# sabah add math p1 & ans 2

20
SULIT 3472/1 ADDITIONAL MATHEMATICS PAPER 1 AUGUST 2008 2 HOURS JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA TAHUN 2008 EXCEL 2  __________ ___________ __________ ADDITIONAL MATHEMATICS PAPER 1 (KERTAS 1) TWO HOURS (DUA JAM)  __________ JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. Tuliskan angka giliran dan nombor kad  pengenalan anda pad a ruang yang disediakan. 2. Calon dikehendaki membaca arahan di halaman 2 .  __________ This question paper consists of 14 printed pages. (Kertas soalan ini terdiri daripada 14 halaman bercetak.) 3472/1 [Turn over (Lihat sebelah)   NAMA : ____________ KELAS : _____________________  NO K.P : ____________ A. GILIRAN : _____-  Excel Sabah SPM 2008 http://edu.joshuatly.com http://www.joshuatly.co

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8/10/2019 Sabah Add Math P1 & Ans 2

SULIT

3472/1

MATHEMATICS

PAPER 1AUGUST 2008

2 HOURS

JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA TAHUN 2008

EXCEL 2

___________________________________________________________________________

TWO HOURS (DUA JAM)

___________________________________________________________________________

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tuliskan angka giliran dan nombor kad

2. Calon dikehendaki membaca arahan di

halaman 2 .

___________________________________________________________________________This question paper consists of 14 printed pages.

(Kertas soalan ini terdiri daripada 14 halaman bercetak.) 3472/1 [Turn over (Lihat sebelah)

NAMA : _____________________

KELAS : _____________________

NO K.P : _____________________

A. GILIRAN : _________________-

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8/10/2019 Sabah Add Math P1 & Ans 2

2

INFORMATION FOR CANDIDATES

1.  This question paper consists of 25 questions.

3.  Give only one answer for each question.

4.  Write your answers clearly in the space provided in the question paper.

5.

6.

If you wish to change your answer, cross out the work that you have done. Then write

7.  The diagrams in the questions provided are not drawn to scale unless stated.

8.

The marks allocated for each question are shown in brackets.

9.

A list of formulae is provided on pages 3 to 5.

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.

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8/10/2019 Sabah Add Math P1 & Ans 2

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

ones commonly used.

ALGEBRA

1.2 4

2

b b ac x

a

2. m n m na a a

3. m n m na a a

4. ( )m n mna a

5. log log loga a amn m n

6. log log loga a a

mm n

n

7. log logn

a am n m

8.log

loglog

ca

c

bb

a

9. ( 1)nT a n d

10. [2 ( 1) ]2

n

nS a n d

11. 1n

nT ar

12.( 1) (1 )

, 11 1

n n

n

a r a r  S r

r r

13. , 11

aS r

r

CALCULUS

1. ,dy dv du

y uv u vdx dx dx

2.2

,

du dvv u

u dy dx dx yv dx v

3.dy dy du

dx du dx

4. Area under a curve

=b

a

y dx  or

=b

a

x dy

5. Volume generated

= 2

b

a

y dx   or

= 2

b

a

x dy

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8/10/2019 Sabah Add Math P1 & Ans 2

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STATISTICS

1.

x

x  N

2. fx

x f

3.

2 2

2( ) x x x

x N N

4.

2 2

2( ) f x x fx

x f f

5.

1

2

m

N F m L c

f

6. 1 100o

Q I

Q

7.i i

i

W I  I

8.

!

!r

nnn r  P

9.

!

! !r

nnn r r C

10.  P A B P A P B P A B

11. , 1n r n r

r  P X r C p q p q

12. Mean, μ = np

13. npq

14.  X  Z

GEOMETRY

1. Distance

= 2 2

1 2 1 2 x x y y

2. Midpoint

1 2 1 2, ,2 2

x x y y x y

3. A point dividing a segment of a

line

1 2 1 2, ,nx mx ny my

x ym n m n

4. 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

5. 2 2r x y

6.2 2

ˆ xi yj

r  x y

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8/10/2019 Sabah Add Math P1 & Ans 2

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TRIGONOMETRY

1.

Arc length,  s r

2.

Area of sector, 21

2 A r

3.  2 2sin cos 1 A A

4.  2 2sec 1 tan A A

5.

2 2

cosec 1 cot A A

6.  sin 2 2sin cos A A A

7.  2 2cos2 cos sin A A A

2

2

2 os 1

1 2 sin

c A

A

8. sin ( ) sin cos cos sin A B A B A B

9. cos( ) os os sin sin A B c Ac B A B

10.tan tan

tan ( )1 tan tan

A B A B

A B

11.2

2tantan 2

1 tan

A A

A

12.sin sin sin

a b c

A B C

13. 2 2 2 2 cosa b c bc A

14. Area of triangle1

sin2

ab C

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8/10/2019 Sabah Add Math P1 & Ans 2

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(a) State the type of relation between set P  and set Q .(b) Using function notation, state the relation between set P  and set Q.

