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MATHS Catch
SPM 2012

USAHA +DOA+TAWAKAL

FOKUS A+

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MATHS Catch
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PAKEJ SOALAN RAMALAN TOPIKAL 2012
TINGKATAN 4
ADDITIONAL MATHEMATICS
TABLE OF CONTENTS / ISI KANDUNGAN CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 CHAPTER 5 CHAPTER 6 CHAPTER 7 CHAPTER 8 CHAPTER 9 : : : : : : : : : Functions Quadratic Equation Quadratic Function Simulataneous Equation Indices and Logartihms Coordinate Geometry Statistics Circular Measures Differentiation Solution of Triangles Index Number

CHAPTER 10 : CHAPTER 11 :

MATHS
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GEMPUR CHAPTER 1: Function Exam Year: ADDITIONAL MATHEMATICS FORM 4 / TINGKATAN 4 2012 Reference: The analysis is base on last 6 year National SPM exam paper 2005-2011 and State trial Exam 2011 Disclaimer/Penafian: The exam tips provided are base on pure forecast and assumptions. Maths Catch Network and www.mathscatch.com will not be liable for any inaccuracy of the information. Students are not encouraged to rely 100% on the tips to score in SPM exams. Students are advised to study hard for their exam. Students can use the tips as a guide. All the materials have not gone for been proof reading or editing process.

Modul didalam tajuk ini dirangka mengikut keutamaan didalam peperiksaan sebenar.Pelajar juga digalakkan melihat Contoh Soalan Peperiksaan Sebenar SPM sebagai panduan dan sumber rujukan utama.Konsep yang digunakan didalam modul ini adalah konsep latihan secara berulang menggunakan Soalan bertaraf peperiksaan sebagai medium utama atas tujuan supaya pelajar dapat mengenal pasti BENTUK SOALAN didalam peperiksaan sebenar secara maksimum. Dari segi kandungan modul ini terbahagi kepada 2 iaitu: BAHAGIAN 1 1.0 FOCUS QUESTION  Soalan + Jawapan +’Exam Tips’ Didalam bahagian pertama ini pelajar akan diperkenalkan dengan bentuk soalan yang pernah keluar pada SPM 2006 hingga 2011.Bahagaian ini boleh dikatakan sebagai pengenalan supaya pelajar mendapat gambaran secara keseluruhan,apakah bentuk soalan yang biasa ditanyakan.Bahagian pertama ini perlu diberi FOKUS utama oleh pelajar BAHAGIAN 2 2.0 INPUT learning  Soalan + Jawapan +’Exam Tips’ Didalam bahagian kedua ini pelajar akan didedahkan pula dengan bentuk dan konsep soalan yang POPULAR didalam SPM bagi KERTAS 1 & 2.Bahagian ini mengandungi 15 Soalan Contoh Popular disebelah kiri yang lengkap dengan jawapan,jalan pengiraan dan juga “exam tips” dikenali sebagai “Input learning”.Disebelah kanannya pula merupakan 15 Soalan Ramalan.Soalan pada bahagian ini sebenarnya merupakan soalan yang diubah suai dari Soalan Contoh popular tadi dikenali sebagai „Output Learning‟.Konsep yang diguna adalah buat dan Ulang semula.

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KERTAS 1
Analisis Soalan Peperiksaan Sebenar SPM 2008-2011 mengikut susunan soalan dan topic QUESTION SPM’08 SPM’09 SPM’10 FORM 4 Function 3 3 Quadratic Equation 1 1 Quadratic Functions 2 2 Simulataneous Equations TIADA TIADA Indices and Logarithms 2 2 Coordinate Geometry 2 1 Statistics 1 1 Circular Measure 1 1 Differentiation 2 1.5 Solution of Triangles TIADA TIADA Index Numbers TIADA TIADA ** Bab yang digelapkan hanya keluar didalam KERTAS 2 sahaja 3 1 2 TIADA 2 2 1 1 2 TIADA TIADA 3 1 2 TIADA 2 1 1 1 1 TIADA TIADA SPM’11

Berikut merupakan statistic soalan peperiksaan sebenar yang pernah keluar didalam Peperiksaan dari 2006- 2010..Sila LIHAT apakah PERSAMAAN dan PEMBEZAAN dari Segi tajuk.

