KSSM MM F4C1

QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

FUNGSI DAN PERSAMAAN KUADRATIK DALAM SATU PEMBOLEH UBAH
KERTAS 1

QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE
PAPER 1

1 Cari nilai k dalam persamaan kuadratik yang berikut.
Find the values of k in the following quadratic equation.

+ 4 3
2 = + 3

A = −1, = 1 C = −3, = 1
B = −6, = −1 D = 2, = 3

2. Rajah di bawah menunjukkan graf suatu fungsi.
The diagram shows the graph of a function.

Cari nilai h. C5
D6
Find the value of h.
A −5 Konstruk: Mengingat dan memahami
B −3

3. Rajah menunjukkan graf bagi fungsi = −3( − 4)2.
Diagram shows the graph of the function = −3( − 4)2.

Cari koordinat bagi titik maximum k C (4, 0)
D (2, 0)
Find the coordinate of the maximum point k
A (12, 0)
B (6, 0)

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

4. Rajah menunjukkan suatu fungsi kuadratik yang dilukis pada satu satah Cartesan.
Diagram shows a quadratic equation drawn on a Cartesian plane.

Cari persamaan bagi graf itu.

Find the equation of the graph. C = 4 − 2
A = 2 − 2 D = 4 + 2
B = 2 + 2

Konstruk:

Mengingat

5. Antara berikut, yang manakah mewakili graf bagi = 3−dm a en −m2.a h2a.mi
Which of the following represents the graph of = 3

AC

BD

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

FUNGSI DAN PERSAMAAN KUADRATIK DALAM SATU PEMBOLEH UBAH
KERTAS 2

QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE
PAPER 2

1. Selesaikan persamaan kuadratik yang berikut.

Solve the following quadratic equation.
1 5
− 2 = 4 + 3

[4 markah/ marks]

Jawapan / Answer:

2. Rajah di bawah menunjukkan sebuah segi tiga bersudut tegak.
The diagram below shows a right-angled triangle.

Cari nilai . [4 markah/ marks]
Find the value of .
Jawapan / Answer: PAGE 3

KSSM FORM 4 MATHEMATICS CHAPTER 1

QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

3. Diberi salah satu punca bagi persamaan kuadratik 2 − 5 = 4 − ialah −4
dengan keadaan ialah pemalar. Cari
Given one of the roots of the quadratic equation 2 − 5 = 4 − is −4 where is
a constant. Find
(a) nilai ,
the value of ,

(b) punca yang satu lagi bagi persamaan. [5 markah/ marks]
the other root of the equation.

Jawapan / Answer:
(a)

(b)

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

4. (a) Lakarkan graf bagi fungsi kuadratik = 2 − 4 − 5.
Sketch the graph of quadratic function = 2 − 4 − 5.

(b) Seterusnya, tentukan [6 markah/ marks]
Hence, determine
(i) persamaan paksi simetri,
the equation of the axis of symmetry,
(ii) nilai minimum bagi .
the minimum value of .

Jawapan / Answer:
(a)

(b) (i)
(ii)

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

5. (a) Tentukan koordinat titik minimum bagi fungsi kuadratik = + − .
Determine the coordinates of the minimum point for the quadratic function
= + − .

(b) Seterusnya, lakarkan graf bagi fungsi kuadratik = 2 + 2 − 3 .
Hence, sketch the graph of quadratic function = 2 + 2 − 3 .
[7 markah/ marks]

Jawapan / Answer:
(a)

(b)

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

6. Pak Samad bercadang untuk membina sebuah kebun sayur yang berbentuk segi empat
tepat ABCD seperti dalam rajah di bawah. Diberi panjang AE = 12 m.
Pak Samad plans to build a vegetable garden which is in the shape of rectangle
ABCD as shown in diagram below. Given the length of AE = 12 m.

(a) Bentuk satu ungkapan bagi luas segi empat ini, L m2, dalam sebutan x.
Form an expression for the area of the rectangle, L m2, in terms of x

(b) Diberi luas kebun sayur tersebut ialah 252 m2. Hitung nilai x.
Given the area of the garden is 252 m2. Calculate the value of x.

