Name :
Form : 4
SEKOLAH MENENGAH JENIS KEBANGSAAN KEAT HWA
PENTAKSIRAN BULAN MEI 2023
ADDITIONAL MATHEMATICS FORM 4
Time : 10.40 – 11.50 am (70 minutes)
Date : 22 May 2023
Instruction : Answer ALL the questions. Show your workings clearly. It may help you to get marks.
[60 marks]
1. State whether each of the following relation is a function. Justify your answer.
(i) {(1, 2), (1, 3), (2, 3)}
(iv)
Odd number ●
(ii)
●
●5
●
●6
Even number ●
1
p
(iii)
●4
●
3
2
[4 marks]
●7
r
q
Answer:
Positive
Negative
-3
1
2
3
2. Complete Table 1 by determining if the following functions in Diagram 1 have inverse function or vice
versa. Explain.
[3 marks]
Diagram 1(a)
Diagram 1(b)
Diagram
Answer
1(a)
1(b)
1(c)
Table 1
Diagram 1(c)
3. Given the function 𝑓: 𝑥 →
𝑥 − 11
, 𝑥 ≠ 8, find
𝑥−8
a) the values of 𝑚 such that 𝑓(2𝑚 − 1) = 𝑚,
b) 𝑓 −1 (5)
[7 marks]
Answer:
4. Hashim is offering food packet delivery service. The cost price for each food packet is RM5.70 and the
selling price is RM6.50. On average, he spends RM24 on petrol for the food delivery per day.
a) Write a profit function, 𝑓(𝑛), where 𝑛 is the number of food packets delivered per day.
b) Find the value of 𝑛 to break even and the value of 𝑓(𝑛) when 𝑛 is 150.
c) Represent your answer in (b) in an arrow diagram.
[5 marks]
Answer:
5. Given the functions 𝑔: 𝑥 → 8𝑥 − 4 and ℎ: 𝑥 →
a) 𝑔−1 ℎ(4),
b) the value of 𝑥 if 2ℎ(𝑥) = 𝑔(𝑥).
𝑥
2
− 6, find
[5 marks]
Answer:
6. a) Function 𝑓 is defined as 𝑓: 𝑥 →
𝑥
𝑥+1
i. Show that 𝑓 2 is given by 𝑓 2 : 𝑥 →
, 𝑥 ≠ −1.
𝑥
, 𝑥 ≠ − 12.
2𝑥 + 1
ii. Find, in similar form, 𝑓 3 (𝑥). Hence, deduce an expression for 𝑓 𝑛 (𝑥).
1
b) Given that 𝑃(−4, ) is a point on the graph of 𝑦 = 𝑓(𝑥). State the coordinate of point 𝑃′ which is
2
located on the graph of 𝑦 = 𝑓 −1 (𝑥).
[7 marks]
7. A function 𝑔 is defined as 𝑔(𝑥) = −|3𝑥 − 8|.
a) Sketch the graph of 𝑔(𝑥) = −|3𝑥 − 8| for the domain −1 ≤ 𝑥 ≤ 5 and state the corresponding range
of 𝑔(𝑥).
b) State a suitable domain for 𝑔(𝑥) such that its inverse function exists.
[7 marks]
8. It is given that 𝑓(𝑥) =
3
,𝑥≠
4𝑥 − 1
1
4
dan 𝑓𝑔(𝑥) =
a) Find the object of 𝑓(𝑥) if the image is
3
4𝑥 2
.
+3
1
.
3
b) Express 𝑚 in terms of 𝑝 if 𝑓(𝑚 + 1) = 3𝑓𝑔(𝑝).
c) (i) Find 𝑔(𝑥).
(ii) Hence, determine whether the inverse function of 𝑔(𝑥) exists or not.
[8 marks]
9. Diagram 2 shows the front view of the four pieces of wood with the same width. The total front area of
the four pieces of wood is 84 cm². The four pieces of wood are used to produce a rectangular painting
frame as shown in Diagram 3.
Diagram 2
Diagram 3
a) Express the total front area of the wood in the form of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 where
𝑎 = 1.
b) Hence, find the width, in cm, of the wood by completing the square method.
[6 marks]
𝑥+3
10. (a) Verify that the function 𝑘(𝑥) = 5𝑥 − 3 has an inverse function, ℎ(𝑥) =.
5
.
(b) Diagram 4 shows the function 𝑓 which maps set 𝐾 to set 𝑀 and the function 𝑔 which maps
set 𝑀 to set 𝑁.
Diagram 4
(i) Complete the box in the Diagram 4.
(ii) Find function which maps set 𝑀 to set 𝐾, in terms of 𝑥.
(iii) Find 𝑔(𝑥).
[8 marks]
Prepared by,
Checked by,
Approved by,
Mdm. Nurul Atiqah Salim
Mr Lee CY
Mdm Kang CL