SULIT Sept 2008 PEPERIKSAAN PERCUBAAN SPM 2008 · PEPERIKSAAN PERCUBAAN SPM 2008 ... 2. Answer all questions. 3. Give only one answer for each question. 4

SULIT 1

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

SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN

PEPERIKSAAN PERCUBAAN SPM 2008

Kertas soalan ini mengandungi 15 halaman bercetak

For examiner’s use only

Question Total Marks Marks Obtained

1 2 2 3 3 3 4 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. Answer all 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 not

drawn to scale unless stated. 8. The marks allocated for each question and sub-part

of 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

http://tutormansor.wordpress.com/

SULIT 3472/1

3472/1 2008 Hak Cipta Zon A Kuching SULIT

2

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

ALGEBRA

1 x =a

acbb2

42

2 am an = a m + n 3 am an = a m n

4 (am) n = a nm 5 log a mn = log a m + log a n

6 log a nm = log a m log a n

7 log a mn = n log a m

8 log a b = ab

c

c

loglog

9 Tn = a + (n 1)d

10 Sn = ])1(2[2

dnan

11 Tn = ar n 1

12 Sn = rra

rra nn

1)1(

1)1( , (r 1)

13 r

aS

1 , r < 1

CALCULUS

1 y = uv , dxduv

dxdvu

dxdy

2 vuy , 2

du dvv udy dx dxdx v

,

3 dxdu

dudy

dxdy

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

5 A point dividing a segment of a line

(x, y) = ,21

nmmxnx

nmmyny 21

6. Area of triangle =

1 2 2 3 3 1 2 1 3 2 1 31 ( ) ( )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) =

221 xx ,

221 yy

3 22 yxr

4 2 2

x i yjr

x y

GEOMETRY


SULIT 3472/1

3472/1 2008 Hak Cipta Zon A Kuching Lihat sebelah SULIT

3

STATISTICS

TRIGONOMETRY

1 Arc length, s = r

2 Area of sector , A = 212

r

3 sin 2A + cos 2A = 1 4 sec2A = 1 + tan2A 5 cosec2 A = 1 + cot2 A

6 sin 2A = 2 sinAcosA 7 cos 2A = cos2A – sin2 A = 2 cos2A 1 = 1 2 sin2A

8 tan2A = A

A2tan1

tan2

9 sin (A B) = sinAcosB cosAsinB

10 cos (A B) = cos AcosB sinAsinB

11 tan (A B) = BABA

tantan1tantan

12 Cc

Bb

Aa

sinsinsin

13 a2 = b2 +c2 2bc cosA

14 Area of triangle = Cabsin21

1 x = N

x

2 x =

ffx

3 = 2( )x x

N =

22x

xN

4 = 2( )f x x

f

=

22fx

xf

5 m = Cf

FNL

m

2

1

6 1000

1 PPI

7 i

i

iw IIw

8 )!(

!rn

nPrn

9 !)!(

!rrn

nCrn

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

11 P(X = r) = rnrr

n qpC , p + q = 1

12 Mean , = np 13 npq

14 z = x


SULIT 3472/1


4

Answer all questions.

1 Diagram 1 shows the linear function f. DIAGRAM 1

(a) State the value of n.

(b) Using the function notation, express f in terms of x. [ 2 marks ]

Answer : (a) ……………………..

(b) ……………………...

2. Two functions are defined by : 1f x x and 2: 3 1g x x x . Given that 2:gf x x ax b , find the value of a and of b.

[ 3 marks ]

Answer : …………………….....

3

2

For examiner’s

use only

x f(x) f

5 4 n 4

0 1 5 9

2

1


SULIT 3472/1

3472/1 2008 Hak Cipta Zon A Kuching [ Lihat sebelah SULIT

5

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

x

,213 .

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 : .........…………………

For examiner’s

use only

3

4

3

3


SULIT 3472/1


6

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 .

[ 3 marks ]

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

___________________________________________________________________________

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

[ 3 marks ]

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

q = ……........................

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

3

5

3

6

For examiner’s

use only

DIAGRAM 2

(2, 3)

(0, 5)

x

y

O


SULIT 3472/1


7

7 Find the range of values of x for which x(x − 2) ≤ 15. [3 marks]

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 or

mathematical tables, find the value of 34log 2 . [ 3 marks ]

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

3

7

3

9

3

8

For examiner’s

use only


SULIT 3472/1


8

10 The thn term of an arithmetic progression is given by .15 nTn Find

(a) the first term and the common difference, (b) the sum of the first 15 terms of the progression. [4 marks]

Answer : (a) ………………………….

(b) ....……………...………..

11 The first three terms of a geometric progression are 219683

, 26561

, 22187

, . . . .

Find the three consecutive terms whose product is 157464. [ 3 marks ]

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

4

10

For examiner’s

use only

3

11


SULIT 3472/1


9

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

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 of h.

[ 3 marks ]

Answer : h = …………………….

y10log

x10log 0

(0, 6)

(4, h )

DIAGRAM 3

3

13

4

12

For examiner’s

use only


SULIT 3472/1


10

14 If the straight line 15

pyx is 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 : .………………….

3

15

3

14

For examiner’s

use only


SULIT 3472/1


11

16 The diagram 4 shows a parallelogram ABCD drawn on a Cartesian plane.

It is given that 3 2AB i j

% %and 4 3BC i j

% %.

Find

(a) BD

,

(b) AC .

[ 4 marks ]

Answer : (a) ……….…….…………...

(b) ………………………….. ___________________________________________________________________________ 17 Solve the equation 2 2sin 5cos 3 cos for 00 3600 . [ 3 marks ]

Answer : …...…………..….......

