Page 31 - Focus SPM KSSM Tg 4.5 - Add Maths

Additional Mathematics SPM Chapter 2 Quadratic Functions

10. The curve of the quadratic function 15.
2
f(x) = – (x + m) + 2n intersects the x-axis at E F
2
3
points (–2, 0) and (4, 0). The straight line y = 6
touches the maximum point of the curve.
(a) Find the value of m and of n. M
(b) Hence, sketch the graph f(x) for –2 < x < 4. x cm
(c) If the graph is reflected on the x-axis, write the
equation of the curve.
H N 2x cm G
11. Given that the straight line 2x – y + 6 = 0 is a
tangent to the curve y = x + kx + 7. The diagram above shows a rectangle EFGH with
2
(a) Find the possible value of k if k . 0. length EF = 64 cm and FG = 40 cm. A triangle FMN
(b) Hence, sketch the graph of y = x + kx + 7. is drawn inside rectangle EFGH where MH = x cm
2
and HN = 2x cm.
(a) Express the area of triangle FMN, A cm , in
2
12. The weekly income, P(x), in RM, for a factory that
produces certain electronic components is given by terms of x.
Form 4
1 (b) Find the minimum area of triangle FMN and the
2
the quadratic function, P(x) = 800x – x , where corresponding value of x.
10
x is the number of electronic components sold per HOTS Analysing
week.
(a) Express P(x) in the vertex form. 16.
(b) Find the Wall
(i) number of electronic components that
must be produced per week to obtain x m
maximum income,
(ii) maximum income.
HOTS
Analysing
13. A projectile is launched vertically upwards from the The diagram above shows a rectangular piece of
surface of the ground. The height, h, in m, at t land fenced right next to a wall. The total length of
2
seconds after the launch is h(t) = 30t – 5t . the wire used to fence the land is 80 m. 2
(a) Express h(t) in the form of a(t – p) + q, where (a) Show that the area of the fenced land, A m is
2
2
a, p and q are constants. A = 80x – 2x .
(b) Determine the (b) Hence, find the maximum area of the fenced
(i) maximum height achieved by the projectile, land and the corresponding value of x.
(ii) time taken to achieve the maximum height. HOTS Applying
HOTS
Applying
14. A stone is thrown vertically upwards from a platform
that is 4 m from the surface of the ground. The
height of the stone, h, in m, at time t seconds after
the throw is h(t) = 4 + 30t – 5t .
2
(a) Find the
(i) time taken by the stone to reach the
maximum height,
(ii) maximum height.
(b) Find the range of time when the stone is at a
height more than 4 m from the surface of the
ground.
HOTS
Analysing

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