Add Maths Form 4 Paper 1 Midterm 2012

8/11/2019 Add Maths Form 4 Paper 1 Midterm 2012

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STUDENTS NAME: __________________________ CLASS:

MID YEAR EXAMINATION

2012

ADDITIONAL MATHEMATICS

PAPER 1

SENIOR 4

TWO HOURS

Instructions to candidate:

DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO

1. This question paper consists of 25 questions.

2. Answer ALL questions.

3. Show your working. It may help you to get marks.

4. The diagrams in the question are not drawn to scale unless stated.

5. You may use a non programmable scientific calculator.

SEKOLAH SERICAHAYA (Kayangan Heights)Lot 5, Jalan Merah Saga, U9/5,40250 Shah Alam, Selangor.Tel: +603 7846 3985Fax: +603 7846 3980Careline: 1-300-88-REAL(7325)www.real.edu.my

This question paper consists of 13 printed pages.


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

ALGEBRA

1

2 42

b b ac x a

2 am an = a m + n

3 am a n = a m - n

4 (a m) n = a nm

5 log a mn = log am + log a n

6 log a nm

= log am - log a n

7 log a mn = n log a m

8 log a b =a

b

c

c

log

log

9 T n = 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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STATISTICS

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

n P r 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

TRIGONOMETRY

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

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


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Answer all questions.

1. Function g is defined by 2

: 7 ,h

g x x h x h

. Given that 4 13 g , find the value

of .h [3 marks ]

Answer : h ..

...

2.

The following information above refers to the functions f and . g

(a) State the value of h.

(b) Find the value of fg -1(3)[3 marks ]

Answer : (a) ..

(b)...

3

2

Forexaminers

use only

3

1


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3. The function g is defined as : 7 4 g x x , find(a) 1 ( ) g x

(b) the value of p when 1( ) 2 g p

[4 marks ]

Answer : (a) ..

(b) ...

4. Given the function ( ) 2 1 g x x and the composite function ( ) 1 4hg x x , find ( ).h x

[3 marks ]

Answer : ( )h x ....

5. Given the function : 3 5 .h x x Find

(a) the image of -2

(b) the values of x such that ( ) 4.h x [3 marks ]

Answer : (a) ..

(c) ...

Forxaminers

use only

3

5

3

4

4

3


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6. Diagram 1 shows the graph of the function ( ) 3 2 , f x x for the domain 0 4. x

Diagram 1State

(a) the value of k,

(b) the range of ( ) f x corresponding to the given domain.

[3 marks ]

Answer : (a) ..

(b) ...

7. It is given that -1 is one of the roots of the quadratic equations 2 3 0,mx x k wherem and k are constants. Express m in terms of k .

[3 marks ]

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

8. Given the equation 2 2 x x k have two distinct roots, find the range of values of k .

[3 marks ]

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

3

6

3

7

3

8

Forexaminers

use only


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9. Given that and are the roots of the quadratic equation 22 5 0, x x k where k isa constant.Find

(a) the value of ,

(b) the value of k such that 3.

[3 marks ]

Answer : (a) ..

(b) ...

10. It is given that -2 and p are the roots of the quadratic equation 2 3 0 x x k . State thevalue of p and of k .

[3 marks ]

Answer : p = ..

k =...

11. The quadratic function 2( ) 2 12 f x x x k can be expressed in the form of2

( ) 2( ) 7 f x x h where h and k are constants.

[3 marks ]

Answer : h = ..

k =...

3

9

Forxaminers

use only

3

10

3

11


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( 5, q )

12. Diagram 2 shows the graph of a quadratic function, 25 y x p where p is a constant. The curve y = f ( x) has the minimum point ( k+1 , 4), where q is aconstant.

State(a) the value of p,

(b) the value of q,

(c) the equation of the axis of symmetry.

[4 marks ]

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

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

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

13. Find the range of values of x for which 24 3 4 . x x [3 marks ]

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

Diagram 2

Forexaminers

use only

4

12

3

13


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14. Find the range of values of y if 1 x y and 5 3 . y xy [3 marks ]

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

15. Find the range of values of x for which (2 5) 12. x x [3 marks ]

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

16. Find the range of values of x which satisfies 24 5 1. x x

[3 marks ]

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

Foraminers

use only

3

14

3

15

3

16


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17. Diagram 3 shows the graph of a quadratic function ( ). y f x . The straight line16. y is a tangent to the curve ( ). y f x

Diagram 3(a) Write the equation of the axis of symmetry of the curve.

(b) Express ( ) f x in the form 2( ) , x b c where b and c are constant.

[4 marks ]

Answer : (a) ..

(b) ...

18. Solve the equation 3 3log (3 2) log ( 1) 0 x x .[4 marks ]

Answer : .........

Forexaminers

use only

4

17

4

18


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19. Solve 2 13 27 .81

n n

[3 marks ]

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

20. Solve the equation:12 5(2 ) 144 x x

[3 marks ]

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

21. Solve the equation1

14 16 .2

x x

[3 marks ]

Answer : .

Forxaminers

use only

3

21

3

19

3

20


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22. Given that 3log 2 m and 3log 5 ,n express 9log 20 in terms of m and n.[4 marks ]

Answer : .

23. Solve the equation 5 5log 1 log ( 4). x x

[3 marks ]

Answer : ..

24. Given that 2log m r and 2log ,n t express 8 3log 16mn

in terms of r and t .

[3 marks ]

Answer : ....

3

23

4

22

Forexaminers

use only

3

24


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25. Solve the equation 3 5log (3 1) log (5 7) 1. x x

[3 marks ]

Answer : ....

END OF QUESTION PAPER

Prepared by: Checked by: Verified by: Received by:

.. .. . Mr. Thiyaku Mr. Mahadevan Mdm. Tee Exam Unit

(Subject Teacher) (Subject Teacher) (HOD Mathematics)

Foraminers

use only

3

25


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Documents

Add Maths Form 4 Paper 1 Midterm 2012