Page 18 - TOP ONE ADDMATHS TG4

Additional Mathematics Form 4 Chapter 2 Quadratic Functions

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11. Given the curve y = (p – 3)x – x + 8, where p is a constant, Paper 2
SPM intersects the straight line y = 4x + 6 at two points, find
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the range of values of p.
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Diberi lengkung y = (p – 3)x – x + 8, dengan keadaan p ialah 1. It is given a and b are the roots of the quadratic equation
pemalar, menyilang garis lurus y = 4x + 6 pada dua titik, cari SPM x(x – 8) = 3h – 15, where h is a constant.
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julat nilai p. Diberi a dan b ialah punca-punca bagi persamaan kuadratik
[3] x(x – 8) = 3h – 15, dengan keadaan h ialah pemalar.
49 (a) Find the range of values of h if a ≠ b.
Ans: p ,
8 Cari julat nilai h jika a ≠ b.
[3]
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12. Given the quadratic equation hx – 5x + k = 0, where h and a b
SPM k are constants, has roots b and 3b, express h in terms of k. (b) Given 2 and 2 are the roots of another quadratic
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Diberi persamaan kuadratik hx – 5x + k = 0, dengan keadaan equation x + kx + 3 = 0, where k is a constant, find
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h dan k ialah pemalar, mempunyai punca-punca b dan 3b. the values of h and k.
Ungkapkan h dalam sebutan k. Diberi a dan b ialah punca-punca suatu persamaan
[3] 2 2
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75 kuadratik yang lain, x + kx + 3 = 0, dengan keadaan k
Ans: h =
16k ialah pemalar, cari nilai-nilai h dan k.
[4]
13. It is given 5 and h + 1 are the roots of the quadratic Ans: (a) h . – 1
equation x + (k – 1)x – 5 = 0, where h and k are constants. 3
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Find the values of h and k. (b) h = 1, k = –4
Diberi 5 dan h + 1 ialah punca-punca bagi persamaan kuadratik
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x + (k – 1)x – 5 = 0 dengan keadaan h dan k ialah pemalar. 2. The curve of the quadratic function f(x) = 2(x – p) + 3q
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Cari nilai-nilai h dan k. SPM intersects the x-axis at points (3, 0) and (7, 0). The straight
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[3] line y = –6 touches the minimum point of the curve.
Ans: h = –2, k = –3 Lengkung bagi fungsi kuadratik f(x) = 2(x – p) + 3q menyilang
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paksi-x pada titik (3, 0) dan (7, 0). Garis lurus y = –6
14. The diagram shows the graph of a quadratic function menyentuh titik minimum lengkung tersebut.
y = f(x). (a) Find the values of p and q.
Rajah di bawah menunjukkan graf bagi suatu fungsi kuadratik Cari nilai-nilai p dan q.
y = f(x). [2]
y (b) Hence, sketch the graph of f(x) for 0 < x < 8.
3 Seterusnya, lakar graf f(x) untuk 0 < x < 8 [3]
y = f(x)
(c) If the curve is reflected about the x-axis, write the
x equation of the curve.
–4 0 6
Jika lengkung tersebut dipantulkan pada paksi-x, tulis
State / Nyatakan persamaan bagi lengkung tersebut. [1]
(a) the roots of the equation when f(x) = 0, Ans: (a) p = 5, q = –2
punca-punca persamaan tersebut apabila f(x) = 0, (b) Refer to Answer Section
(b) the equation of the axis of symmetry of the curve. (c) f(x) = –2(x – 5) + 6
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persamaan paksi simetri lengkung itu.
[2] 3. The quadratic equation x – 7x + 12 = 0 has two roots p
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Ans: (a) –4 and 6 and q, where p . q.
(b) x = 1 Persamaan kuadratik x – 7x + 12 = 0 mempunyai dua punca
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p dan q, dengan keadaan p . q.
(a) Find / Cari
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15. It is given the quadratic function f(x) = x – 4x + 3 can (i) the values of p and q,
be expressed in the form f(x) = (x – 2) + m, where m is a nilai-nilai p dan q,
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constant. (ii) the range of values of x if x – 7x + 12 . 0.
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Diberi fungsi kuadratik f(x) = x – 4x + 3 boleh diungkapkan julat nilai x jika x –7x + 12 . 0.
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dalam bentuk f(x) = (x – 2) + m, dengan keadaan m ialah [4]
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pemalar. (b) By using the values of p and q in 3(a)(i), form a
(a) Find the value of m. quadratic equation which has the roots p – 2 and q + 4.
Cari nilai m. Dengan menggunakan nilai-nilai p dan q di 3(a)(i), bentuk
(b) Sketch the graph of the function f(x). satu persamaan kuadratik yang mempunyai punca-punca
Lakar graf bagi fungsi f(x). p – 2 dan q + 4.
[5] [3]
Ans: (a) m = –1 Ans: (a) (i) p = 4, q = 3; (ii) x , 3 or x . 4
(b) Refer to Answer Section (b) x – 9x + 14 = 0
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