holiday homework penggal 1 2013
TRANSCRIPT
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HOLIDAY HOMEWORK SET 1 (23/3/2013-1/4/2013)
(Chapter: Function, Quadratic Equation and Quadratic Function)
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8. Given 4
7)(
1 kxxg
−=− and 74)(
2 += xxf . Find
(a) g (x)
(b) the value of k so that )(2)( 2xfxg −=
[4 marks]
Answer: (a) _________________
(b) _________________
Solve the quadratic equation x (4x – 3) = 3x – 1. Give your answers correct to three
decimal palaces
Form the quadratic equation which has the roots –4 and 3
1 . Give your answer in the
form ax2 + bx + c = 0
Answer: ______________________
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9. The function 12)( 2 +++= khxxxf has a minimum value of –15 when x = –3. Find the values of h and k [4 marks]
Answer: ____________________
10. Given h + 1 and k – 3 are the roots of the equation x2 + 7x + 12 = 0 . Find the possible values of h and k [4 marks]
Answer: ____________________
11. A quadratic equation x2 + mx + 4 = 2x has two equal roots. Find the possible values of m [3 marks]
Answer: ____________________
12. Diagram below shows the graph of a quadratic function khxaxf +−= 2)()( , where p and q are constants [4 marks]
.
State
(a) the values of a, h and k
(b) the equation of the axis of symmetry
Answer:_____________________
13. The quadratic equation 3x2 + px + q = 0 has the roots -4 and 2. Find the values of p and q [3 marks]
Answer: ____________________
(0, -8)
-2
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14.
The given diagram shows the mapping of x onto y by the
function bxxb
axf ≠
−→ ,: and the mapping of z onto y
by the function 03
5: ≠
+→ z
z
bzzg . Find
(a) the value of a and of b,
(b) the function that maps y onto z
(c) the function x onto z
[10 marks]
15. (a) The function f (x) =x2 – 6kx +10k
2 + 1 has a minimum value of r
2 + 2k, with r and k as a constant
(i) By the completing the square,, show that r = k – 1
(ii) Hence or otherwise, find the values of k and r if the graph is symmetrical about x = r2 – 1
(b) If m and n are the roots of the quadratic equation 3x2 + 5x – 1 = 0, form a quadratic equation which
has roots 3m – 1 and 3n – 1
[10 marks]
Answer:
(1) 9)(0;2
1≤≤ xf (2) 4/5; 25x2 – 1 (3) 4, 3 (4)5 (5) p > 0; q = -3; r = -4 (6) 1.309, 0.191 (7) 3x2+ 11x – 4 = 0 (8) (7 – 4x)/k ; -1/2 (9) 3, -7
(10) h = -4, k = -1; h = -5, k = 0 (11) 6, -2 (12) -2, 0, -2 (13) 6, -24 (14) 2, 4; 5/3x-4 ; (20-5x)/(4x-10) (15) k=0, r=-1; k=5, r=4 ; x2+7x + 3= 0
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HOLIDAY HOMEWORK SET 2 (23/3/2013-1/4/2013)
(Chapter: Function, Quadratic Equation and Quadratic Function)
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5
6
7
8
9
10
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11. Given that α2 and β2 are the roots of quadratic equation 0862 =+− xx whereas the equation
052 =++ mxx has roots α
k and
β
k . Find the values of m and k [4 marks]
Answer: _________________
12. Given the function mxxh += 6)( and 18
73)(
1 +=−kxxh , where m and k are constants,
find the values of m and k [3 marks]
Answer: ________________
13. The function khxxxf 32)(2 ++= has a minimum value of 3 when x =
4
3− . Find the value of k and h [4 marks]
14. Given that βα dan are the roots of quadratic equation 042 2 =−+ xx . Find the quadratic equation which
has root α
3 and
β
3 [4 marks]
Answer: _________________
15. Given that 25)(2 +−= xxxf and 5: +→ xxg . Find
a) the value of k if g (k) = f (2)
b) the function fg (x)
[4 marks]
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Answer: _________________
16. Given 2)12(3)( −−= xxf and P(2m, 3n) is the maximum point of the curve, find the value of m and n and
equation of axis symmetry [3 marks]
17. (a) Given that α and β are the roots of quadratic equation 0232 =+− kxx where 3−=
β
α. Find the values of k, α and β
[5 marks] (b) A quadratic equation is given as x
2 + px + q = 0, where p and q are constant
(i) Express q in terms of p such that the equation has two equal roots.
(ii) Find the values of p and q if –2 and 3 are the roots of the equation
[5 marks]
18. Given that function 32)( += xxf and 1110)( += xxgf .
a) Find the function g (x)
b) the values of h if 5)(2 −=− hhfg
c) Sketch the graph of )(xf for the domain 12 ≤≤− x and state the corresponding range of f (x) [8 marks]
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(1). many to one; x2 (2) 4 (3) 8, -4 (4) x = 3; (x – 3)2 – 4 (5) 2, 8 (6) (2x – 5)/x , 3/4 (7) 2x + 5 (8) p > 1 (9) 3.351, 0.149 (10) -1, 2, x = 1
(11) -10/3, 50/3, (12) 1/18, -7/3 (13) 3, 11/8 (14) 4x2 – 3x – 18 = 0 (15) -9, x2 + 5x + 2 (16) 1/4, 1, 1/2 (17) -1, 1, -1/3 (18) 5x – 4 ; 0, -10; q = p2/4; -1, -6