Page 10 - PRAKTIS HEBAT ADDMATHS TG4

Additional Mathematics Form 4 Practice 2 Quadratic Functions

b
a
4. Given that — and — are the roots of the quadratic equation mx(2x – 3) = 10x – n, calculate the values of
3
3
TEXTBOOK 19 45
pp. 36 – 44 m and n if a + b = ––– and ab = –––. PL5 Subtopic 2.1
2 2
b
a
Diberi — dan — ialah punca-punca persamaan kuadratik mx(2x – 3) = 10x – n, hitung nilai m dan nilai
3 3
45
19
n jika a + b = —– dan ab = —–.
2 2
2
5. The diagram shows the graph of y = 2x + px + q. PL4 Subtopic 2.1 y
Rajah di sebelah menunjukkan graf bagi y = 2x + px + q.
2
TEXTBOOK
pp. 36 – 44
(a) If a and b are the roots of the quadratic equation 2x + px + q = 0, q
2
state the value of
Jika a dan b ialah punca-punca persamaan kuadratik 2x + px + q = 0,
2
nyatakan nilai 0 2 5 x
(i) a + b,
(ii) ab.
(b) Find the values of p and q.
Cari nilai p dan nilai q.
2
6. The diagram shows the curve of y = –x + 4x + p. PL4 Subtopic 2.1 & 2.2 y
Rajah di sebelah menunjukkan graf bagi lengkung y = –x + 4x + p.
2
TEXTBOOK
pp. 36 – 48
(a) Show that the quadratic equation –x + 4x + p = 0 has real roots if
2
p + 4 > 0. m 0 n x
Tunjukkan bahawa persamaan kuadratik –x + 4x + p = 0 mempunyai y = f(x)
2
punca nyata jika p + 4 > 0.
(b) Find the roots, m and n, when p = 12.
Cari punca-punca, m dan n, apabila p = 12.
7. The diagram shows two curves, y = x + 2x + hx + k and y
2
1
TEXTBOOK y = 3(x – 1) + k – 1, that meet at a point on the x-axis. Find y 2 y 1
2
pp. 36 – 63 2
Rajah di sebelah menunjukkan graf bagi dua lengkung,
y = x + 2x + hx + k dan y = 3(x – 1) + k – 1, yang bertemu pada
2
2
2
1
satu titik pada paksi-x. Cari PL5 Subtopic 2.1 & 2.3 0 x
(a) the values of h and k,
nilai h dan nilai k,
(b) the root of the equations if y = y = 0.
2
1
punca persamaan jika y = y = 0.
1 2
8. It is given that a and b are the roots of the quadratic equation x(x – 4) = 3h + 2 where h is a constant.
TEXTBOOK Diberi bahawa a dan b merupakan punca-punca bagi persamaan kuadratik x(x – 4) = 3h + 2 dengan
pp. 36 – 48
keadaan h ialah pemalar. PL5 Subtopic 2.1 & 2.2
(a) Find the range of values of h if a ≠ b.
Cari julat nilah h jika a ≠ b.
b
a
(b) Given — and — are the roots of another quadratic equation, 4x – kx – 5 = 0 where k is a constant.
2
2 2
Find the values of h and k.
a
b
Diberi — dan — merupakan punca-punca bagi persamaan kuadratik yang lain, iaitu 4x – kx – 5 = 0
2
2
2
dengan keadaan k ialah pemalar. Cari nilai h dan k.
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