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Soalan

Markah Markah

1 2

2 43 3

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11 2

12 4

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14 2

15 4

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17 3

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Jumlah 80

SEKOLAH TUN FATIMAH,JOHOR BAHRU

PEPERIKSAAN PERTENGAHAN TAHUN 2011 347ADDITIONAL MATHEMATICS

Kertas 1 2 jam Dua jam

1 x =a

acbb

2

42

2 am

an = am + n

3 am

an

= am - n

4 (am

)n

= anm

5 logamn = log am + logan

6 logan

m= log am - logan

7 log amn

= n log am

8 logab =a

b

c

c

loglog

9 Distance = 221

2

21)()( yyxx

10 Midpoint (x , y) =

2

21xx

,

2

21yy

11 A point dividing a segment of a line

( x,y) = ,21

nm

mxnx

nm

myny21

12. Area of triangle

= )()(2

1312312133221 1

yxyxyxyxyxyx

NAMA: KELAS:

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ANSWER ALL QUESTIONS

(80 marks)

1 The arrow diagram shows the relation between set P and set Q.

State

(a) the range of the relation

(b) the type of the relation

[2marks]

2 Given the function g:x 6 7x. Find

(a) the object if the image is 13

(b) the value of x if g(x) = 3x - 8

[3marks]

3 A function f is defined by f:x

, x k.

(a) State the value of k

(b) the values of p such that f(p2) = f(2p)

[4marks]

SET Q

SET P

t

s

r

q

p

c

b

a

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4 The arrow diagram shows function m:x 12 5x.

Find

(a) the values of r and s

(b) the value of x such that m maps onto itself

[4marks]

5 Given that h:x5x+2 and k:xx2

-3x + 2. Find

(a)h-1

(4)

(b)kh(x)

[4marks]

6 Given the function f:x a 3x and f-1

:x 6bx +

, where a and b are

constants.Find the values of a and b

[3marks]

s

r

m

-1

4

YX

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7 Solve the quadratic equation 5x(x 1)=(3-x)(x+2).Give your answer correct to

four significant figures

[3marks]

8 Given that p -1 and q +2 are the roots of the quadratic equation x(x-7)= -12,

find the possible values of p and q

[4marks]

9 Given

and

are the roots of the quadratic equation 4x

2= k + 24x,where

k is a constant.find the values of a and k

[3marks]

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10 Find the range of values of h if the quadratic equation (2x-1)(x+3)=h+5 has

two distinct roots

[3marks]

11 If and are the roots of the quadratic equation 4x2 -3x + 2=0, form the

equation with roots 3 + 1, 3 + 1

[4marks]

12 Find the range of value of c if the straight line y= 3x+c does not intersect the

curve y= 3x2 5x +8.

[3marks]

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13 The diagram shows the graph of a quadratic function y=f(x) which intersects

the x-axis at points (2,0) and (8,0).The minimum point is (p,-9) where p is a

constant.

(a) State the value of p

(b) Find the equation of the curve

[3marks]

14 Given f(x) = 7 px x2

= 16 ( q + x )2, where p and q are both positive. Find

the value of p and q

[3marks]

15 The function f(x)= 2x2 5x + k has a minimum value of

.Find the value of

k.

[3marks]

y

y=f(x)

0

(p,-9)

2 8x

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16 Find the range of values of x for which 2x2 7x >15 [2marks]

17 Solve 53n

.

)

n= 125 [ 2 marks]

18 Solve the equation + 2 = 3 [3marks]

19 Solve 2x

. 32x

= 17 [3marks]

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20 Solve the equation + = 4 [4marks]

21 Solve 2m

- 2m+2

+ 2m+3

= 20 [3marks]

22 The following information refers to the equation PQ and RS,which are

perpendicular to each other .

+

= 1

3y = kx + 9

Find the value of k

[3marks]

23 The vertices of a triangle are P(t,-2), Q(5,2) and R(4,6). Given that the area of

the triangle is 36 unit2, find the values of t.

[4marks]

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24 The diagram shows a straight line CD which is perpendicular to AB

a)Given that 3AC = CB, find the coordinate of C

b)State the y-intercept of CD

[4marks]

25 The coordinates of points A and B are (-3,1) and (4,6) respectively. A point R

moves such that RA:RB = 2:3. Find the equation of the locus of R

[3marks]

B(0,4)

O

C

D

A(-8,0)X

y

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