add math p1 trial spm zon a kuching 2008

8/14/2019 Add Math p1 Trial Spm Zon A Kuching 2008

1/15

SULIT 1

SEKOLAH MENENGAH ZON A KUCHINGLEMBAGA PEPERIKSAAN

PEPERIKSAAN PERCUBAAN SPM 2008

Kertas soalan ini mengandungi 15 halaman bercetak

3472/1 2008 Hak Cipta Zon A Kuching [Lihat Sebelah

SULIT

For examiners use only

Question Total MarksMarks

Obtained

1 2

2 3

3 34 3

5 3

6 3

7 3

8 3

9 3

10 4

11 3

12 4

13 3

14 3

15 3

16 4

17 3

18 3

19 4

20 4

21 4

22 3

23 3

24 3

25 3

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

Sept 2008

2 Jam


2/15

SULIT 3472/1

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

ones commonly used.

ALGEBRA

1 x = a

acbb

2

42

2 am an = a m + n

3 am an = a mn

4 (am)n = a nm

5 log amn = log a m + log an

6 log a

n

m= log a m log an

7 log amn = n log am

8 log a b = 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< 1

CALCULUS

1 y = uv ,dx

duv

dx

dvu

dx

dy+=

2v

uy = ,

2

du dvv u

dy dx dx

dx v

= ,

3dx

du

du

dy

dx

dy=

4 Area under a curve

= b

a

y dx or

= b

a

x dy

5 Volume generated

= b

a

y 2 dx or

= b

a

x 2 dy

3472/1 2008 Hak Cipta Zon A Kuching SULIT

2

5 A point dividing a segment of a line

(x,y) = ,21

++

nm

mxnx

++

nm

myny 21

6. Area of triangle =

1 2 2 3 3 1 2 1 3 2 1 3

1( ) ( )

2

x y x y x y x y x y x y+ + + +

1 Distance = 2 22 1 12( ) ( )x x y y +

2 Midpoint

(x ,y) = +

2

21 xx,

+

2

21 yy

3 22 yxr +=

42 2

x i yjr

x y

GEOM ETRY


3/15

SULIT 3472/1

STATISTICS

3472/1 2008 Hak Cipta Zon A Kuching Lihat sebelah

SULIT

3

TRIGONOMETRY

1 Arc length,s = r

2 Area of sector ,A =

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2A = 1 + cot2A

6 sin 2A = 2 sinAcosA

7 cos 2A = cos2A sin2A

= 2 cos2A 1

= 1 2 sin2A

8 tan2A =

9 sin (AB) = sinAcosB cosAsinB

10 cos (AB) = cosAcosB sinAsinB

11 tan (AB) =

12

13 a2 = b2 +c2 2bc cosA

14 Area of triangle =

1 =

2 =

3 = =

4 = =

5 m =

6

7

8

9

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

11 P(X= r) = , p + q = 1

12 Mean , = np

13

14 z =


4/15

Answerall questions.

1 Diagram 1 shows the linear functionf.

DIAGRAM 1

(a) State the value ofn.

(b) Using the function notation, expressfin terms ofx.

[ 2 marks ]

Answer: (a) ..

(b) ...

2. Two functions are defined by : 1 f x x and 2: 3 1g x x x . Given that

2:gf x x ax b , find the value of a andofb.

[ 3 marks]

Answer: .....

3 The function ofp is defined as p(x) hxx

x

,

21

3.


For examiners

use only

3

2

For examiners

use only

f(x)f

5

4

n

4

0

1

5

9

2

1


5/15

SULIT 3472/1

Find

(a) the value of h,

(b) )(1 xp .

[ 3 marks ]

Answer: (a) ..

(b) ...

4 Find the range of values of t if the following quadratic equation has no roots

(t+ 2)x2 + 6x + 3 = 0.[ 3 marks ]

Answer: .........

5 Given that and are the roots of the quadratic equation 22 3 7x x .

Form the quadratic equation whose roots are 2

and 2 .


SULIT

5

3

4

3

3

For examinersuse only


6/15

[ 3 marks ]

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

___________________________________________________________________________

6 Diagram 2 shows the graph of a curvey = a(x +p) + q that passes through the point(0, 5) and has the minimum point (2, 3). Find the values ofa,p and q.

[ 3 marks ]

Answer: p = ........................

q = ........................

a = ..................................

