value of x when y is minimum

(b) the minimum value of y.

[4 marks]

For examiners

use only

4

16

4

15

R

P

OQ S

2 cm


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SULIT 3 3472/1

Answer: (a)

(b)

18. Differentiate 2x (3x 1) 4 with respect to x.

[3 marks]

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

19. Given that xxy += 25 , find

(a) the value ofdx

dyif x = 2

(b) the small change in y when x increases from 2 to 2.01

[4 marks]

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

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

20. Given that =6

2

10)( dxxf , evaluate ++4

2

6

4

)(])([ dxxfdxxxf

[3 marks]

[ Lihat sebelah

3472/1 SULIT

r examinersuse only

4

17

3

18

4

19


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

21 Diagram 5 shows part of the curve2

5

xy = .

y

DIAGRAM 5

Given that the area of shaded region A is equal to the area of the shaded region B,

find the value of k.

[4 marks]

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

22. Diagram 6 shows the curve 12 +=xy

y

4

21

A B

O 2 k 5 x

2

5

xy =

3

20

12 +=xyA

B O C(k,0) x

For examiners

use only


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SULIT 3 3472/1

DIAGRAM 6

Given that the volume generated when the region ABC is revolved through 360 0 about

x-axis is2

25 unit3. Find the value of k.

[4 marks]

Answer:..

23 Given thatx

xxy

223 = and )(3 xk

dx

dy= , where k(x) is a function in terms ofx,

Find the value of 2

1

)( dxxk

[3 marks]

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

24. The mean of a set of numbers x2, x + 6, 2x+5, 2x 1, x + 7, x 3 is 6. Find

(a) the value of x

(b) the standard deviation

[4 marks]

[ Lihat sebelah

3472/1 SULIT

For examiners

use only

3

22

3

23


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

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

25. A box contains 6 green balls andp brown balls. If a ball is drawn from the box,

the probability of the ball chosen is brown is7

4. Calculate the value ofp.

[3 marks]

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

END OF THE QUESTION PAPER

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2007 MidTerm F5 Johor (Addmath_P1)

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