KERTAS 2
Section A (Answer all question) Total Marks= 40 marks Bahagian A mengandungi 6 SOALAN WAJIB yang mesti dijawab. SPM’06 SPM’07 SPM’08 1 Simultaneous Simultaneous Simultaneous Equation Equation Equation 2 Functions Coordinate Quadratic Geometry Functions 3 Progressions Trigonometric Progressions Function 4 Trigonometric Differentiation Trigonometric Function +Integration Function 5 Vector Statistics Statistics 6 Statistics Progressions Vector

SPM’09 Simultaneous Equation Quadratic Equation Differentiation +Integration Trigonometric Function Vector Progressions

SPM’10 Simultaneous Equation Trigonometric Function Progressions Integration Geometry Coordinate Statistics

SPM’11 Simultaneous Equation Indices and Logarithms Progressions Statistics Geometry Coordinate Trigonometric Function

Section B (Answer 4 Question only from 5 question) Setiap Soalan=10 markah X 4 Total Mark s= 40 marks SPM’06 7 8 9 10 11 Linear Law Integration Geometry Coordinate Cricular Measure Probablility Distribution SPM’07 Linear Law Vector Circular Measure Integration Probablility Distribution SPM’08 Integration Linear Law Circular Measure Geometry Coordinate Probablility Distribution SPM’09 Integration Linear Law Geometry Coordinate Circular Measure Probablility Distribution SPM’10 Linear Law Differentiation Vector Probablility Distribution Circular Measure

SPM’11
Linear Law Integration Circular Measure Vector Probablility Distribution

Section C (Answer 2 Question only from 4 question) Total Marks=20 marks SPM’06 12 13 14 Solution of Triangle Index Number SPM’07 Solution of Triangle Index Number SPM’08 Solution of Triangle Index Number SPM’09 Solution of Triangle Index Number SPM’10 Solution of Triangle Index Number

SPM’11
Motion Along straight Line Index Number

Linear Linear Linear Linear Linear Solution of Programming Programming Programming Programming Programming Triangle 15 Motion Along Motion Along Motion Along Motion Along Motion Along Linear straight Line straight Line straight Line straight Line straight Line Programming Remark: Mengikut statistic 2005-2010 bab yang tidak pernah keluar didalam kertas dua adalah, permuatation & combination serta probability.

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1.0 FOCUS QUESTION  Soalan + Jawapan +’Exam Tips’ Perkara Wajib Pelajar Tahu Dalam Function a) b) c) d) Function Relation  Kertas 1 Absolute Function  Kertas 1 Composite Function  Kertas 1 Inverse Function  Kertas 1 & Kertas 2

A) FUNCTION RELATION/NOTATION
Domain Codomain Object Image Range = {4, 9, 16} = {2, 3, 4, 5} = 4,9,16 = 2, 3, 4 = {2, 3, 4} *Image yang mempunyai objek sahaja*

Relation between set A and B? =

f ( x)  x

EXAM TIPS: Pastikan anda tahu apa itu domain,apa itu codomain dan lain-lain perbezaan

B) ABSOLUTE FUNCTION Exam Tips 2 Untuk (b) Sangat penting.jika anda mahu hilangkan modulus “ I I “ maka Jawapanya mestilah dipecah kepada dua iaitu (+) dan (-).

D) INVERSE FUNCTION (Wajib Tahu)

Exam Tips 3 Langkah 1: tambahkan sendiri „y‟ [penting] Langkah 2 :terbalikkan kedudukan y dan x.ini bertujuan untuk menghilangkan p 1 kepada p sahaja Langkah 3: Cari nilai „y‟.maka nila y yang anda perolehi itulah inverse function

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FOKUS A+ BAHAGIAN 2
2.0 (A) INPUT learning & 2.0 (B) OUTPUT learning 
*Semua konsep dan bentuk soalan yang wajib pelajar tahu didalam bab ini didedahkan didalam soalan dibawah.sila belajar dan kaji sehingga faham*