[2 marks]

(b) ……………………..

2.  Given that : 7 4 f x x . Find the value of  p if (2) 5 3 f p .

[2 marks]

For Examiner’s

Use

1

2

2

2

1. In Diagram 1, set  P  is the domain and set Q is the codomain of a relation.

4

9

16

4

3

2

Set P   Set Q

Diagram 1

2

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8/10/2019 Sabah Add Math P1 & Ans 2

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3. Given that 1 3: 2, and ( ) .

2 g x ax g x b x  Find the values of a and b.

[3 marks]

b =………………………..

4. (a) Solve the following quadratic equation:24 4 3 0 x x

(b) Given the quadratic equation 2 9 0 x px  has two equal roots. Find the

values of  p. [4 marks]

(b)….……………………

5. Find the range of the values of x for 2( 1) (2 3)( 1). x x x   [3 marks]

3

3

4

4

For

Examiner’s Use

5

3

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8/10/2019 Sabah Add Math P1 & Ans 2

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6. The quadratic function 2( ) 3 6 5 can be expressed in the f x x x  2form 3( ) x p q , where p and q are constants. Find the values of  p and q.

[3 marks]

q = ….………….……

7. Given that log 2a

p  and1

log2

a q    , find the value of

2

loga

p q

a.

[3 marks]

8. Solve the equation1

2 1

16 4

y

y y  .  [3 marks ]

For Examiner’s

Use

7

3

8

3

6

3

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8/10/2019 Sabah Add Math P1 & Ans 2

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9. An arithmetic progression has 15 as the second term and 3  as the common

difference. List the first five terms of the progression. [2 marks]

10. The first three terms of an arithmetic progression are 4, 3,2 2 p p p .

Find(a) the value of p,

(b) the sum of the first 8 terms of the progression. [4 marks]

(b)….……………………

11. The first term and the fourth term of a geometric progression are 16 and 2

respectively. Calculate the sum to infinity of the geometric progression.

[3 marks]

9

2

For Examiner’s

Use

10

4

11

3

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8/10/2019 Sabah Add Math P1 & Ans 2

8/10/2019 Sabah Add Math P1 & Ans 2

8/10/2019 Sabah Add Math P1 & Ans 2

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(b).. ……….……………..

17. Solve the equation 3cos 2 8sin 5 for 0 360o o   . [ 4 marks ]

18. The curve ( ) y f x  is such that2

1dy pdx x

, where p is a constant.

The gradient of the curve at 2 x   is1

2 . Find the value of  p. [2 marks]

19. Diagram 4 shows a circle with centre O and radius 4 cm . Given that the area of the

minor sector AOB is 9 cm2, calculate the length, in cm, of the major arc AB.

[Use  = 3.142] [4 marks]

Diagram 4

For

Examiner’s Use

17

4

18

2

19

4

O

A

B

4 cm

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8/10/2019 Sabah Add Math P1 & Ans 2

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20. The curve 22 8 3 y x x  has a maximum point at x = p , where p is a

constant. Find the value of p . [3 marks]

21. Given that3

1

( ) 6 g x dx  , find

(a) the value of1

3

( ) , g x dx

(b) the value of p if3

1

[ ( )] 18 px g x dx . [4 marks]

(b) ...………………………

22. A set of data consists of five numbers. The sum of the numbers is 175 and the

sum of the squares of the numbers is 6845. Find, for the five numbers(a) the mean,

(b) the standard deviation. [3 marks]

(b) ...………………………

For Examiner’s

Use

22

3

21

4

20

3

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8/10/2019 Sabah Add Math P1 & Ans 2

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23. A badminton team that consists of 8 students is to be chosen from a group of 7male students and 6 female students . Calculate the number of different teams

that can be formed if each team must consist of(a) exactly 3 male students,

(b) not more than 2 female students. [4 marks]

(b) ……………………….

24. In a shooting competition, the probability that Lim will strike the target is 0.75.

If Lim fires 6 shots, calculate the probability that(a) all the shots hit the target,

(b) at least one of the shots hits the target. [4 marks]

(b) ……………………….

25.  X  is a random variable of a normal distribution with a mean of 75 and a standard

deviation of 3 .(a) Find the Z -score if X  is 70.

(b) (72 79) P X  . [4 marks]

(b) ……………………….

