add maths form 4, form 4 add maths, march test add maths

1. 1 | Add Maths F4/March Test 2013/S u l i t
SMK USJ 12,
UEP SUBANG JAYA, SELANGOR
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MARCH TEST 2013
ADDITIONAL MATHEMATICS
FORM 4
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1 HOUR 30 MINUTES
NAME: __________________________ FORM 4: _______________
Instructions :
Arahan :
1. This question paper consists of two sections: Section A and Section B.
Kertas soalan ini terdiri daripada 2 bahagian: Bahagian A dan Bahagian B.
2. Answer all questions.
Jawab semua solan.
3. Write your answers for section A in the spaces provided and the answers for Section B in your test pad.
Tulis jawapan anda bagi Bahagian A pada ruang yang disediakan dalam kertas soalan dan jawapan
bagi bahagian B pada kertas jawapan anda sendiri.
4. Show your workings. It may help you to get marks.
Tunjukkan jalan kerja. Jalan kerja mungkin membantu anda untuk mendapatkan markah.
5. The diagrams provided in the questions are not drawn to scale unless stated.
Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.
6. The mark allocated for each question and sub part of a question are shown in brackets.
Markah yang diperuntukkan bagi setiap soalan dan pecahan soalan ditunjukkan dalam kurungan.
7. You may use a scientific calculator.
Penggunaan kalkulator saintifik dibenarkan.
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Section A/ Bahagian A
40 Marks / 40 Markah
1. It is given that the relation between Set A and Set B is “ City of the state in Malaysia”.
Diberi hubungan antara Set A dan Set B ialah “Bandar negeri-negeri di Malaysia”
Set A = {𝐾𝑒𝑙𝑎𝑛𝑡𝑎𝑛, 𝑃𝑒𝑟𝑎𝑘, 𝑆𝑒𝑙𝑎𝑛𝑔𝑜𝑟}
Set B = {𝑆ℎ𝑎ℎ 𝐴𝑙𝑎𝑚, 𝐾𝑜𝑡𝑎 𝐵ℎ𝑎𝑟𝑢, 𝐼𝑝𝑜ℎ}
Relation: “City of the state in Malaysia”
Hubungan: “Bandar negeri-negeri di Malaysia”.
(a) Express the relation between set A and Set B in the form of
Tunjukkan hubungan di antara set A dan set B dalam bentuk
(i) ordered pair
pasangan bertertib (1 mark)
(ii) graph
graf (2 mark)

2. 2 | Add Maths F4/March Test 2013/S u l i t
(b) State the type of the relation
Nyatakan jenis hubungan tersebut (1 𝑀𝑎𝑟𝑘𝑠)
Answer / Jawapan :
(a)
(b)
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2. State the type of the following relations
Nyatakan jenis hubungan berikut (3 𝑀𝑎𝑟𝑘𝑠)
(a)
𝑥 𝑥2
Answer / Jawapan : ______________________________________
(b)
𝑥 √ 𝑥
Answer / Jawapan : ______________________________________
4
9
3
2
-3
3
2
−2
−3
4
9

3. 3 | Add Maths F4/March Test 2013/S u l i t
(c)
Answer / Jawapan : ______________________________________
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3.
A relation from P into Q is defined by the set of ordered pairs
Hubungan antara set P dengan set Q diwakilkan dengan pasangan bertertib
{(1, −2)(1, 1)(2,0)(2, −2)}
State:
Nyatakan:
(6 𝑀𝑎𝑟𝑘𝑠)
(a) the image of 1 ___________________________
imej bagi 1
(b) the objects of 2 ___________________________
objek bagi 2
(c) the domain ___________________________
domain
(d) the codomain ___________________________
kodomain
(e) the range ___________________________
julat
(f) the type of relation ___________________________
jenis hubungan
Set P = {0, 1, 2}
Set Q = {−2, −1, 0, 1, 2}
A relation from set P into set Q is defined by the set of ordered pairs
Hubungan antara set P dengan set Q diwakilkan dengan pasangan bertertib
{(1,4)(1,6)(2,6)(3,7)}

4. 4 | Add Maths F4/March Test 2013/S u l i t
4. Given the function 𝑓 ∶ 𝑥 →
9
𝑥
+ 6 , find :
Diberi fungsi 𝑓 ∶ 𝑥 →
9
𝑥
+ 6, cari: (3 𝑀𝑎𝑟𝑘𝑠)
(a) f(1)
f(1)
(b) the object when the image is -3
nilai bagi objek yang mempunyai imej -3
Answer / Jawapan :
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5. Given the function ℎ (𝑥) =
𝑥−3
2
,find:
Diberi fungsi ℎ (𝑥) =
𝑥−3
2
, cari: (3 𝑀𝑎𝑟𝑘𝑠)
(a) the value of x if the function h(x) maps onto itself
nilai bagi x jika fungsi h(x) memetakan kepada dirinya sendiri
(b) The value of x such that ℎ2 (𝑥) = −2
Nilai bagi x supaya ℎ2 (𝑥) = −2
Answer / Jawapan :