KERTAS 1 INPUT
1

OUTPUT
1

[Pelajari dan kaji dahulu soalan dibahagian ini] Given set X = {4, 5} and set Y = {8, 13, 18, 23}. Represent the relation 'is less than' from set X to set Y using an arrow diagram. Diberi set X = {4, 5} dan set Y = {8, 13, 18, 23}. Tunjukkan hubungan 'lebih kecil daripada' dari set X ke set Y dengan menggunakan gambar rajah anak panah. [1 mark] Answer:

[Selesaikan Semua Soalan dibahagian Ini] Given set S = {6, 20} and set T = {2, 3, 7}. Represent the relation 'can be divided by' from set S to set T using an arrow diagram. Diberi set S = {6, 20} dan set T = {2, 3, 7}. Tunjukkan hubungan 'boleh dibahagikan dengan' dari set S ke set T dengan menggunakan gambar rajah anak panah. [1 mark] Answer: Jawapan:

Exam Tips : using an arrow diagram.

2

Given set X = {4, 6, 9, 12} and set Y = {2, 3, 5, 7}. Represent the relation 'can be divided by' from set X to set Y using ordered pairs. Diberi set X = {4, 6, 9, 12} dan set Y = {2, 3, 5, 7}. Tunjukkan hubungan 'boleh dibahagikan dengan' dari set X ke set Y dengan menggunakan pasangan tertib. [1 mark] [1 markah] Answer:

2

Given set S = {9, 15} and set T = {2, 3, 5, 7}. Represent the relation 'can be divided by' from set S to set T using ordered pairs. Diberi set S = {9, 15} dan set T = {2, 3, 5, 7}. Tunjukkan hubungan 'boleh dibahagikan dengan' dari set S ke set T dengan menggunakan pasangan tertib. [1 mark] [1 markah] Answer:

{(4, 2), (6, 2), (6, 3), (9, 3), (12, 2), (12, 3)} Exam Tips : using using ordered pairs.

3

Given set S = {9, 16, 20} and set T = {2, 3, 5, 7}. Represent the relation 'is a multiple of' from set S to set T using ordered pairs. Diberi set S = {9, 16, 20} dan set T = {2, 3, 5, 7}. Tunjukkan hubungan 'ialah gandaan' dari set S ke set T dengan menggunakan pasangan tertib. [1 mark] [1 markah] Answer:

3

Given set S = {4, 14, 21} and set T = {2, 3, 5, 7}. Represent the relation 'can be divided by' from set S to set T using ordered pairs. Diberi set S = {4, 14, 21} dan set T = {2, 3, 5, 7}. Tunjukkan hubungan 'boleh dibahagikan dengan' dari set S ke set T dengan menggunakan pasangan tertib. [1 mark] [1 markah] Answer:

{(9, 3), (16, 2), (20, 2), (20, 5)} Exam Tips : using ordered pairs.

4

Given set S = {8, 16} and set T = {2, 3, 5}. Represent the relation 'can be divided by' from set S to set T using a graph. Diberi set S = {8, 16} dan set T = {2, 3, 5}. Tunjukkan hubungan 'boleh dibahagikan dengan' dari set S ke set T dengan menggunakan graf. [1 mark] [1 markah] Answer:

4

Given set S = {6, 14, 15} and set T = {3, 5, 7}. Represent the relation 'can be divided by' from set S to set T using a graph. Diberi set S = {6, 14, 15} dan set T = {3, 5, 7}. Tunjukkan hubungan 'boleh dibahagikan dengan' dari set S ke set T dengan menggunakan graf. [1 mark] [1 markah] Answer:

Exam Tips : using a graph.

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5 Diagram 1 shows the relation between set P and set Q in the graph form. Rajah 1 menunjukkan hubungan antara set P dan set Q dalam bentuk graf. 5 Diagram 1 shows the relation between set P and set Q in the graph form. Rajah 1 menunjukkan hubungan antara set P dan set Q dalam bentuk graf.