3

17

For examiner’s

use only

4

16

y

O

A

B

C

D

x

DIAGRAM 4


SULIT 3472/1


12

18 Given that sin x = 35

and 90 < x < 270, find the value of sec 2x.

[ 3 marks ]

Answer : …...…………..….......

___________________________________________________________________________ 19 The diagram 5 shows a semicircle of centre O and radius r cm. C A O B

The length of the arc AC is 72 cm and the angle of COB is 2692 radians. Calculate (a) the value of r, (b) the area of the shaded region. [Use π = 3.142] [ 4 marks ]

Answer : (a) ……………………..

(b) ……………………..

3

18

For examiner’s

use only

DIAGRAM 5


SULIT 13 3472/1


20 Find the coordinates of the turning points of the curve y = x3 + 3x2 – 2 . [4 marks]

Answer : …...…………..…....... ___________________________________________________________________________ 21 Given that y = 3m2 and m = 2x + 3.

Find

(a) dxdy in terms of x,

(b) the small change in y when x increases from 3 to 301. [ 4 marks ]

Answer : (a) ……………………..

(b) ……………………..

22 Find dx

x313

[ 3 marks ]

Answer : ……………………..

3

20

4

21

3

22

For examiner’s

use only


SULIT 14 3472/1


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

are 15

and 23

respectively.

Calculate the probability that at least one person passes the test. [ 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) ……………………..

For examiner’s

use only

3

24

3

23


SULIT 15 3472/1


25 A random variable X has a normal distribution with mean 50 and variance 2 . Given that P[X > 51] = 0288, find the value of .

[ 3 marks ]

Answer : …...…………..….......

END OF QUESTION PAPER

3

25

For examiner’s

use only

SULIT http://tutormansor.wordpress.com/

SULIT 3472/1 Additional Mathematics Paper 1 Sept 2008

SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN

PEPERIKSAAN PERCUBAAN SPM TINGKATAN 5

2008

ADDITIONAL MATHEMATICS

Paper 1

MARKING SCHEME

This marking scheme consists of 6 printed pages


2

PAPER 1 MARKING SCHEME 3472/1

Number Solution and marking scheme Sub Marks

Full Marks

1 (a)

(b)

0 x 5 or f : x x 5 or f(x) = x 5

1 1

2

2

a = 1 and b = 1 gf(x) = x2 + x 1 (x 1)2 + 3(x 1) + 1

3

B2

B1

3

3 (a)

(b)

12

3 1,

2 1 2x xx

y = 31 2x

x

1 2

B1

3

4

t > 1 –12t < 12 or equivalent (6)2 – 12 (t +2)(3) < 0

3

B2

B1

3

5

x2 + 3x + 14 = 0 2(2) = 14 and 2 + 2 = 3

3 7and =2 2

3 B2 B1

3


3


Full Marks

6

a = 21

a(−2)² + 3 = 5 p = −2 and q = 3

3

B2

B1

3

7

−3 ≤ x ≤ 5 (x − 5)(x + 3) ≤ 0 x² − 2x − 15 ≤ 0

3

B2

B1

3

8

4x

1 2 3x x or equivalent

1 2 33 3x x or 1

233 3

3

x

x

3

B2

B1

3

9

5 1 lg 2 lg17

lg 2

lg34lg 2

3

B2

B1

3

10 (a)

(b)

5d

a @ T1 = 4 or T2 = 9 585

2

B1 1

3

11 18, 54, 162 n = 12 or 54 or 18 or equivalent (Solving)

a = 219683

and r = 3

3

B2

B1

3


4


Full Marks

12 (a)

(b)

1000000k

xy 1010 log4log + k10log

22h

4046

h

2

B1 2

B1

4

13

2h

1 2 0 5 0 92

h h h h

1 2 0 5 02

h h h h

3

B2

B1

3

14

6p

5 1

5 6p

or equivalent

1 5pm or 2

56

m

3

B2

B1

3

15 m = 1 1 2

5 5m

5 1a b i m j

% % % %

3 B2

B1

3

16 (a)

(b)

5BD i j uuur

% %

or BD BA AD BA BC

uuur uuur uuur uuur uuur

50

7AC i j

uuur

% %

2

B1 2 B1

4


5


Full Marks

17

66.42 ,293.58

2cos5

1 5cos 3 or equivalent

o o

3

B2

B1

3

18

257

21

31 25

1

cos 2x

3

B2

B1

3

19 (a)

(b)

r = 16 AOC = 0.45 or 7.2 = r (0.45) 344576 or 33458 or 3346

21 (16) (2 692)2

2

B1 2

B1

4

20

(2, 2) and (0, 2) x = 0, 2

dxdy = 0 or 3x(x + 2) = 0

dxdy = 3x2 + 6x

4

B3

B2 B1

4


6


Full Marks

21 (a)

(b)

24 36 or equivalent

6 and 2

dy xdx

dy dmmdm dx

108

[24(3) 36] 0 01y

2

B1

2

B1

4

22

122(1 3 )x c

12

12

3(1 3 )3x c

123(1 3 )x or

12 3

3

B2

B1

3

23

1115

4 11 or equivalent5 3

4 1or5 3

3

B2

B1

3

24 (a) (b)

6 120 6 4

3 2C C

1 2

B1

3

25

1.789

51 50 0.559

0.559

3 B2 B1

3


Documents

SULIT Sept 2008 PEPERIKSAAN PERCUBAAN SPM 2008 · PEPERIKSAAN PERCUBAAN SPM 2008 ... 2. Answer all questions. 3. Give only one answer for each question. 4