Mama march 13

1 | Add Maths F4/March Test 2013/S u l i t

SMK USJ 12,

UEP SUBANG JAYA, SELANGOR ________________________________________________________________________________

MARCH TEST 2013 ADDITIONAL MATHEMATICS

FORM 4 ________________________________________________________________________________

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.

________________________________________________________________________________ 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)


(b) State the type of the relation Nyatakan jenis hubungan tersebut (1 𝑀𝑎𝑟𝑘𝑠)

Answer / Jawapan :

(a)

(b)

________________________________________________________________________________________ 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


(c)

Answer / Jawapan : ______________________________________

________________________________________________________________________________________ 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. 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 :

_______________________________________________________________________________________

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 :


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 :

________________________________________________________________________________________

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 :


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 :

________________________________________________________________________________________ 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 :


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 :


_______________________________________________________________________________________

Section B / Bahagian B

20 Marks / 20 Markah ________________________________________________________________________________________

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) ________________________________________________________________________________________

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)

________________________________________________________________________________________ 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 ________________________________________________________________________________________

Mama march 13

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