State the relation in the form of ordered pairs. Nyatakan hubungan itu dalam bentuk pasangan tertib. [1 mark] [1 markah] Answer:
{(5, 3), (6, 3), (6, 5)} Keywords: relation in the form of ordered pairs Exam Tips :Lihat pada paksi x (set p) dahulu

State the relation in the form of ordered pairs. Nyatakan hubungan itu dalam bentuk pasangan tertib. [1 mark] [1 markah] Answer:

6

Diagram 2 shows the relation between set S and set T in the arrow diagram.

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Diagram 2 shows the relation between set M and set N in the arrow diagram.

State the Nyatakan (a) images of 5 imej 5 (b) objects of 10 objek 10 (c) domain of this relation domain bagi hubungan ini (d) range of this relation julat hubungan ini [1 mark] [1 markah] Answer:
(a) (b) (c) (d) 6, 10, 14 5, 6 {5, 6} {6, 10, 14}

State the Nyatakan (a) images of 6 imej 6 (b) objects of 10 objek 10 (c) domain of this relation domain bagi hubungan ini (d) range of this relation julat hubungan ini [1 mark] [1 markah] Answer: Jawapan:

Exam Tips : Range (Julat) = imej yang ada objek sahaja 7 Diagram 3 shows the relation between set P and set Q in the graph form. Rajah 3 menunjukkan hubungan antara set P dan set Q dalam bentuk graf.

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Diagram 3 shows the relation between set S and set T in the graph form. Rajah 3 menunjukkan hubungan antara set S dan set T dalam bentuk graf.

Diagram 3 Rajah 3

Diagram 3 Rajah 3

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State the Nyatakan (a) images of 3 imej 3 (b) objects of 6 objek 6 (c) domain of this relation domain bagi hubungan ini (d) range of this relation julat hubungan ini [1 mark] [1 markah] Answer:
(a) (b) (c) (d) 6, 12 2, 3 {2, 3, 5} {6, 12, 20}

State the Nyatakan (a) images of 6 imej 6 (b) object of 7 objek 7 (c) domain of this relation domain bagi hubungan ini (d) range of this relation julat hubungan ini [1 mark] [1 markah] Answer: Jawapan:

Exam Tips : Object &Domain terletak pada Set P.Images codomain terletak pada set Q 8 Diagram 4 shows the relation between set A and set B in the graph form. Rajah 4 menunjukkan hubungan antara set A dan set B dalam bentuk graf.

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Diagram 4 shows the relation between set S and set T in the graph form. Rajah 4 menunjukkan hubungan antara set S dan set T dalam bentuk graf.

State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] [1 markah] Answer:
One-to-one relation Hubungan satu dengan satu

State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] [1 markah] Answer:

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Diagram 5 shows the relation between set M and set N in the arrow diagram. Rajah 5 menunjukkan hubungan antara set M dan set N dalam gambar rajah anak panah.

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Diagram 5 shows the relation between set F and set G in the arrow diagram. Rajah 5 menunjukkan hubungan antara set F dan set G dalam gambar rajah anak panah.

State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] [1 markah] Answer:
One-to-one relation Hubungan satu dengan satu

State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] [1 markah] Answer:

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10 Diagram 6 shows the relation between set M and set N in the graph form. Rajah 6 menunjukkan hubungan antara set M dan set N dalam bentuk graf. 10 Diagram 6 shows the relation between set A and set B in the graph form. Rajah 6 menunjukkan hubungan antara set A dan set B dalam bentuk graf.

State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] Answer:
Many-to-many relation Hubungan banyak dengan banyak

State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] Answer:

11 Given {(8, a), (8, b), (2, c), (2, d)}. Diberi {(8, a), (8, b), (2, c), (2, d)}. State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] Answer:
One-to-many relation Hubungan satu dengan banyak

11 Given {(4, h), (6, i), (8, h), (8, f), (8, g), (10, f), (10, i)}. Diberi {(4, h), (6, i), (8, h), (8, f), (8, g), (10, f), (10, i)}. State the type of the relation. Nyatakan jenis hubungan itu. [1 mark] Answer:

12 Given function f : x → 5x + 8, find the Diberi fungsi f : x → 5x + 8, cari (a) image of −8 imej −8 (b) object which has the image 43 objek yang mempunyai imej 43 [1 mark] Answer:
(a) Langkah 1:f(−8) = 5(−8) + 8 Langkah 2: = −32 (b) Langkah 1: f(x) = 43 Langkah 2 : 5x + 8 = 43 Langkah 3 :5x = 35 Langkah 4 :x = 7

