Holiday Homework Penggal 1 2013

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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)( 2 xfxg =

    [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 2 and 2 are the roots of quadratic equation 0862 =+ xx whereas the equation

    052 =++ mxx has roots

    k and

    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 dan are the roots of quadratic equation 0422 =+ xx . Find the quadratic equation which

    has root

    3 and

    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 and are the roots of quadratic equation 0232 =+ kxx where 3=

    . Find the values of k, and

    [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