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SEKOLAH TUN FATIMAH,JOHOR BAHRU

PEPERIKSAAN PERTENGAHAN TAHUN 2012

MATEMATIK TAMBAHAN

TINGKATAN 4

Kertas 1 2 jam

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

ones commonly used.

1.

24

2

b b acx

a

2 am

an= a m + n

3 am

an

= am - n

4 (am

)n= a

nm

5 logamn = log am + logan

6 logan

m= log am - logan

7 log amn

= n log am

8 logab =a

b

c

c

log

log

NAMA: KELAS:

9. Distance =2

21

2

21 )()( yyxx

10 Midpoint

(x , y) =

2

21 xx ,

2

21 yy

11 A point dividing a segment of a line

(x,y) = ,21

nm

mxnx

nm

myny 21

12 Area of triangle =

)()(2

1312312133221 1

yxyxyxyxyxyx

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SULIT 3472/1

ANSWER ALL QUESTIONS(80 marks)

1 Diagram 1 shows a linear function f(x) = 2x + 1.State(a) f (2)

(b) f-1 ( 7)

Diagram 1

(2marks)

2 Given the function g(x) = { 2x + 1 , x 4x 3 ,x > 4 , find

(a) g(6)(b) g(-2)

(2marks)

3 Given the functions h:x 3x+2, and g:x6x-5. Find(a) h-1(4)(b) gh-1(x)

(4marks)

4 Given the functions f(x) = 4 8x and gf(x) = 2x + 9, find g(x) (3marks)

x

f(x)

9

8

7

6

5

4

3

2

1

1 32 4O

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SULIT 3472/1

5 Diagram 5 shows the graph of the function f(x) = 2x + 3 - 2, for thedomain -3 x2.

(4marks)

6 Form the quadratic equation which has the roots

and 3.Give your answer

in the form of ax

2

+ bx + c =0, where a, b , and c are constants

(2marks)

7 Solve the equation

-

= 2. Give your answer correct to three decimal

places

(3marks)

8 The roots of the quadratic equation x2 + 2x -8 =0 are 2 and q. Find the valueof q

(2marks)

9 The quadratic equation x2 2x + 1=k(-x-2) has two equal roots.Find the

possible values of k

(4marks)

State

(a) the value of k

(b)the range of f(x) corresponding to

the given domain

Diagram 5

f(x)

(-3,1)

k -2

O x

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SULIT 3472/1

4

10 A quadratic equation x2 + x = px 4 has two distinct roots. Find the range of

values of p(4marks)

11

O

(3marks)

12 The quadratic function f(x) = 5n - (3m + x )2

has a maximum point

(-2,10).Find

(a) the value of m and n

(b)the equation of the curve if it is being reflected through the x -axis

(3marks)

13 Find the range of the values of x for (x-3)2

< 3 x (3marks)

Diagram 11 shows the graph of a

quadratic function y= (x+p)2

-1, where

p and k are constants.Given (4,k) is

the minimum point of the curve.

(a)Find the value of p and k

(b)Write the equation of the axis of

symmetry of the curve

Diagram 11

y

x

4 k

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14 Given y mx=0 is the equation of a tangent to the curve y2

= 5x -9.Find the

possible values of m

(3marks)

15 Diagram 15 shows the graph of y = 3k kx x2

Diagram 15

Find the range of k

(3marks)

16Solve the equation 81

3x=

(3marks)

17 Express 42n+1

+ 42n

- 12 ( 42n-1

) to its simplest form (3marks)

18 Solve the equation 2 + = 2 (3marks)

x

y

O

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19 Given that = , find the value of y (4marks)

20 Solve the equation 6x+2 = 7 3x+1 (4marks)

21Given that = x and = y, express

in terms of x

and y

(4marks)

22 (4marks)

3x 6y=2

y + kx 4 = 0

Determine the value of k if the two

straight lines are

(a)parallel to each other

(b) perpendicular to each other

The following information refers to

the equations of two straight lines.

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SULIT 3472/1

7

23

y

B2

Diagram 23

(3marks)

24y

4 T

O S

Diagram 24

(b) A point P(x,y) moves such that PS=PT. Find the equation of locus of P

(3marks)

Diagram 23 shows the straight line AB

which is extended to a point C such

that AB:BC= 2:3.Find the coordinateof point C

Diagram 24 shows a straight

line ST.

(a).Write down the equation

of the straight line in the

form of

+

=1

A 4 8

x

3

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SULIT 3472/1

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25 y

P

O x

Q

(4marks)Diagram 25 shows a straight line PQ

with the equation 4x 3y = 12.Thepoint P lies on the x-axis and the point

Q lies on the y-axis.Find

(a) the mid point of PQ

(b)the equation of the perpendicular

bisector of PQ

Diagram 25