Page 19 - PBD Plus Matematik Tambahan T4 (EG)

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi

(b) Kadar sewa sebuah gelanggang futsal bagi
KERTAS 2
satu jam pertama ialah RM20 dan RM15
bagi setiap jam berikutnya. P ialah jumlah
1. Rajah bawah menunjukkan pemetaan fungsi f bayaran sewa gelanggang, dalam RM, bagi h
dan diikuti dengan fungsi g.
The diagram below shows the mapping of function f, followed jam. SP 1.1.3
by function g. The rental rate of a futsal court is RM20 for the first hour
and RM15 for the subsequent hour. P is the total rental
charge in RM, of the futsal court, for h hours.
f g
x x – 1 4x + 5 (i) Tuliskan jumlah bayaran, P dalam
tatatanda fungsi.
Write the total charge, P in function notation.
Cari / Find (ii) Badrul dan rakan-rakannya merancang
(a) g(x), SP 1.2.4 untuk menyewa gelanggang futsal
[3 markah / 3 marks] selama 4 jam. Mereka telah mengumpul
2
(b) (i) f (x), wang sesama mereka berjumlah
(ii) f (x). Seterusnya, deduksikan f (x). RM65. Adakah wang itu mencukupi
n
3
SP 1.2.5 untuk mereka menyewa gelanggang
n
3
f (x). Hence, deduce f (x). tersebut? Berikan alasan anda.
[4 markah / 4 marks] Badrul and his friends plan to rent the futsal court
for 4 hours. They have collected money among
Jawapan / Answer : themselves with a total of RM65. Is the money
(a) f(x) = x − 1; gf(x) = 4x + 5 enough for them to rent the futsal? Give your
Katakan / Let y = f(x) reason.
y = x − 1 [5 markah / 5 marks]
x = y + 1 Jawapan / Answer :
(a) f(10) = 6
gf(x) = 4x + 5 10 – b = 6
g(y) = 4(y + 1) + 5 a
= 4y + 9 10 = 6 + b
a
∴ g(x) = 4x + 9 Penerbitan Pelangi Sdn. Bhd.
10 = 6a + ab .................a
(b) (i) f (x) = ff(x) f(–12) = –4
2
= (x − 1) − 1 – 12 – b = –4
= x − 2 a

– 12 = b – 4
3
2
(ii) f (x) = ff (x) a
= f(x − 2) –12 = ab – 4a .................b
= (x − 2) − 1 a – b: 22 = 10a
= x − 3 11
a =
5
n
∴ f (x) = x − n
11
10 = 6   + 11 b
5
5
2. (a) Rajah di bawah menunjukkan fungsi b = – 16
x
f(x) = – b dengan keadaan a dan b ialah 11
a
pemalar. SP 1.1.3
x
The diagram below shows the function f(x = a – b, (b) (i) P(h) = 20 + 15(h – 1)
where a and b are constants.
f x (ii) P(4) = 20 + 15(3) = 65
x – b
a
Jumlah sewa gelanggang futsal bagi
6 4 jam ialah RM65. Wang yang dikumpul
oleh Badrul dan rakan-rakannya adalah
10 mencukupi.
–4
–12 The total rental charge of the futsal court is RM65.
The money collected by Badrul and his friends is
enough.
Hitung nilai a dan nilai b.
Calculate the value of a and of b.
[5 markah / 5 marks]

© Penerbitan Pelangi Sdn. Bhd. 12