Page 30 - Focus SPM KSSM Tg 4.5 - Add Maths

Additional Mathematics SPM Chapter 2 Quadratic Functions

18. A rectangular wall of Amin’s bedroom is white in the shape of cuboid. The height of the box is
SPM coloured with length of 4x m and width of 3x m. He enough to store the entire chocolate bar such that
2018
draws similar squares with sides x m at every corner the chocolate bar touches the side surface and the
of the wall and paints the squares with blue colour. base of the box. It is found that point C of the
Find the range of values of x if the part of the wall chocolate bar is at 2 cm from the side of the box
that remains white coloured is at least (x + 7) m . and 1 cm from the base of the box. The width of
2
2
the box is 18 cm. Determine whether two similar
19. The diagram below shows a graph of a quadratic chocolate bars can be stored into the box. Justify
SPM h
2019 function f(x) = + kx − 2b such that h, k, a, b and your answer.
x a
q are constants. 3. A piece of wire with length of 76 cm is cut into two
parts with different lengths. Each part is bent to form
f(x) a square such that the total area of both squares is
185 cm . Find the lengths of both parts of the cut
2
wire. HOTS Form 4
–q 0 q x Analysing
4. Initially, a group of n students share the cost of
RM150.00 to buy a present for Emily’s birthday.
(a) Determine the value of a. When 4 more students join the initial group of
(b) If f(x) = 0 and the product of roots is b, state the students to share the cost of the present, it is found
value of that each student pays RM6.25 less than the original
(i) h, payment. Find the amount to be paid by each
(ii) k. student of the new group. HOTS
Evaluating
2
20. The graph of a quadratic function f(x) = 3[2h − (x − 4) ], 2
SPM such that h is a constant, has a maximum point at 5. (a) Express f(x) = – 4x + 4x – 1 in the form of
2019 f(x) = a(x – h) + k, where a, h and k are
2
(4, h − 5). constants.
(a) State the value of h. (b) Sketch the graph of f(x) = – 4x + 4x – 1 and
2
(b) Determine the type of roots for f(x) = 0. Justify state the coordinates of the maximum point.
your answer.
2
21. Given that the quadratic equation (px) + 8qx + 4 = 0 6. The quadratic function f(x) = x – hx – 5 has a
2
SPM has two equal roots and the quadratic equation minimum point at (2, k).
2019 (a) Find the values of h and k.
kx − 2x + 3p = 0 has imaginary roots, such that k, p
2
and q are constants. Express the range of q in terms (b) Find the intersection point of the graph of
function f(x) with the x-axis. Hence, sketch the
of k.
graph of f(x).
PAPER 2
7. (a) Express f(x) = –3x + 8x – 11 in the form of
2
f(x) = a(x – m) + n, where a, m and n are
2
1. The quadratic equation x(x – 4) = 2p – 3, where p is constants.
a constant, has roots α and b. (b) Sketch the graph of f(x).
(a) Find the range of values of p if α ≠ b. (c) State the axis of symmetry of the graph of the
(b) Another quadratic equation 3x + qx – 4 = 0, function.
2
where q is a constant, has roots α and b .
3
3
Find the values of p and q. 8. (a) Find the value of p if the graph of a quadratic
function f(x) = p – 2 + 2px – x touches the
2
x-axis at one point.
2. (b) Hence, sketch the graph f(x) for negative values
SPM of p.
2017
9. (a) Sketch f(x) = 2x – 8x + 5. State the coordinates
2
Chocolate bar
of the vertex and the x-intercept of the graph of
the function.
(b) Based on the graph in (a), find
C
(i) the values of x that satisfy the inequality
2x + 5 < 8x,
2
18 cm
(ii) the range of values of t if 2x – 8x + 5 + t = 0
2
has no roots.
The diagram above shows the cross-section of a
cylindrical-shaped chocolate bar stored inside a box
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