7 Find the range of values ofx for which x(x 2) 15.

[3 marks]


3

5

3

6

For examinersuse only

DIAGRAM 2

(2, 3)

(0, 5)

x

y

O


7/15

SULIT 3472/1

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

8 Solve 279

3 1=

x

x

[ 3 marks ]

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

9 Given that lg 2 0 3= and lg 17 1 23= , find, without using scientific calculator ormathematical tables, find the value of 34log 2 .

[ 3 marks ]

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

10 The thn term of an arithmetic progression is given by .15 = nTnFind

(a) the first term and the common difference,

(b) the sum of the first 15 terms


SULIT

7

3

7

3

9

3

8

For examiners

use only


8/15

of the progression.

[4 marks]

Answer: (a) .

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

11 The first three terms of a geometric progression are2

19683,

2

6561,

2

2187, . . . .

Find the three consecutive terms whose product is 157464.

[ 3 marks ]

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

12 Diagram 3 shows the straight line obtained by plotting y10log against log 10x.


3

8

4

10

3

11

Forxaminers use

only


9/15

SULIT 3472/1

The variables x and y are related by the equation ,4kxy = where k is a constant.

Find the value of

(a) k,

(b) .h

[ 4 marks ]

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

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

___________________________________________________________________________

13 The coordinates of the vertices of a triangle PQR are P(2, h), Q(1, 0) and R(5, h).If the area of the PQR is 9 units 2 , find the values ofh.

[ 3 marks ]

Answer: h = .


SULIT

x10log

(0, 6)

(4, )

DIAGRAM 3

9

3

13

4

12


10/15

14 If the straight line 15

=p

yxis perpendicular to the straight line

,031210 =+ yx find the value of .p[ 3 marks ]

Answer: .

15 Given the vectors 3a i mj= , 8b i j and 5 2c i j . If vector a b is parallel to

vector~c , find the value of the constant m.

[ 3 marks ]

Answer: ..

16 The diagram 4 shows a parallelogramABCD drawn on a Cartesian plane.


3

15

3

14

For examiners

use only

For examiners

use only

y

O

A

B

CD x


11/15

SULIT 3472/1

It is given that 3 2 AB i j

and 4 3 BC i j

.

Find

(a) BD

,

(b) AC .

[ 4 marks ]

Answer: (a) .....

(b) ..

___________________________________________________________________________

17 Solve the equation 2 2sin 5cos 3 cos for00 3600 . [ 3 marks ]

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

18 Given that sinx = 35

and 90


12/15

[ 3 marks ]

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

___________________________________________________________________________

19 The diagram 5 shows a semicircle of centre O and radius rcm.

C

A O B

The length of the arcACis 72 cm and the angle ofCOB is 2692 radians.

Calculate

(a) the value ofr,

(b) the area of the shaded region.

[Use = 3.142]

[ 4 marks ]

Answer: (a) ..

(b) ..

20 Find the coordinates of the turning points of the curvey =x3 + 3x2 2 .

[4 marks]


3

18

For examiners

use only

DIAGRAM 5


13/15

SULIT 3472/1

Answer: ............___________________________________________________________________________

21 Given thaty = 3m2 and m = 2x + 3.

Find

(a)dx

dyin terms ofx,

(b) the small change iny whenx increases from 3 to 301.[ 4 marks ]

Answer: (a) ..

(b) ..

22 Find dxx313

[ 3 marks ]

Answer: ..

23 Ben and Shafiq are taking driving test. The probability that Ben and Shafiq pass the test

are1

5and

2

3respectively.

Calculate the probability that at least one person passes the test.


SULIT

13

3

20

4

21

For examiners

use only

3

22


14/15

[ 3 marks ]

Answer: ..

___________________________________________________________________________

24 A committee of 5 members is to be selected from 6 boys and 4 girls. Find the number of

ways in which this can be done if

(a) the committee has no girls,

(b) the committee has exactly 3 boys.[ 3 marks ]

Answer: (a) ..

(b) ..

25 A random variableXhas a normal distribution with mean 50 and variance 2 .

Given thatP[X> 51] = 0288, find the value of .[ 3 marks ]


3

24

3

23

For examiners

use only


15/15

SULIT 3472/1

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

END OF QUESTION PAPER


SULIT

15

3

25

SULIT

add math p1 trial spm zon a kuching 2008

Documents