12 Given function f : x → −7x − 6, find the Diberi fungsi f : x → −7x − 6, cari (a) image of 4 imej 4 (b) object which has the image −27 objek yang mempunyai imej −27 [1 mark] Answer:

13 Given function f : x → 7x2 + 8, find the Diberi fungsi f : x → 7x2 + 8, cari (a) image of 8 imej 8 (b) object which has the image 120 objek yang mempunyai imej 120 Answer:
(a) f(8) = 7(8)2 + 8 = 456 (b) Langkah 1 :f(x) = 120 Langkah 2 :7x2 + 8 = 120 Langkah 3 :7x2 = 112 Langkah 4 :x2 = 16 Langkah 5: x = 4, −4

13 Given function f : x → −3x2 + 6, find the Diberi fungsi f : x → −3x2 + 6, cari (a) image of 7 imej 7 (b) object which has the image −69 objek yang mempunyai imej −69 Answer: Jawapan:

14 Given function f : x → sin 3x, 0° ≤ x ≤ 360°, find the value of Diberi fungsi f : x → sin 3x, 0° ≤ x ≤ 360°, cari nilai (a) f(30°) (b) x when f(x) = −1 x apabila f(x) = −1 [1 mark]

14 Given function f : x → sin x, 180° ≤ x ≤ 360°, find the value of Diberi fungsi f : x → sin x, 180° ≤ x ≤ 360°, cari nilai (a) f(360°) (b) x when f(x) = −0.5 x apabila f(x) = −0.5 [1 mark]

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Answer:
(a) Langkah 1 :f : x → sin 3x Langkah 2 :f(30°) = sin 90° =1 (b) Langkah 1 : f(3x) = −1 Langkah 2: sin 3x = −1 Langkah 3: 3x = 270°, 630°, 990° Langkah 4 : x = 90°, 210°, 330°

[1 markah] Answer:

15 Given function f : x → cos x, 180° ≤ x ≤ 360°, find the value of Diberi fungsi f : x → cos x, 180° ≤ x ≤ 360°, cari nilai (a) f(360°) (b) x when f(x) = 1 x apabila f(x) = 1 [1 mark] [1 markah] Answer:
(a) Langkah 1 : f : x → cos x Langkah 2 : f(360°) = cos 360° =1 (b) Langkah 1 : f(x) = 1 Langkah 2 : cos x = 1 Langkah 3 : x = 360°

15 Given function f : x → cos 3x, 0° ≤ x ≤ 180°, find the value of Diberi fungsi f : x → cos 3x, 0° ≤ x ≤ 180°, cari nilai (a) f(0°) (b) x when f(x) = 1 x apabila f(x) = 1 [1 mark] [1 markah] Answer: Jawapan:

16 Given function f : x → tan 2x, 180° ≤ x ≤ 360°, find the value of Diberi fungsi f : x → tan 2x, 180° ≤ x ≤ 360°, cari nilai (a) f(112.5°) (b) x when f(x) = 0 x apabila f(x) = 0 [1 mark] Answer:
(a) Langkah 1 : f : x → tan 2x Langkah 2: f(112.5°) = tan 225° =1 (b) Langkah 1 : f(2x) = 0 Langkah 2 : tan 2x = 0 Langkah3 : 2x = 360°, 540°, 720° Langkah 4 : x = 180°, 270°, 360°

16 Given function f : x → tan 2x, 0° ≤ x ≤ 180°, find the value of Diberi fungsi f : x → tan 2x, 0° ≤ x ≤ 180°, cari nilai (a) f(90°) (b) x when f(x) = 0 x apabila f(x) = 0 [1 mark] Answer: Jawapan:

