Page 8 - 1202 Question Bank Additional Mathematics Form 4

1 11. The number of story books read by Amin depends
8. The function f is defined by f (x) = x + x – 12.
2
2 on his spare time and his spare time depends on the
HOTS Analysing amount of home work given by the school. Given that
(a) Find, in a similar form, x(t) = 3t – 5 where x is the number of story books,
(i) f (x + a), t is the spare time in hours and t(k) = 4 + 2k where k
f (x + a) – f (x) is the number of homework given.
(ii) a . (a) Find the number of story books he can read if he
[4 marks]
has 2 homeworks.
f (x + a) – f (x) [4 marks]
(b) Hence, find the value for a if (b) If he can read 7 story books, find the amount of
x = 0.1 when a = 2. [3 marks] spare time he has and the number of homework
given.
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[4 marks]
9. A train moves on a straight line. Its acceleration,
a m s , is depends on time t, in seconds, and is given
−2
by a(t) = pt + q where p and q are constants. 12. The diagram shows a cylinder whose volume depends
(a) Given that when the time t = 0 s, the acceleration on its radius of the base, r m and its height, t m.
is −5 m s and when the time t = 4 s, the
−2
acceleration is 15 m s .
−2
Find the values of p and q. [4 marks]
(b) Find the time when the acceleration is 25 m s .
−2
[3 marks] V(t) = t + 1
2

10. The expenditure, RMC, for an annual dinner of a
2
3
company depends on the number of employees in the Given that the volume V(t) = (t + 1) m and the height
factory. In a certain year, the number of employees is t(r) = 1 1 r + 4 m.
2
x and the expenditure of employees per head for the 2
annual dinner is RM(x + p). (a) Express the volume, V, in terms of r. [4 marks]
(a) Express the total expenditure in that year, in (b) Find the volume and radius of the base if the
terms of p. [3 marks] height of the cylinder is 6.5 m. [4 marks]
(b) Find the value of p if the expenditure is RM2 650 HOTS Analysing
and the number of employees is 50. [4 marks]

Section B

13. A function is defined by HOTS Analysing 14. A function f is defined by f : x → x , x ≠ k.
2x + 1
f (x) = |1 – x| for x < 2 (a) State the value of k. [1 mark]
x – 4 for x . 2 (b) Find f –1 1 2 . [2 marks]
2
(a) Sketch the graph of f (x) for the domain 5
1
0 < x < 4. [4 marks] (c) Show that f (x) = x , where x ≠ – .
2
4
(b) Hence, find the corresponding range for the given 4x + 1 [3 marks]
domain of f (x). [2 marks] n x
(c) Find the values of x if f (x) = 1 for the domain (d) Hence, show that f (x) = 2nx + 1 , where
0 < x < 4. [4 marks] n = 1, 2, 3….. and x ≠ – 1 . [4 marks]
2n

10 Question 12:
SOS TIP (a) V(t) = t + 1, t(r) = r + 4. Thus Vt(r) will express V in terms of r. 1010
1
2
2
(b) Find V when t = 6.5.
Find r when t = 6.5.

01_1202 QB AMath F4.indd 10 09/05/2022 11:30 AM