Page 6 - Top Class Mathematics F4

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

(c) The diagram below shows the positions of two divers, A and B on different height.
Rajah di bawah menunjukkan kedudukan dua penerjun A dan B pada ketinggian berbeza.

B
7.5 m
A
5 m

(i) Based on the graphs of height-time below, (ii) Calculate the time taken, in second, by both
determine which graph represents each of divers to reach water.
the following divers? Then, state the value Hitung masa yang diambil, dalam saat, oleh kedua-
of p and of q. dua penerjun mencecah air.
Berdasarkan graf tinggi-masa di bawah, tentukan Equation for diver A: h = –14t + 5
2
graf yang manakah mewakili setiap penerjun itu? Persamaan bagi penerjun A: h = –14t + 5
2
Kemudian, nyatakan nilai p dan nilai q.
–14t + 5 = 0
2
Height, h(m) Height, h(m) t = –5
2
Tinggi, h(m) Tinggi, h(m) –14
p t = 0.60
q Equation for diver B: h = –14t + 7.5
2
2
2
h(t) = –14t + p h(t) = –14t + q
Persamaan bagi penerjun B: h = –14t + 7.5
2
–14t + 7.5 = 0
2
–7.5
Time, t(s) Time, t(s) t =
2
O O
Masa, t(s) Masa, t(s) –14
t = 0.73
Diver Diver
A
Penerjun B Penerjun
p = 7.5 q = 5
(d) An entrepreneur of rental car has the total hours of 180 hours per week when a car is rented for RM10
per hour. The entrepreneur will receive an additional of 12 hours for every decrease RM1 in rental rate.
Seorang pengusaha sewa kereta mempunyai jumlah masa sebanyak 180 jam setiap minggu apabila sebuah kereta disewa dengan
harga RM10 per jam. Penyusaha itu akan menerima tambahan 12 jam bagi setiap pengurangan RM1 pada kadar sewaan.
(i) Form a quadratic equation for the weekly (ii) If the entrepreneur obtained the weekly
total rental, in RM, obtained if he reduces total rental of RM1 200 after reducing the
the rental rate. rental rate, find the rental rate of a car per
Bentukkan satu persamaan kuadratik bagi jumlah hour that week.
sewaan mingguan, dalam RM, yang diperoleh jika dia Jika pengusaha itu memperoleh jumlah sewaan
mengurangkan kadar sewa. mingguan sebanyak RM1 200 selepas mengurangkan
kadar sewa, cari kadar sewa sebuah kereta per jam
Let x be the reduce of every RM1 for the pada minggu itu.
rental rate per hour and S(x) is the total S(x) = 1 200
2
rental rate weekly. –12x – 60x + 1 800 = 1 200
2
Katakan x ialah pengurangan setiap RM1 bagi kadar 12x + 60x – 1 800 = –1 200
sewa per jam dan S(x) ialah jumlah sewaan mingguan. 12x + 60x – 600 = 0
2
(x – 5)(x + 10) = 0
Total of rental rate weekly
Jumlah sewaan mingguan x – 5 = 0 or x + 10 = 0
= Rental rate per hour × Number of hours x = 5 atau x = –10
Kadar sewa per jam × Bilangan jam Reduced rental rate per hour = RM5
= (10 – x) × (180 + 12x) Pengurangan kadar sewa per jam
= 1 800 + 120x – 180x – 12x 2
= –12x – 60x + 1 800 Thus, rental rate of a car per hour
2
Maka, kadar sewa sebuah kereta per jam
= RM10 – RM5
= RM5

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