Page 48 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 2 Fungsi Kuadratik

2
Kertas 2 (b) f(x) = 2x + 4x + 8
f(0) = 2(0) + 4(0) + 8
2
= 8
2
1. (a) Ungkapkan f(x) = 5 – x – 2x dalam bentuk
2
f(x) = a(x – h) + k dan seterusnya, cari titik ∴ Q(0, 8)
maksimum fungsi itu. (c) f(x)  8
2
2
Express f(x) = 5 – x – 2x in the form f(x) = a(x – h) + k 2x + 4x + 8  8
2
and hence, find the maximum point of the function. 2x + 4x  0
2
(b) Cari julat nilai bagi p jika persamaan 2x(x + 2)  0
p – x + 3x = 0 tidak mempunyai punca. x  −2, x  0
2
2
Find the range of values of p if p – x + 3x = 0 has no roots.
[5 markah / 5 marks]
Jawapan / Answer : 3. (a) Selesaikan persamaan kuadratik berikut.
(a) f(x) = 5 − x − 2x 2 Berikan jawapan betul kepada 5 angka
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
= −2 x + x  + 5 bererti.
2
Solve the following quadratic equation. Give answer
2

= −2 x + 1  2 – 1  + 5 correct to 5 significant figures.
3
4 16 1 + 2x + x(x – 1) = 50 000

= −2 x + 1  2 + 41 2 [3 markah / 3 marks]
4
8
Titik maksimum / Maximum point (b) Seterusnya, cari julat nilai x bagi
1 41

= – ,  Hence, find the range of values of x for
3
4 8
1 + 2x + x(x – 1)  50 000
(b) p − x + 3x = 0 2 [2 markah / 2 marks]
2
Tidak mempunyai punca / Has no roots (c) Dalam satu rangkaian internet, bilangan
b − 4ac  0 talian telefon yang dihubungkan dengan
2
2
(−1) − 4(3)(p)  0 n pengguna komputer diberikan oleh
−12p  −1 1 + 2n + 3 n(n – 1). Jika satu rangkaian
1 2
p  internet dapat menyambungkan 50 000
12
talian telefon, cari bilangan maksimum
pengguna komputer dalam rangkaian itu.
2. Rajah berikut menunjukkan f(x) In an internet network, the number of telephone
graf bagi fungsi kuadratik lines connected to n computer users is given by
3
f(x) = 2x + 4x + k. Q 1 + 2n + n(n – 1). If an internet network can connect up
2
2
The diagram shows the graph of to 50 000 telephone lines, find the maximum number of
quadratic function f(x) = 2x + 4x + k. (m, 6) users in the network.
2
(a) Cari / Find x [1 markah / 1 mark]
(i) nilai bagi k, 0 Jawapan / Answer :
the value of k, 3
(i) nilai bagi m. (a) 1 + 2x + x(x – 1) = 50 000
2
the value of m. 2 + 4x + 3x(x − 1) = 100 000
[4 markah / 4 marks] 2 + 4x + 3x − 3x = 100 000
2
(b) Nyatakan koordinat titik Q. 3x + x − 99 998 = 0
2
State the coordinates of point Q.
[1 markah / 1 mark] x = –1 ±  – 4(3)(–99 998)
1
2
(c) Tentukan julat nilai x jika f(x)  8. 2(3)
Determine the range of values of x if f(x)  8. x = −182.74, 182.41
[3 markah / 3 marks]
Jawapan / Answer : (b) 1 + 2x + x(x – 1)  50 000
3
(a) (i) f(x) = 2x + 4x + k 2
2
2
= 2(x + 2x) + k 3x + x − 99 998  0
2
= 2(x + 1) – 2 + k −182.74  x  182.41 x
2
–2 + k = 6 –182.74 182.41
k = 8
(ii) m = –1 (c) Bilangan maksimum pengguna = 182
Maximum number of users
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