5. 5 | Add Maths F4/March Test 2013/S u l i t
6. Given the function 𝑓 ∶ 𝑥 →
2
𝑥+1
, 𝑥 ≠ −1 and 𝑔 (𝑥) → 𝑥 + 5, find
Diberi fungsi 𝑓 ∶ 𝑥 →
2
𝑥+1
, 𝑥 ≠ −1 dan 𝑔 (𝑥) → 𝑥 + 5, cari (4 𝑀𝑎𝑟𝑘𝑠)
(a) 𝑓𝑔 (𝑥).
(b) 𝑔2 (3).
Answer / Jawapan :
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7. Given a function 𝑔 (𝑥 ) = 𝑥 − 2 and a composite function 𝑓𝑔 (𝑥) = 𝑥2
− 4𝑥 + 7, determine the function
f(x)
Diberi fungsi 𝑔 (𝑥 ) = 𝑥 − 2 dan fungsi gubahan 𝑓𝑔 (𝑥) = 𝑥2
− 4𝑥 + 7, cari fungsi f(x) (3 𝑀𝑎𝑟𝑘𝑠)
Answer / Jawapan :

6. 6 | Add Maths F4/March Test 2013/S u l i t
8. Given the function 𝑔 ∶ 𝑥 → 4𝑥 + 7 and 𝑓 ∶ 𝑥 →
𝑥 − 3
𝑥 +2
, 𝑥 ≠ 𝒌. Find,
Diberi fungsi 𝑔 ∶ 𝑥 → 4𝑥 + 7 dan 𝑓 ∶ 𝑥 →
𝑥 − 3
𝑥 +2
, 𝑥 ≠ 𝒌. Cari, (5 𝑀𝑎𝑟𝑘𝑠)
(a) the value of k,
nilai k,
(b) 𝑔−1 ( 3)
(c) 𝑓−1
(𝑥)
Answer / Jawapan :
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9. Find the roots of the quadratic equation below.
Cari punca setiap persamaan kuadratik berikut. (5 𝑀𝑎𝑟𝑘𝑠)
(a) −3𝑥2
− 2𝑥 + 8 = 0, by factorisation.
−3𝑥2
− 2𝑥 + 8 = 0, dengan kaedah pemfaktoran.
(b) 𝑘(𝑘 + 3) − 2𝑘(𝑘 − 1) = 3 by using the formula.(Correct to 4 s.f)
𝑘(𝑘 + 3) − 2𝑘(𝑘 − 1) = 3 dengan kaedah rumus.(Tepat kepada 4 angka bererti)
Answer / Jawapan :

7. 7 | Add Maths F4/March Test 2013/S u l i t
10. Form the quadratic equation which has the roots -2 and 5. Write your answer in the form of
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0, where a, b and c are constants.Hence, state the value of a, b and c
Bentukkan persamaan kuadratik yang mempunyai punca -2 dan 5. Berikan jawapan anda dalam
bentuk 𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0, dengan keadaan a, b dan c adalah pemalar.Kemudian nyatakan nilai a, b
dan c. (4 𝑀𝑎𝑟𝑘𝑠)
Answer / Jawapan :

8. 8 | Add Maths F4/March Test 2013/S u l i t
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Section B / Bahagian B
20 Marks / 20 Markah
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1. The functions f and g are defined by 𝑓 ; 𝑥 → 5 − 3𝑥 and 𝑔 ∶ 𝑥 → 2𝑎𝑥 + 𝑏 respectively, where a and b
are constants. If the composite function 𝑓𝑔(𝑥) = 8 − 3𝑥,
Fungsi f dan g ditakrifkam sebagai 𝑓 ; 𝑥 → 5 − 3𝑥 dan 𝑔 ∶ 𝑥 → 2𝑎𝑥 + 𝑏, dengan keadaan a, b dan c
adalah pemalar. Jika fungsi gubahan 𝑓𝑔(𝑥) = 8 − 3𝑥,
(a) find the value of a and of b
carikan nilai a dan b (4 𝑀𝑎𝑟𝑘𝑠)
.
(b) sketch the graph of 𝑔 ∶ 𝑥 → |2𝑎𝑥 + 𝑏|, −2 ≤ 𝑥 ≤ 2 and state the corresponding range
lakarkan graf 𝑔 ∶ 𝑥 → |2𝑎𝑥 + 𝑏|, −2 ≤ 𝑥 ≤ 2 dan nyatakan julatnya (4𝑀𝑎𝑟𝑘𝑠)
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2. Given the quadratic equations 2𝑥2
+ 𝑥 = 6 has the roots of 𝑚 and 𝑛. Form a quadratic equation which
has roots 𝑚 − 2 and 𝑛 − 2.
Diberi persamaan kuadratik 2𝑥2
+ 𝑥 = 6 mempunyai punca of 𝑚 and 𝑛. Bentukkan persamaan
kuadratik yang mempunyai punca 𝑚 − 2 and 𝑛 − 2. (6 𝑀𝑎𝑟𝑘𝑠)
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3. Solve each of the following quadratic equations by completing the square. .(Correct to 4 s.f)
Selesaikan setiap persamaan kuadratik berikut dengan menggunakan kaedah penyempurnaan kuasa
dua. .(Tepat kepada 4 angka bererti)
(a) 3𝑥2
+ 8𝑥 − 4 = 0 (3 𝑀𝑎𝑟𝑘𝑠)
(b) 2𝑥2
= 4(𝑥 + 1) (3 𝑀𝑎𝑟𝑘𝑠)
END OF QUESTION PAPER
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