Page 11 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

15. Solve each of the following. PL 5 Daily Application
Selesaikan setiap yang berikut.

Example
5
The temperature in Fahrenheit, F, can be converted to Celsius, C, using the function C(F) = (F – 32).
9 9
The temperature in Kelvin, K, can be converted to Fahrenheit, F, using F(K) = (K – 273) + 32. Suraya
5
obtained a result of temperature of 258 K in an experiment. Convert the temperature to Celsius, in °C.
5
Suhu dalam Fahrenheit, F, boleh ditukar kepada Celsius, C, dengan menggunakan fungsi C(F) = 9 (F – 32). Suhu dalam Kelvin, K,
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boleh ditukar kepada Fahrenheit, F, dengan menggunakan fungsi F(K) = 5 (K – 273) + 32. Suraya memperoleh hasil suhu 258 K
dalam suatu eksperimen. Tukar suhu tersebut ke Celsius, dalam °C.
9
F(258) = (258 – 273) + 32 C[F(258)] = C(5)
5 5
= 5 = (5 – 32)
9
= –15
Hence, 258 K can be converted to –15°C.

(a) The height of water, h cm, in a cylindrical container is increasing with respect to time, t s, and
its function is h(t) = 1.4t. The volume of water, V cm , in the container is given by the function
3
88
V(h) = h.
7
Ketinggian air, h cm, dalam suatu bekas berbentuk silinder semakin meningkat mengikut masa, t s, dan fungsinya ialah
88
h(t) = 1.4t. Isi padu air, V cm , dalam bekas tersebut diberi oleh fungsi V(h) = h.
3
7
(i) State the volume of water, V, as a function of time, t.
Nyatakan isi padu air, V, sebagai fungsi masa, t.
3
(ii) Find the volume of water, in cm , in the container after 5 seconds.
Cari isi padu air, dalam cm , dalam bekas tersebut selepas 5 saat.
3
(i) V[h(t)] = V(1.4t)
88
= (1.4t)
7
= 17.6t
∴ V : t → 17.6t

(ii) V(5) = 17.6(5)
= 88
Hence, the volume of water in the container after 5 seconds is 88 cm .
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(c) Azlan works in a furniture store. Every month, he receives a basic salary of RM2 000 plus a 5%
commission on sales over RM3 000. Let x represents his sales per month.
Azlan bekerja di sebuah kedai perabot. Setiap bulan, dia menerima gaji asas sebanyak RM2 000 dan komisen 5% pada jualan
yang melebihi RM3 000. Let x mewakili jualannya setiap bulan.
(i) Given f(x) = x – 3 000 and g(x) = 0.05x, write the function of gf(x) and explain its meaning.
Diberi f(x) = x – 3 000 dan g(x) = 0.05x, tulis fungsi gf(x) dan terangkan maksudnya.
(ii) If Azlan’s sales are RM6 499, find his salary.
Jika jualan Azlan ialah RM6 499, cari gajinya.

(i) gf(x) = g(x – 3 000)
= 0.05(x – 3 000)
gf(x) is the commission received by Azlan, that is 5% on sales over RM3 000.

(ii) gf(6 499) = 0.05(6 499 – 3 000)
= 174.95
Salary = 2 000 + 174.95
= 2 174.95
Hence, his salary is RM2 174.95

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