For Examiner’s

Use

23

4

24

4

25

4

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8/10/2019 Sabah Add Math P1 & Ans 2

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END OF QUESTION PAPER

PERATURAN PEMARKAHAN EXCEL 2 PAPER 1

NO. SOLUTION AND MARK SCHEME SUBMARK

TOTALMARK

1. (a) many to one

(b) 2 2: or ( ) f x x f x x

11

2

2. P = 3

B1 : 7(2) + 4 = 5p + 3

2 2

3.a =

2, 3 [both]

3b

B2 :2 3 1 2

2 or ,3 2

b ba a

B1 : 1 2 2 2( ) or ( )

3 3

x g x b x g x

a a

3 3

4.(a)

1 3,

2 2 x    (both)

B1 :24 4 4(4)( 3)

(2 1)(2 3) 0 or2(4)

x x

(b) p = 6

B1 : 2 4(1)(9) 0 p

2

2

4

5  4 < x < 1 or 1> x > 4

B2 :   + +

+

4 1

B1 : ( x + 4 ) ( x  –  1 ) < 0

3 3

6  p = 1 , q  = 2 (both)

B2 : 3 ( x    1 ) 2  + 2

B1 : 3 ( x2

2 x  + 3

5  )

3 3

73

2

1or

2

7or 3.5

B2 : 4 +2

1  1

B1: log a p2 + log a q  –  log a a

3 3

8  y = 4

B2 : 4( 1) 2 y y y   or 3 y = 4 y  –  4

3 3

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8/10/2019 Sabah Add Math P1 & Ans 2

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B1 :4( 1) 2

2 1

2 2

y

y y    or equivalent

9 18, 15, 12, 9, 6

B1: a = 18

2 2

10 (a)  p = 8

B1 : ( 4)(2 2) 2( 3) p p p  or equivalent

(b) 228

B1 : S 8   =2

8[ 2 (4) + 7 ( 7) ] or equivalent

2

2

4

11 32

B2 :

)2

1(1

16

or equivalent

B1 : r  =2

3 3

12q  =

2

1  ,  p = 1 ( both)

B2 : 4 = 5 2q  or  p = 2 ( 3) + 5

B1 : x

y2

=  2 x + 5

3 3

13 5

B2 :3

m =

3

3

5  (both)

3 3

14h =

5

8 , h = 1 (both)

B2 : 5h 2  + 3h  –  8 = 0

B1 :

2110 2 8 2 2 10 2 8

2

4 (5 1) 4 1OR or equivalent

2 2 2 2

h h h h

h

h h

3 3

15

2

3( 5 a + 3 b )

3 3

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8/10/2019 Sabah Add Math P1 & Ans 2

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B2 :3

(10 6 )4

PH a b

B1 : 10 6 PT a b

16 (a)

54   or 4 i  + 5  j

B1 :

3

2

2

2  or 2 i  + 3  j    ( 2 i   2  j )

(b)2

1( i  +  j ) or

2

1

1

1  or equivalent

B1 : 44   Or 8  Or 2 2

2

2

4

17 41.81, 138.19

B3 : sin     =3

2  , sin     = 2 ( both)

B2 : (3 sin   2) (4 sin +2) = 0

B1 :3 ( 1 –  2 sin 2  ) = 8 sin    5

4 4

18  p = 2

B1 : 2

1

2 1( 2)

p

2 2

19  s = 20.64 cmB3 :  s = 4 (5.159) rad

B2 : major AOB = (2−8

B1 : 9 =21 ( 4) 2

4 4

20  p = 2

B2 :  x  –  2 = 0 or 4 p + 8 = 0

B1 : 2 [ ( x  2 )2

( 2)2

+ 2

3

] or 4 8

dy

xdx

3 3

21 (a) 6

(b)  p = 6

B2 :2 2(3) 1

( ) 6 18 or equivalent2 2

p

B1 :

32

1

6 182

px

1

3

4

22 (a) mean = 35 1 3

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8/10/2019 Sabah Add Math P1 & Ans 2

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(b) 12

B1: 26845(35)

5   or equivalent

2

23 (a) 210B1 : 7 C 3   x 6 C 5

(b) 111

B1 : 7 C 7   x 6 C1  + 7 C 6   x 6 C

2

2

4

24 (a) 0.1780

B1 : 6 C 6  ( 0.75) 6 (0.25) 0   or equivalent

(b) 0.9998

B1 : 1   P( x = 0)

2

2

4

25 (a)  Z = 1.667

B1 :3

7570   or equivalent

(b) 0.7449 –  0.7501

B1 : 1 – P( x    1) –  P( x   1.333) or equivalent

2

2

4

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8/10/2019 Sabah Add Math P1 & Ans 2

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CO-ORDINATOR

JUDY LIAN YEE LING

LIST OF PANEL MEMBERS

1.  Shirney Chua (Leader) SMK Kolombong, Inanam

2.  Phoon Chiew Fun SMK Chung Hwa, Tenom

3.  Seak Sain Yon SMK Konven St. Ursula, Tawau

4. Aileen Beh Chik Heang SMK Datuk Peter Mojuntin, Penampang

5. Sudirman Darise SMK Bongawan, Papar

6. Surianih Sewan SMK Sri Nangka, Tuaran

7. Ting Kai Chu SMK St. Michael, Penampang

8. Farah Ibrahim SMK Agama, Kota Kinabalu

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8/10/2019 Sabah Add Math P1 & Ans 2