Page 8 - Top Class Mathematics F4

Mathematics Form 4 Chapter 1 Quadratic Functions and Equations in One Variable

2
3. It is given a quadratic function f(x) = 2x + 3x – 9. 4. An aquarium has a length of (x + 5) cm, a width of x cm
Diberi fungsi kuadratik f(x) = 2x + 3x – 9. SPM and a height of 40 cm. The total volume of the aquarium
2
2017 3
(a) Calculate the roots of the quadratic function. is 30 000 cm . The aquarium will be filled fully with water.
Hitung punca-punca bagi fungsi kuadratik itu. Calculate the value of x.
(b) Then, sketch the graph of the function. Sebuah akuarium mempunyai panjang (x + 5) cm, lebar
Kemudian, lakarkan graf bagi fungsi itu. x cm dan tinggi 40 cm. Jumlah isi padu akuarium itu ialah
3
30 000 cm . Akuarium itu akan diisi penuh dengan air. Hitung
Answer / Jawapan: nilai x.
2
(a) 2x + 3x – 9 = 0
(2x – 3)(x + 3) = 0 Answer / Jawapan:
(x + 5)(x)(40) = 30 000
2x – 3 = 0 or / atau x + 3 = 0 (x + 5)(40x) = 30 000
x = 3 x = –3 2
2 40x + 200x = 30 000
2
40x + 200x – 30 000 = 0
(b) a = 2  0, thus the graph shape is . x + 5x – 750 = 0
2
a = 2  0, maka graf berbentuk . (x – 25)(x + 30) = 0
When x = 0, x – 25 = 0 or / atau x + 30 = 0
Apabila x = 0, x = 25 x = –30
2
f(0) = 2(0) + 3(0) – 9 Thus/ Maka, x = 25 cm
= –9
f(x)

x
–3 O –
3
2
–9

HOTS Challenge

The diagram below shows four circles in a rectangle.
Rajah di bawah menunjukkan empat bulatan dalam sebuah segi empat tepat.

(x + 20) cm

(5x – 40) cm

2
Given that the area of the rectangle is 7.84 m . Find the diameter, in cm, of a circle.
2
DIberi luas bagi segi empat tepat tersebut ialah 7.84 m . Cari radius, dalam cm, bagi satu bulatan.
Answer / Jawapan:
(5x – 40)(x + 20) = 78 400
5x + 100x – 40x – 800 = 78 400
2
5x + 60x – 800 – 78 400 = 0
2
2
5x + 60x – 79 200 = 0
2
x + 12x – 15 840 = 0
(x – 120)(x + 132) = 0
x = 120, x = –132 (not valid/ tidak diterima)
Diameter of a circle/ Diameter bagi satu bulatan
= x + 20
= 120 + 20 HOTS
= 140 cm

Quiz 1
21
PAK-

© Penerbitan Pelangi Sdn. Bhd. 12

01 Top Class Math F4.indd 12 05/12/2020 5:00 PM