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SULIT ADD MATH PPT F4 2019

JAWAB SEMUA SOALAN

1. Diagram shows the relation between set A and set B
Rajah menunjukkan hubungan antara set A dan set B

Set A Set B
r
p s
q t
w
State/ Nyatakan
(a) the type of relations [3 marks]

jenis hubungan
(b) the image of p

Imej bagi p
(b) the range of the relations

julat bagi hubungan itu

a)

b)
c)

1

SULIT ADD MATH PPT F4 2019

2. Diagram shows, elements in set B is the images of the elements of the set A
Rajah menunjukkan unsur dalam set B adalah imej bagi unsur dalam set A

6 36
5 25
-5 Set B
-6

Set A

(a) State the type of relation between set A and set B
Nyatakan jenis hubungan antara set A dan set B

(b) Write a relation between set A and set B by using the function notation.
Tuliskan hubungan antara set A dan set B menggunakan tatatanda fungsi

[3 marks]

a)

b)

.
3. Diagram shows the function f maps x to y and the function g maps y to z .
Diagram shows the function f memetakan x ke y dan fungsi g memetakan y ke z

Determine / Tentukan (b) gf (−6) [3 marks]
2
(a) f −1 (−1)
a)

b)

SULIT ADD MATH PPT F4 2019
[3 marks]
4. Given that f : x → 5 − x , find
6

Diberi f : x → 5 − x , cari
6

(a) function f −1 / fungsi f −1
(b) the value of f −1 (2) / nilai f −1 (2)

a)

b)

5. Given the function f : x → hx − 3 and f −1 : x → 2x + k , where h and k are constants.
Find the value of h and k .

Diberi fungsi f : x → hx − 3 dan f −1 : x → 2x + k , dengan keadaan h and k adalah

pemalar. Cari nilai h dan k .

[3 marks]

3

SULIT ADD MATH PPT F4 2019

6. Functions f and g are defined as f : x → 3x − 2 and g : x → 1 − x , x  0 , find
x

gf (x)

Fungsi f dan g ditakrifkan sebagai f : x → 3x − 2 dan g : x → 1 − x , x  0 , cari
x

gf (x)

[3 marks]

7. Given that f : x → 3x −16 and fg : x → 3x2 + 9x − 4 , find [5 marks]
Diberi f : x → 3x −16 dan fg : x → 3x2 + 9x − 4 , cari

(a) function g
fungsi g

(b) the values of x if fg(x) = g(x)
nilai x jika fg(x) = g(x)

4

SULIT ADD MATH PPT F4 2019
[4 marks]
8. Given g : x → 5x − 2 and gf (x) → 3x2 + 4 , find
Diberi g : x → 5x − 2 dan gf (x) → 3x2 + 4 , cari
(a) g −1 (2)
(b) f (x)

a)

b)

9. Solve the quadratic equation 2 ( − 4) = (1 + )( + 2) by using formula. Write
Selesaikan persamaan kuadratik 2 ( − 4) = (1 + )( + 2) menggunakan rumus.
Tulis jawapan anda betul kepada 4 angka bererti.

[4 marks]

5

SULIT ADD MATH PPT F4 2019

10. Solve the equation 1 − 1 = 3 by using completing the square. Write your answers
2 2

correct to four significant figure.

Selesaikan persamaan 1 − 1 = 3 dengan menggunakan penyempurnaan kuasa dua
2 2

Tulis jawapan anda betul kepada 4 angka bererti..

[4 marks]

11. If α and β are the roots for the quadratic equiation 2 2 + 3 + 4 = 0 ,find a new

1 1 .

quadratic equation for if their root is and

Jika α dan β adalah punca-punca bagi persamaan 2 2 + 3 + 4 = 0 ,bentukkan

satu persamaan kuadratik yang baru jika punca-puncanya 1 dan 1.

[4 marks]

6

SULIT ADD MATH PPT F4 2019

12. If α and β are the roots for the quadratic equiation 5 + 1 = −2 2 ,find a new

quadratic equation for if their root is + 2 and + 2.

Jika α dan β adalah punca-punca bagi persamaan 5 + 1 = −2 2 ,bentukkan satu

persamaan kuadratik yang baru jika punca-puncanya + 2 dan + 2.

[4 marks]

13. Find the values of k if the quadratic equation x2+2kx+k+6=0 has equal roots.
Cari nilai-nilai bagi k jika persamaan x2+2kx+k+6=0 mempunyai dua punca yang

sama.

[3 marks]

7

SULIT ADD MATH PPT F4 2019

14. Given that px2+(q+2) x - 4=0 has two equal roots, express p in term of q.
Diberi bahawa px2+(q+2) x - 4=0 mempunyai dua punca yang sama, ungkapkan p

dalam sebutan q.
[3 marks]

15. Diagram shows the graph of the function y = 8 + (x − k)2 where k is constant.

4 (6, 4)

Find / Cari [4 marks]
(a) the value of k 8
nilai k
(b) the equation of the axis of symmetry
persamaan paksi simetri
(c) the coordinates of the maksimum point
koordinat titik maksimum

a)

b)

c)

SULIT ADD MATH PPT F4 2019

16. Diagram shows the graph of f (x) = a(x + p)2 + q where a, p and q are constants The
curve y = f (x) has a minimum point (4, - 5)
Rajah menunjukkan graf f (x) = a(x + p)2 + q dengan keadaan a, p dan q adalah
pemalar. Lengkung y = f (x) mempunyai titik minimum (4, - 5)

State / Nyatakan [ 4 marks ]
(a) the range of the values of a, / julat nilai a
(b) the value of p / nilai p
(c) the value of q / nilai q
(d) the equation of the axis of symmetry.

persamaan paksi simetri

a)

b)

c)

d)

9

SULIT ADD MATH PPT F4 2019

17. The quadratic function f(x) = -x2 +2x + k2, where k is a constant, has maximum value
of 5 , find the value of k.

Fungsi kuadratik f(x) = -x2 +2x + k2 , dengan keadaan k ialah pemalar, mempunyai
nilai maksimum 5. Cari nilai-nilai yang mungkin bagi k.

[4 marks]

18. Find the range of values of x for ( 2 − 1)( + 4) > 11 . [3 marks]
Cari julat nilai x bagi ( 2 − 1)( + 4) > 11

10

SULIT ADD MATH PPT F4 2019

19. Given that ( ) = 28 + 2 − 2 , find the range of values of x if ( ) ≤ 4
Diberi ( ) = 28 + 2 − 2 , cari julat nilai x jika ( ) ≤ 4
[3 marks]

20. Sketch the graph of quadratic function ( ) = −4 2 − 5 + 12 , then determine the
maximum or minimum point and the equation of axis symmetry.
Lakarkan graf bagi fungsi kuadratik ( ) = −4 2 − 5 + 12 , kemudian tentukan
titik maksimum atau minimum dan persamaan paksi simetri.

[6 marks]