Page 19 - TOP ONE ADDMATHS TG4

Additional Mathematics Form 4 Chapter 2 Quadratic Functions

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4. A quadratic equation x + 3(x – p) = 0, where p is a (b) Find the minimum or maximum value of the quadratic
constant, has the roots q and –2q, q ≠ 0. function f(x).
Persamaan kuadratik x + 3(x – p) = 0, dengan keadaan p ialah Cari nilai minimum atau maksimum fungsi kuadratik f(x).
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pemalar, mempunyai punca-punca q dan –2q, q ≠ 0. [1]
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(a) Find the values of p and q. (c) Sketch the graph of f(x) = x – x – 12 for –4 < x < 5.
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Cari nilai-nilai p dan q. Lakar graf f(x) = x – x – 12 untuk –4 < x < 5.
[4] [4]
(b) Hence, form a quadratic equation which has the roots (d) State the equation of the curve when the graph is
p – 3 and p + 1. reflected about the x-axis.
Seterusnya, bentuk satu persamaan kuadratik yang Nyatakan persamaan lengkung apabila graf tersebut
mempunyai punca-punca p – 3 dan p + 1. dipantulkan pada paksi-x.
[3]
Ans: (a) p = 6, q = 3 [1]
(b) x – 10x + 21 = 0 1 2 1
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
Ans: (a) x – 2  – 12
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5. It is given the quadratic function f(x) = x – x – 12. (b) Minimum value = –12
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Diberi fungsi kuadratik f(x) = x – x – 12. (c) Refer to Answer Section
(a) Express f(x) in the form f(x)= a(x + p) + q. 1 2 1
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
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Ungkapkan f(x) dalam bentuk f(x) = a(x + p) + q. (d) f(x) = – x – 2  + 12 or f(x) = –x + x + 12
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[2]
HOTS Challenge
1. The diagram shows a right-angled triangle PQR. HOTS Applying
Rajah di sebelah menunjukkan sebuah segi tiga bersudut tegak PQR. P
(a) Find the value of x. Give your answer correct to four significant figures. (2x + 3) cm
Cari nilai x. Berikan jawapan anda betul kepada empat angka bererti. (x – 2) cm
(b) By using the value of x obtained in 1(a), calculate the area, in cm , of
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the right-angled triangle PQR.
Dengan menggunakan nilai x yang diperoleh di 1(a), hitung luas, dalam cm , Q (2x + 1) cm R
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segi tiga bersudut tegak PQR.
Answer Guide
Use Pythagoras’ theorem to find the value of x.
Gunakan teorem Pythagoras untuk mencari nilai x.

Ans: (a) x = 12.32
(b) 132.30 cm 2

6q + 1
2. It is given the quadratic function f(x) = px – 3x + q can be expressed in the form f(x) = p(x – ) + .
3 2
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4 4p
Find HOTS Applying
3 6q + 1
Diberi fungsi kuadratik f(x) = px – 3x + q boleh diungkapkan dalam bentuk f(x) = p(x – 4 ) + 4p . Cari
2
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(a) the values of p and q,
nilai-nilai p dan q,
(b) the range of values of x if f(x) > 4.
julat nilai x jika f(x) > 4.
Answer Guide
Express the function in vertex form using ‘completing the square’ method.
Ungkapkan fungsi itu dalam bentuk verteks dengan menggunakan kaedah penyempurnaan kuasa dua.

Ans: (a) p = 2, q = 5
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(b) x < or x > 1
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