Page 30 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi
(b) Kadar sewa sebuah gelanggang futsal bagi 2. Rajah di sebelah y
satu jam pertama ialah RM20 dan RM15 menunjukkan graf
bagi setiap jam berikutnya. P ialah jumlah bagi fungsi y = f(x). 1
bayaran sewa gelanggang, dalam RM, bagi h Diberi bahawa –1 0 3 x
jam. f(x) = ax + b dengan
The rental rate of a futsal court is RM20 for the first hour keadaan a dan b ialah
and RM15 for the subsequent hour. P is the total rental pemalar. Cari
charge in RM, of the futsal court, for h hours. The diagram shows the –5
(i) Tuliskan jumlah bayaran, P dalam graph of function y = f(x).
tatatanda fungsi. It is given that f(x) = ax + b where a and b are constants. Find
Write the total charge, P in function notation. (a) nilai a dan nilai b,
[5 markah / 5 marks] the value of a and of b,
(ii) Badrul dan rakan-rakannya merancang [4 markah / 4 marks]
untuk menyewa gelanggang futsal (b) objek bagi 7,
selama 4 jam. Mereka telah mengumpul the object of 7,
wang sesama mereka berjumlah [2 markah / 2 marks]
2
–1
RM65. Adakah wang itu mencukupi (c) nilai x jika f (x) = f (x).
–1
2
untuk mereka menyewa gelanggang the value of x if f (x) = f (x).
tersebut? Berikan alasan anda. [4 markah / 4 marks]
Badrul and his friends plan to rent the futsal court Jawapan / Answer :
for 4 hours. They have collected money among (a) f(3) = 1
themselves with a total of RM65. Is the money 3a + b = 1 .................a
enough for them to rent the futsal? Give your
reason. f(–1) = –5
[5 markah / 5 marks] –a + b = –5 .................b
Jawapan / Answer : a – b: 4a = 6
3
(a) f(10) = 6 a =
10 – b = 6 2
a 3
10 = 6 + b – + b = –5
2
7
a 11 Penerbitan Pelangi Sdn Bhd. All Rights Reserved
b = –
10 = 6a + ab .................a 2
f(–12) = –4 (b) f(x) = 7
7
– 12 – b = –4 3 x – = 7
a 2 2
12 3x – 7 = 14
– = b – 4
a x = 7
–12 = ab – 4a .................b 3 7
(c) y = x –
a – b: 22 = 10a 2 2
a = 11 2y = 3x – 7
5 2y + 7 = 3x
2y + 7
x =
11
10 = 6   + 11 b f (y) = x 3
5
5
–1
b = – 16 = 2y + 7
3
2x + 7
∴ f (x) =
–1
(b) (i) P(h) = 20 + 15(h – 1) 3 3 7

(ii) P(4) = 20 + 15(3) = 65 ff(x) = f x – 2 
2
Jumlah sewa gelanggang futsal bagi = x – 7  – 7
3 3

4 jam ialah RM65. Wang yang dikumpul 2 2 2 2
9
oleh Badrul dan rakan-rakannya adalah = x – 35
mencukupi. 4 4
The total rental charge of the futsal court is RM65. f (x) = f (x)
2
–1
The money collected by Badrul and his friends is 2x 7 9x 35
enough. 3 + = 4 – 4
3
x = 7
© Penerbitan Pelangi Sdn. Bhd. 12

01 Hybrid PBD Mate Tambahan Tg4.indd 12 29/09/2021 3:23 PM