2 Quadratic Form4 Add Math

SULIT 6 3472/1

3472/1 SULIT

4 The quadratic equation 21 2 1 0q x x , where q is a constant, has two different roots. Find the range of values of q. [3 marks]

Persamaan kuadratik 21 2 1 0q x x , dengan keadaan q ialah pemalar, mempunyai dua punca yang berbeza. Cari julat nilai q. [3 markah]

Answer/Jawapan:

5

Find the range of values of x for 5

3 32

xx x . [3 marks]

Cari julat nilai x bagi 5

3 32

xx x . [3 markah]

Answer/Jawapan:

For examiners

use only

3

5

3

4

http://edu.joshuatly.com/ http://fb.me/edu.joshuatly

3472/1 [ Lihat sebelah

4 Find the values of k if x2 + 2kx + 2 k = 0 has two equal roots.Cari nilai-nilai k jika x2 + 2kx + 2 k = 0 mempunyai dua punca sama.

[3 marks ][3 markah ]

Answer /Jawapan:

5 Find the range of values of x for (x 4)2 < 6 x.Cari julat nilai x bagi (x 4)2 < 6 x.

[3 marks][3 markah]

Answer/Jawapan:

Forexaminers

use only

3

4

3

5

6


SULIT 9 3472/1

4 Given one of the roots of the quadratic equation 042 2 pxx is three times the other. Find the value of p.

Diberi salah satu daripada punca persamaan kuadratik 042 2 pxx ialah tiga kali ganda punca yang satu lagi. Cari nilai p.

[3 marks] [3 markah]

Answer / Jawapan :

.

5 Find the range of values of x for 16)12(53 2 xxxx . [3 marks]

Cari julat nilai x bagi 16)12(53 2 xxxx . [3 markah] Answer / Jawapan :

4

3

For Examiners

Use

5

3

[Lihat sebelah] Negeri Sembilan SPM 2013 http://edu.joshuatly.com/

http://edu.joshuatly.com/

SULIT 7 3472/1

3472/1 [ Lihat halaman sebelah SULIT

6 Diagram 6 shows the graph of a quadratic function 2f x p x q r , where

p, q and r are constants, has a maximum point at 1, 3 .

Rajah 6 menunjukkan graf fungsi kuadratik 2f x p x q r , dengan keadaan

p, q dan r ialah pemalar, mempunyai titik maksimum di 1, 3 .

Diagram 6 Rajah 6 (a) Find the value of p and of r .

Cari nilai p dan nilai r .

(b) State the equation of the axis of symmetry of the curve. Nyatakan persamaan paksi simetri bagi lengkung itu.


Answer/Jawapan: (a)

(b)

For examiners

use only

4

6

f (x)

x ( 1, 3 )

O

5


33

3472/1

5. Sketch the graph of the function 2( ) ( 3) 4f x x on the given axes for 0 x 5

Lakar pada paksi-paksi yang diberi, graf fungsi kuadratik 2( ) ( 3) 4f x x , untuk 0 x 5. Answer / Jawapan : [2 markah]

6. Given that f(x) = ( 3) 10x x . Find the range of values of x when f (x) 0. Diberi f(x) = ( 3) 10x x . Cari julat nilai x apabila f (x) 0.

[3 markah] Answer / Jawapan :

7. Solve the equation

Selesaikan persamaan 4 x + 2 4 x + 1 = 6. [3 markah]

Answer / Jawapan :

8. Solve the equation 3 3log 6 2 log (3 1)x x

Selesaikan persamaan 3 3log 6 2 log (3 1)x x

. [3 markah] Answer / Jawapan

:

f (x)

x O

3

8

3

7

3

6

2

5



8. Diagram 8 shows the graph of the quadratic function y = f(x). The straight line y = 14is a tangent to the curve y = f(x).Rajah 8 menunjukkan fungsi kuadratik y = f(x). Garis lurus y = 14 ialah tangen kepadalengkung y = f(x).

Diagram 8Rajah 8

(a) State the equation of the axis of symmetry of the curve.Nyatakan persamaan paksi simetri bagi lengkung itu.

(b) Express f(x) in the form of (x + p)2 + q, where p and q are constants.Ungkapkan f(x) dalam bentuk (x + p)2 + q, di mana p dan q adalah pemalar.

(c) Express f(x) in general form.Ungkapkan f(x) dalam bentuk am.

[3 marks][3 markah]

Answer / Jawapan :

(a)

(b)

(c)

51

y

y = 14

x0

Forexaminers

use only

3

8

8



19 Given the equation of the curve, y = 2x2 16 x + 25.Diberi persamaan lengkung, y = 2x2 16 x + 25.

Find,Cari

(a) the coordinate x of turning point.koordinat x bagi titik pertukaran.

(b) the equation of tangent at point A ( 3 , 4).persamaan tangen pada titik A (3,4)

[ 4 marks][4 markah]

Answer / Jawapan:

(a)

(b)

Forexaminers

use only

4

19

17


SULIT 10 3472/1

6 Diagram 1 shows the graph of quadratic function 2( ) ( 1)f x a x k , where a and k are constants. The graph has a minimum point (1, 8) .

Rajah 1 menunjukkan graf fungsi kuadratik 2( ) ( 1)f x a x k , dengan keadaan a dan k adalah pemalar. Graf itu mempunyai titik minimum (1, 8).

Diagram 1 Rajah 1

State

Nyatakan

(a) the value of k,

nilai bagi k,

(b) the value of a,

nilai bagi a, (c) the equation of axis of symmetry.

persamaan bagi paksi simetri.


Answer / Jawapan :

(a)

(b)

(c)

For Examiners

Use

6

3

f (x)

(1, 8)

x O 3

[Lihat sebelah] Negeri Sembilan SPM 2013 http://edu.joshuatly.com/

8

SULIT 3472/1

3472/1 2013 Hak Cipta BPSBPSK SULIT

6 Diagram 6 shows the graph of a quadratic function for .)(7)( 2kxmxf

Rajah 6 menunjukkan graf fungsi kuadratik bagi .)(7)( 2kxmxf

Find

Cari

(a) the value of k,

nilai k,

(b) the value of m,

nilai m,

(c) the coordinates of the maximum point.

koordinat bagi titik maksimum.

[ 4 marks ]

[4 markah]

Answer/Jawapan :

(a)

(b)

(c)

0

Diagram 6

Rajah 6

7 x

y

5

-1

For

Examiners Use

4

6


http://edu.joshuatly.com/

7

SULIT 3472/1

3472/1 2013 Hak Cipta BPSBPSK SULIT

5. The straight line 32 xy does not intersects the curve .32 qxxy

Find the range of values of q.

Garis lurus 32 xy tidak menyilang lengkung .32 qxxy

Cari julat nilai q.

[ 3 marks ]

[3 markah]

Answer/Jawapan :

For Examiners

Use

3

5


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2 Quadratic Form4 Add Math