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HOLIDAY HOMEWORK SET 1 (23/3/2013-1/4/2013)

(Chapter: Function, Quadratic Equation and Quadratic Function)

ZBN/ZBN/ZBN/ZBN/http://www.ssijbaddmaths.blogspot.com]

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

ZBN/ZBN/ZBN/ZBN/http://www.ssijbaddmaths.blogspot.com]

HOLIDAY HOMEWORK SET 2 (23/3/2013-1/4/2013)

(Chapter: Function, Quadratic Equation and Quadratic Function)

ZBN/ZBN/ZBN/ZBN/http://www.ssijbaddmaths.blogspot.com]

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