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Section 1 (Paper 1)

Answerallquestions.

1. Diagram 1 shows the relation between set Mand setN. State

Gambarajah 1 menunjukkan hubungan antara set M dan set N. Nyatakan(a) the object of 4,

objek bagi 4,

(b) the type of the relation. [2 marks]

jenis hubungan,

Diagram 1

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

(b)

2. The arrow diagram below shows the relation between setPand set Q.

Gambarajah anak panah di bawah menunjukkan hubungan antara set P dan set Q.

(a) the co domain,

codomain,

(b) the range, of the function.

julat, bagi fungsi tersebut.

[2 marks]

Diagram 2

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

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

3. It is given that1

and2

. Find

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1

1

2

2

3

3 4

4

0-1Set M

Set N

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Diberi1

dan2

. Cari

(a) g,

(b) fg. [3 marks]

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

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

4. Given the function = , find the value ofm if1

= .

Diberi fungsi , cari nilai m jika1

. [3 marks]

Answer: m = ......................................

5. Given the functions: 2 4x x +

and

10: 2x x

, f ind

Diberi f ungsi : 2 4x x + dan 10

, cari

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(a) the functiong,

fungsi g,

(b) the value ofx when the functionf mapped onto itself. [3 marks]

nilai x apabila fungsi f dipetakan kepada diri sendiri.

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

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

6. Solve the quadratic equation ( ) ( )2 1 3 8 1x x x+ = + . Give your answers correct tofour significant figures.

Selesaikan persamaan kuadratik ( ) ( )2 1 3 8 1x x x+ = + . Beri jawapan anda betul kepadaempat angka beerti.

[ 3 marks]

Answer: x = ......................................

7. Form the quadratic equation which has the roots3

2and 4 . Give your answer in the

form of 2 0ax bx c+ + = , where a, b and c are constants.

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Bentukkan persamaan kuadratik yang mempunyai punca3

2dan 4 . Berikan jawapan anda

dalam bentuk 2 0ax bx c+ + = , dimana a, b dan c adalah pemalar. [2 marks]

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

8. Given that the roots of the quadratic equation 2 8 0x hx + = arep and 2p, find the

values ofh.

Diberi punca bagi persamaan kuadratik 2 ialah p dan 2p, cari nilai h.

[3 marks]

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

9. Given that the quadratic equation ( ) 3232 =+ mxmx has two equal roots, findthe values ofm. [3 marks]

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Diberi persamaan kuadratik ( ) 3232 =+ mxmx mempunyai dua punca yang sama.Cari nilai-nilai yang mungkin bagi m.

Answer: m =

10. Find the range of values ofksuch that the quadratic equation ( )2 8 2 x x k x k + + = has two real roots.

Cari julat nilai k supaya persamaan kuadratik ( )2

8 2 x x k x k + + = mempunyai dua nilai

yang nyata. [3 marks]

Answer: ..

11. Given2= . State

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Diberi2

.Nyatakan

(i) the minimum value of ,

nilai minimum bagi

(ii) the corresponding value ofx.

Nilai x yang sepadan. [3 marks]

Answer: (i) ...............................

(ii)x =..........................

12. In the Diagram 2 below, point (2, 3) is a turning point of the graph which has an

equation of ( )2

y p x h k = + + . find values ofp, h and k. [3 marks]

Dalam rajah 2 di bawah, titik(2, 3) ialah titik lengkok balas bagi graf fungsi

( )2

y p x h k = + + . Cari nilai p, h dan k.

Diagram 3

Answers :p = ....................................

h = ....................................

k= ....................................

13. Sketch graph of quadratic function ( ) ( )2

2 1 18f x x= + on the axes below and

label they-intercept, maximum or minimum point and the axis of symmetry.

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( )0,23

( )2,3x

y

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Lakarkan graf fungsi kuadratik ( ) ( )2

2 1 18f x x= + pada paksi di bawah dan tandakan

pintasan y, titik maksimum atau minimum dan paksi simetri. [4 marks]

Answer:

14. Find the range of values ofx for which 6 27x x . [ 3marks ]

Cari julat nilai x jika .

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

....

Section 2 (Paper 2)

Answer all questions.

