Page 17 - PBD Plus Matematik Tambahan T4 (EG)

Praktis SPM 1

Praktis Ekstra SPM 1
4. Dalam rajah di bawah, fungsi f memetakan y
KERTAS 1
kepada x dan fungsi g memetakan y kepada z.
1. Diberi fungsi m(x) = 3x dan n(x) = h – kx dengan In the diagram below, the function f maps y to x and the
function g maps y to z.
keadaan h dan k ialah pemalar. Ungkapkan h
dalam sebutan k dengan keadaan nm(1) = 4. x f y g z
It is given the functions m(x) = 3x and n(x) = h – kx where h and r
k are constants. Express h in terms of k such that nm(1) = 4.
SP 1.2.5 [3 markah / 3 marks] q
Jawapan / Answer :
nm(x) = h – k(3x) p
= h – 3kx
nm(1) = 4 –1
h – 3k(1) = 4 (a) Cari gf (p). SP 1.3.1
Find gf (p).
–1
h – 3k = 4 (b) Ungkapkan q dalam sebutan p jika diberi
h = 4 + 3k 3y – 5
f(y) = , y ≠ 0. SP 1.1.3
y 3y – 5
Express q in terms of p if it is given f(y) = y , y ≠ 0.
[3 markah / 3 marks]
2. Diberi fungsi f(x) = px + 1, g(x) = 3x – 5 dan Jawapan / Answer :
fg(x) = 3px + q. Ungkapkan p dalam sebutan q. (a) f(q) = p dan / and g(q) = r
It is given the functions f(x) = px + 1, g(x) = 3x – 5 and f (p) = q
–1
fg(x) = 3px + q. Express p in terms of q. SP 1.2.5 gf (p) = g(q)
–1
[3 markah / 3 marks] = r
Jawapan / Answer : Penerbitan Pelangi Sdn. Bhd.
fg(x) = p(3x – 5) + 1 (b) f(q) = p
= 3px – 5p + 1 3q – 5 = p
q
3px – 5p + 1 = 3px + q 3q – 5 = pq
–5p + 1 = q 3q – pq = 5
1 – q = 5p q(3 – p) = 5
1 – q 5
p = q =
5 3 – p

5. (a) Rajah di bawah menunjukkan hubungan
antara set X dan set Y.
3. Diberi fungsi f(x) = 3x + 4 dan fg(x) = 6x + 7, cari The diagram shows the relation between set X and set Y.
Given functions f(x) = 3x + 4 and fg(x) = 6x + 7, find X f(x) Y
(a) fg(4), SP 1.2.3
1 ● ● 1
(b) g(x). SP 1.2.4 4 ● ● 0.25
[3 markah / 3 marks] 10 ● ● 0.1
Jawapan / Answer : p ● ● 0.04
(a) fg(4) = 6(4) + 7
= 31
(i) Dengan menggunakan tatatanda fungsi,
(b) fg(x) = 6x + 7 ungkapkan f dalam sebutan x. SP 1.1.1
Using the function notation, express f in terms of x.
3g(x) + 4 = 6x + 7
3g(x) = 6x + 3 (ii) Cari nilai p. SP 1.1.2
g(x) = 2x + 1 Find the value of p.
[3 markah / 3 marks]

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