(c) Pak Samad turut bercadang untuk memagari kawasan berlorek dengan pagar
dawai bagi mengelakkan pencerobohan haiwan liar. Beliau membeli 2
gulung pagar dawai dengan Panjang setiap gulung ialah 35 m. Tentukan
sama ada pagar dawai yang dibeli itu mencukupi untuk memagari kebun
tersebut.
Pak Samad also plans to fence the shaded region with mesh wire for
preventing the aggression of wild animals. He bought 2 rolls of mesh wire
with a length of each roll is 35 m. Determine whether the mesh wire bought
is sufficient to fence the garden.
[10 markah/ marks]

Jawapan/ Answer:
(a)

(b)

(c)

KSSM FORM 4 MATHEMATICS CHAPTER 1 PAGE 7

QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE [ 4 markah / marks]

EXTRA EXERCISES
1. Selesaikan persamaan kuadratik berikut:

Solve the following quadratic equation:
(2 − 1)2 = 3 − 2

Jawapan/Answer

2. Lakar graf fungsi kuadratik yang berikut. [ 4 markah / marks]
Sketch the following graph of quadratic functions.
( ) = 2 − 10 + 16

Jawapan/Answer

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

3. Sempena cuti hujung minggu, Diana ingin membuat sebuah taman bunga di laman
rumahnya. ABCD ialah pelan laman rumahnya. Taman bunga APQ berbentuk segitiga.
Diberi luas seluruh ruangan laman rumahnya ialah 20 m2. Cari panjang dan lebar, dalam m,
seluruh laman rumahnya.
During the weekend holidays, Diana plans to create a flower garden at her lawn. ABCD is
the plan for her house lawn. The flower garden is APQ and triangle-shaped. Her entire lawn
area is 20 m2. Find the length and width, in m for her house lawn.

[ 4 markah / marks]

Jawapan/Answer

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

4. Rajah di bawah menunjukkan sebahagian daripada graf bagi fungsi kuadratik ( ) = ( −
)( − ) dengan keadaan p < q. Titik R ialah titik maximum bagi graf fungsi kuadratik
tersebut.
The diagram below shows part of the graph of the quadratic function ( ) = ( − )( −
) where p < q. Point R is the maximum point of the graph of the quadratic function.

a) Hitung nilai

Calculate the value of

(i) p (ii) q (iii) a

b) Tuliskan persamaan kuadratik tersebut. [ 3 markah / marks]
Write the quadratic equation of the function. [ 2 markah / marks]
[ 2 markah / marks]
c) Tentukan persamaan paksi simetri. [ 2 markah / marks]
Determine the equation of the axis of symmetry.

d) Nyatakan koordinat titik R.
State the coordinates of point R.

Jawapan / Answer:
a) p = …………………

q = ………………...
a = …………………
b)

c)

d)

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

5. Rajah menunjukkan sebuah segitiga.
Diagram shows a triangle.

a) Bentukkan satu ungkapan kuadratik, dalam sebutan h, bagi luas segi tiga itu.
Form a quadratic expression, in terms of h, for the area of the triangle.
[ 2 markah / marks]

b) Diberi bahawa luas segitiga itu ialah 152 m2, cari nilai h
Given that the area of the triangle is 152 m2, find the value of h
[ 4 markah / marks]

c) Asyraf ingin memasang jubin berukuran 0.5 × 0.5 pada keseluruhan kawasan
segitiga tersebut. Berapakah jubin yang diperlukan oleh Asyraf?
Asyraf wants to install tiles measuring 0.5m × 0.5m on the entire area of the triangle.
How many tiles does Asyraf need?
[ 3 markah / marks]

Jawapan / Answer:
a)

b)

c)

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QUADRATIC FUNCTIONS AND EQUATIONS IN ONE VARIABLE

6. Sebuah kereta bertolak dari Tanjung Malim ke Taiping dalam masa (3t – 5) jam.
A car travels from Tanjung Malim to Taiping in (3t – 5) hours.
a) Jika purata laju kereta itu ialah 30t km/j, bentukkan satu ungkapan kuadratik, dalam
sebutan t, untuk mewakili jumlah jarak yang dilalui oleh kereta itu.
If the average speed of the car is 30t km/h, form a quadratic expression, in terms of t,
to represent the total distance travelled by the car.
[ 2 markah / marks]
b) Diberi jarak antara Tanjung Malim ke Taiping ialah 187.5 km, cari jumlah masa dalam
minit yang diambil oleh kereta tersebut.
Given that the distance between Tanjung Malim to Taiping is 187.5 km, find the total
time in minutes taken by the car.
[ 4 markah / marks]
c) Jika kereta tersebut berhenti untuk berehat di Ipoh selama 30 minit, kirakan purata laju
kereta tersebut dalam km/j.
If the car stops to rest in Ipoh for 30 minutes, calculate the average speed of the car in
km/h.
[ 3 markah / marks]

Jawapan / Answer:
a)

b)

c)

KSSM FORM 4 MATHEMATICS CHAPTER 1 PAGE 12