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1. Given that functionsfandgare defined as2:f x x and :g x ax b + where a

and b are constants.

Diberi fungsi f dan g ditakrifkan oleh2

:f x x dan :g x ax b + di mana a dan b

adalah pemalar.

(a) Given that ( ) ( )1 1f g= and ( ) ( )3 5f g= , find the values of a and b.

Diberi ( ) ( )1 1f g= dan ( ) ( )3 5f g= , cari nilai a dan b.

(b) With the values a and b obtained from (a), find ( )gg x and 1g .

Dengan nilai a dan b yang diperolehi, cari ( )gg x dan 1g . [8 marks]

2. Given : 3 2f x x and : 15

xg x + , find

Diberi : 3 2f x x dan : 15

xg x + , cari

(a) ( )1f x , [2 marks]

(b) ( )1f g x , [3 marks]

(c) x such that ( )1f g x = 3. [3 marks]

x jika ( )1f g x = 3.

3. (a) Given that and are the roots of the quadratic equation 22 7 6 0x x+ = ,

form a quadratic equation with roots ( + 1) and ( + 1). [4

marks]

Diberi dan adalah punca-punca bagi persamaan kuadratik 22 7 6 0x x+ = ,

bentukkan persamaan kuadratik yang mempunyai punca-punca ( + 1) dan ( + 1).

(b) Find the value ofp such that ( ) ( )2 4 2 2 1 0p x p x p+ + + = has equal roots.

Hence, find the root of the equation based on the value ofp obtained.

Cari nilai p jika ( ) ( )2

4 2 2 1 0p x p x p+ + + = mempunyai dua punca yang sama.

Seterusnya, cari punca bagi persamaan tersebut berdasarkan nilai p yang diperolehi.

[4 marks]

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4. Given the function ( ) ( )227 16f x mx x x n= = +- - - for all real values ofx where

m and n are positive, find

Diberi fungsi ( ) ( )22

7 16f x mx x x n= = +- - - untuk semua nilai nyata x di mana m

dan n adalah positif, cari

(a) the values of m and n,

Nilai m dan n, [2 marks]

(b) the maximum point off(x),Titik maksimum bagi f(x) [2 marks]

(c) the range of values ofx so thatf(x) is negative. Hence, sketch the graph off(x) and

state the axis of symmetry.

Julat nilai x supaya f(x) adalah negatif. [6 marks]

5. The below figure shows the curves of2 3 8y x x qx= + and ( )

23 3y x p= +

that intersect at 2 pointsA andB on thex-axis. Find

Rajah di bawah menunjukkan lengkok2

3 8y x x qx= + dan ( )2

3 3y x p= + yang

bersilang di dua titik A dan B pada paksi x. Cari

(a) the value ofp and qnilai p dan q [5 marks]

(b) the minimum value of each curve.

Nilai minimum bagi setiap lengkok. [5 marks]

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( )2

3 3 y x p= +

2

3 8 y x x qx= +

A Bx

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6. A piece of wire of length 24 cm is cut into two pieces, with one piece bent to form a

squareABCD and the other bent to form a right-angled trianglePQR. The diagram

below shows the dimensions ofthe two geometrical shapes formed.

Seutas dawai sepanjang 24 cm dipotong kepada dua bahagian, dengan satu bahagian

dibentukkan menjadi segiempat sama ABCD dan satu lagi dibentukkan menjadi segitiga tepat

PQR. Rajah di bawah menunjukkan ukuran bagi kedua-dua bentuk tersebut.

The total area of two shapes is 15 cm2,Jumlah luas kedua-dua bentuk adalah 15 cm2,

(a) show that 6 21x y+ = and ( )22 1 30x y x+ + = .

Tunjukkan 6 21x y+ = dan ( )2

2 1 30x y x+ + = . [4 marks]

(b) Find the values ofx andy. Cari nilai x dan y. [6 marks]

7. Solve the simultaneous equations and give your answers correct to three decimal

places,

Selesaikan persamaan serentak di bawah dan berkan jawapan anda betul kepada 3 tempat

perpuluhan,

2 2x y+ =22 7 0y xy = [6 marks]

END OF QUESTIONS

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x cm

x cm ( )1 x cm+( )2 x cm+

y cm

A

CD

B P

R S