Add Mathas Spb 2008 - Paper 1

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3472/2 2008 Hak Cipta SBP [Lihat sebelahSULIT

SEKOLAH BERASRAMA PENUHBAHAGIAN PENGURUSAN

SEKOLAH BERASRAMA PENUH / KLUSTERKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAANSIJIL PELAJARAN MALAYSIA 2008

Kertas soalan ini mengandungi 15 halaman bercetak

For examiners use only

Question Total MarksMarks

Obtained1 32 33 34 35 36 37 38 39 3

10 411 412 413 414 315 216 317 418 3

19 320 321 322 323 324 425 3

TOTAL 80

MATEMATIK TAMBAHAN

Kertas 1Dua jam

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

1 This question paper consists of 25 questions.

2. Answer all questions.

3. Give onlyone answer for each question.

4. Write your answers clearly in the spaces provided inthe 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 newanswer.

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 : ..

3472/1Matematik TambahanKertas 1Ogos 20082 Jam

Tutor Maths Mr Muruli


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

ALGEBRA

12 4

2b b ac

xa

2 a m a n = a m + n

3 a m a n = a m - n

4 (a m) n = a nm

5 log a mn = log am + log a n

6 log anm

= log am - log a n

7 log a mn = n log a m

8 log ab =a

b

c

c

loglog

9 Tn = a + (n-1)d

10 S n = ])1(2[2

d nan

11 T n = arn-1

12 S n =r r a

r r a nn

1)1(

1)1(

, (r 1)

13r

aS

1, r


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3

STATISTIC

1 Arc length, s = r

2 Area of sector , L = 212

r

3 sin 2 A + cos 2 A = 1

4 sec 2 A = 1 + tan 2 A

5 cosec 2 A = 1 + cot 2 A

6 sin 2 A = 2 sin A cos A

7 cos 2 A = cos 2 A sin 2 A= 2 cos 2 A - 1= 1 - 2 sin 2 A

8 tan 2 A = A

A2tan1

tan2

TRIGONOMETRY

9 sin ( A B) = sin A cos B cos A sin B

10 cos ( A B) = cos A cos B sin A sin B

11 tan ( A B) = B A B A

tantan1tantan

12C

c B

b A

asinsinsin

13 a 2 = b2 + c2 - 2bc cos A

14 Area of triangle = C ab sin21

1 x = N

x

2 x = f

fx

3 = N

x x 2)(=

2_2

x N

x

4 = f

x x f 2)(=

22

x f

fx

5 m = C f

F N L

m

21

6 10

100Q

I Q

71

11

w I w

I

8)!(

!r n

nPr n

9!)!(

!r r n

nC r

n

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

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

12 Mean = np

13 npq

14 z =

x



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2

Blank Page



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Answer all questions.

1 . A function f maps the elements from set { 3,4,9,16,25}P m

to set Q = { 0, 3, 8, 15, 24 } as shown below in ordered pairs :{ ( 3m , 0), (4, 3), (9, 8), (16, 15 ), (25, 24 ) }

(a) Write down the function notation for f .

(b) State the value of m.

(c) State the codomain.

[ 3 marks ]

Answer : ( a )..

( b )......

( c )..................................

2 . Given that function : 3, 0 f x ax a and 2 : 16 f x x b , find the value of a and of b.

[ 3 marks ]

Answer : a =.

b =.............................. 3

2

3

1

For examiners

use only



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4

3 . Given that function : 3 , 0k

f x x x

, and 1 4: , f x x h x h

, find the value of h

and of k .

[ 3 markah ]

Answer : h = .........

k =.....................................

4. Given m and -3 are the roots of a quadratic equation 22 4 1 x x k , find the valueof m and of k .

[ 3 marks ]

Answer : m =.........

k =.....................

For examiners

use only

3

4

3

3



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5. Given that quadratic equation x(3 x p) = 2 x 3 has no roots, find the range of valuesof p.

[ 3 marks ]

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

___________________________________________________________________________

6. Diagram 1 shows the graph of a curve q p x x f 2)(2)( , where pand q are constants.

Diagram 1

Given the straight line 3 x is the axis of symmetry of the curve and parallel to the y-axis. Find

(a) the value of p,

(b) the value of q,

(c) the turning point of the curve )( x f .

[3 marks ]

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

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

(c). .................................

3

5

3

6

For examiners

use only

x

q p x x f 2)(2)(

8

O

3 x

f(x)



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7. Find the range of the values of x for which )52(2)12(3 x x x .[3 marks ]

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

8. Solve the equation2

3

2

18 x

x .

[3 marks ]

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

9. Solve the equation x x 2log1)25(log 55 .[3 marks ]

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

7

9

3

8

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10. Given that 2log2log 927 q p , express p in terms of q.[4 marks ]

Answer : .........

11 . An arithmetic progression has 9 terms. The sum of the first four terms is 24 and the

sum of all the odd number terms is 55. Find

a) the first term and the common difference,

b) the seventh term.

[4 marks ]

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

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

4

10

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use only

4

11



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12 . For a geometric progression, the sum of the first two terms is 30 and the third

term exceeds the first term by 15. Find the common ratio and the first term

of the geometric progression.

[4 marks ]

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

13. Diagram 2 shows the graph of xy against 2 x .

The variables x and y are related by the equation xk

x y2 , where k is a

constant. Find the value of h and of k .[4 marks ]

Answer : h = .

k = ......4

13

4

12

For examiners

use only

(0 , h)

2 x

(7 , 2)

O

xy

Diagram 2



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14. In Diagram 3 below, the equation of straight line LM is6 x

14 y

. The points

L and M lie on the x-axis and y-axis respectively.

Find the equation of a straight line which is perpendicular to LM and passes

through the point M .[3 marks ]

Answer : .

15. In Diagram 4 , OA a and OB b . On the same square grid , draw the line that

represents the vector 3OC a b .[ 2 marks ]

2

15

3

14

For examiners

use only

x

y

0

M

L

Diagram 3

O

A

B

Diagram 4



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16. Given (2, 5), (3,4) A B and ( , )C p q . Find the values of p and q such that

~ ~2 9 5 AB BC i j

.

[3 marks ]

Answer : ......

___________________________________________________________________________

17. Solve the equation 3sin2cos4 x x for 3600 x .

[4 marks ]

Answer: ............4

17

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use only

3

16



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18 . Diagram 5 shows a sector BOC of a circle with centre O .

Given the perimeter of the sector BOC is 24.5 cm , calculate

(a) the radius of the sector

(b) the area of the sector.[3 marks ]

Answer : a)...

b) .___________________________________________________________________________

19 . Given 3)35(2

)( x

x f , find the value of (2) f .

[3 marks ]

Answer:

3

19

3

18

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use only

B

O

C

0.45 rad

Diagram 5



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20 . Find the equation of normal to the curve x x y 53 at the point when 1 x .

[ 3 marks ]

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

21 . Given that2

5

6)( dx x f , calculate dx x

x f 5

2 4)( .

[3 marks ]

Answer : ..

22 . It is given that the sum of 5 numbers is . The mean of the sum of the square is 200and the variance is 3 2 . Express in terms of .

[3 marks ]

Answer : ..

3

20

3

21

3

22

For examiners

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3472/1 2007 Hak Cipta SBP SULIT

23. A pack of present containing three pens are chosen from 4 blue pens and 5 black pens.Find the probability of getting at least one black pen in the pack of present.

[3 marks ]

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

___________________________________________________________________________

24.

Diagram 6

Diagram 6 shows six cards of different letters.

(a) Find the number of possible arrangements beginning with P .

(b) Find the number of these arrangements in which the vowels are separated.

[ 4 marks ]

Answer : ( a )

( b )

For examiners

use only

4

24

3

23

P O L I T E



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25. X is a random variable which is normally distributed with mean and standard

deviation of 6. Find

(a) the value of , if the z-value is 1.5 when x = 42 ,

(b) P( X < 47 ).

[3 marks ]

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

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

END OF QUESTION PAPER

3

25

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Add Mathas Spb 2008 - Paper 1

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