17 Diagram 7 represents a function f: x → x2 + bx + c. Rajah 7 mewakili fungsi f: x → x2 + bx + c.

17 Diagram 7 represents a function f: x → x2 + bx + c. Rajah 7 mewakili fungsi f: x → x2 + bx + c.

Find the (a) values of b and c, nilai b dan c, (b) the image of −2 under the function. imej −2 di bawah fungsi itu. [1 mark] [1 markah] Answer:
(a) Langkah 1 : Langkah 2 : Langkah 3 : Langkah 4 : Langkah 5 : Langkah 1 : Langkah 2 : Langkah 3 : Langkah 4 : f(x) = x2 + bx + c f(6) = −17 (6)2 + b(6) + c = −17 36 + 6b + c = −17 6b + c = −53 −−−− E1 f(7) = −13 (7)2 + b(6) + c = −13 49 + 7b + c = −13 7b + c = −62 −−−− E2

Find the Cari (a) values of b and c, nilai b dan c, (b) the image of 3 under the function. imej 3 di bawah fungsi itu. [1 mark] [1 markah] Answer: Jawapan:

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Langkah 5 : E1 − E2: −b = 9 b = −9 Langkah 6 : Substitute b = −9 into E1. 6(−9) + c = −53 c=1 (b) Langkah 1 : f(x) = x2 − 9x + 1 Langkah 2 : f(−2) = (−2)2 − 9(−2) + 1 Langkah 3 : = 4 + 18 + 1 Langkah 4 : = 23

18 Diagram 8 represents a function f: x → px2 + qx − 9. Rajah 8 mewakili fungsi f: x → px2 + qx − 9.

18 Diagram 8 represents a function f: x → px2 + qx + 3. Rajah 8 mewakili fungsi f: x → px2 + qx + 3.

Find the Cari (a) values of p and q, nilai p dan q, (b) the object which is mapped onto itself. objek yang memetakan kepada diri sendiri. [1 mark] [1 markah] Answer:
(a) Langkah 1 : Langkah 2 : Langkah 3 : Langkah 4 : Langkah 5 : Langkah 6 : Langkah 7: Langkah 8 : Langkah 9: f(x) = px2 + qx − 9 f(−6) = 21 p(−6)2 + q(−6) − 9 = 21 36p − 6q − 9 = 21 36p − 6q = 30 −−−− E1 f(−3) = −3 p(−3)2 + q(−3) − 9 = −3 9p − 3q − 9 = −3 9p − 3q = 6 −−−− E2

Find the Cari (a) values of p and q, nilai p dan q, (b) the object which is mapped onto itself. objek yang memetakan kepada diri sendiri. [1 mark] [1 markah] Answer: Jawapan:

Langkah 10 : E1 × (−3): −108p + 18q = −90 Langkah 11 : E2 × (−6): −54p + 18q = −36 Langkah 12: E3 − E4: −54p = −54 p=1

−−−− E3

−−−− E4

Langkah 13 : Substitute p = 1 into E1. 36(1) − 6q = 30 −6q = 30 − 36 = −6 q=1 (b) Langkah 1 : f(x) = x2 + x − 9 Langkah 2 : x2 + x − 9 = x Langkah 3 : x2 − 9 = 0 Langkah 4 : (x − 3)(x + 3) = 0 Langkah 5 : x = 3, −3

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19 Given the function f : x → |x − 2|. Diberi fungsi f : x → |x − 2|. (a) Find the images of −5, 0 and 9. Cari imej bagi −5, 0 dan 9. (b) Sketch the graph of f(x) for the domain −5 ≤ x ≤ 9. Lukis graf f(x) bagi domain −5 ≤ x ≤ 9. [1 mark] [1 markah] Answer:
(a) f(x) = |x − 2| f(−5) = |(−5) − 2| = |−7| =7 f(0) = |(0) − 2| = |−2| =2 f(9) = |(9) − 2| = |7| =7 (b) f(x) = 0 |x − 2|= 0 x−2=0 x=2

USAHA +DOA+TAWAKAL

FOKUS A+

19 Given the function f : x → |−x − 5|. Diberi fungsi f : x → |−x − 5|. (a) Find the images of −9, 0 and 2. Cari imej bagi −9, 0 dan 2. (b) Sketch the graph of f(x) for the domain −9 ≤ x ≤ 2. Lukis graf f(x) bagi domain −9 ≤ x ≤ 2. [1 mark] [1 markah] Answer: Jawapan:

20 Given the function f : x → |x2 − 9|. Diberi fungsi f : x → |x2 − 9|. (a) Find the images of −9, 3 and 9. Cari imej bagi −9, 3 dan 9. (b) Find objects which have the image of 4. Cari objek-objek yang mempunyai imej 4. [1 mark] [1 markah] Answer:
(a) f(−9) = |(−9)2 − 9| = |72| = 72 f(3) = |(3)2 − 9| = |0| =0 f(9) = |(9)2 − 9| = |72| = 72 (b) f(x) = 4 |x2 − 9| = 4 So, x2 − 9 = 4 x2 = 13 x = − 13, 13 and −(x2 − 9) = 4 x2 = 5 x = − 5, 5

20 Given the function f : x → |x2 − 6|. Diberi fungsi f : x → |x2 − 6|. (a) Find the images of −4, 5 and 6. Cari imej bagi −4, 5 dan 6. (b) Find objects which have the image of 4. Cari objek-objek yang mempunyai imej 4. [1 mark] [1 markah] Answer: Jawapan:

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MATHS Catch
SPM 2012
21 Given function f : x → |cos x|, 0° ≤ x ≤ 360°. Find the values of f(60°) and f(255°). [1 mark] Answer: f(x) = |cos x| f(60°) = |cos 60°| = 0.5 f(255°) = |cos 255°| = |−cos (255° − 180°)| = |−cos 75°| = 0.2588

USAHA +DOA+TAWAKAL

FOKUS A+

21 Given function f : x → |cos x|, 0° ≤ x ≤ 360°. Find the values of f(15°) and f(135°). Diberi fungsi f : x → |cos x|, 0° ≤ x ≤ 360°. Cari nilai f(15°) dan f(135°). [1 mark] Answer::

22 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 9 − 9x dan g : x → −3x − 7. Cari fungsi gubahan gf dan fg. [1 mark] Answer:
Given f(x) = 9 − 9x and g(x) = −3x − 7. Diberi f(x) = 9 − 9x dan g(x) = −3x − 7. gf(x) = g(f(x)) = g(9 − 9x) = −3(9 − 9x) − 7 = 27x − 34 fg(x) = f(g(x)) = f(−3x − 7) = 9 − 9(−3x − 7) = 27x + 72

22 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 4x − 9 dan g : x → −4x − 3. Cari fungsi gubahan gf dan fg. [1 mark] Answer:

23 The functions of f and g are defined as f : x → x + 9 and g : x → x − 6. Find the composite function of gf and the value of gf(−4). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x + 9 dan g : x → x − 6. Cari fungsi gubahan gf dan nilai gf(−4). [1 mark] Answer:
Given f(x) = x + 9 and g(x) = x − 6. Diberi f(x) = x + 9 dan g(x) = x − 6. gf(x) = g(f(x)) = g(x + 9) = (x + 9) − 6 =x+3 gf(−4) = (−4) + 3 = −1

23 The functions of f and g are defined as f : x → x − 4 and g : x → x + 2. Find the composite function of gf and the value of gf(−1). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x − 4 dan g : x → x + 2. Cari fungsi gubahan gf dan nilai gf(−1). [1 mark] Answer:

24 The functions of f and g are defined as f : x → −x + 4 and x g : x → − . Find the composite function of gf and fg. 6 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −x + 4 x dan g : x → − . Cari fungsi gubahan gf dan fg. 6 [1 mark] Answer: x Given f(x) = −x + 4 and g(x) = − . 6 x Diberi f(x) = −x + 4 dan g(x) = − . 6 gf(x) = g(f(x)) = g(−x + 4) x−4 = 6 fg(x) = f(g(x)) x =f − 6 x =− − +4 6 1 = x+4 6

24 The functions of f and g are defined as f : x → −x − 2 and x g : x → . Find the composite function of gf and fg. 6 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −x − 2 x dan g : x → . Cari fungsi gubahan gf dan fg. 6 [1 mark] Answer:

( ) ( )

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MATHS Catch
SPM 2012
25 The functions of f and g are defined as f : x → −x + 2 and x g : x → . Find the composite function of gf and the 3 value of gf(−4). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −x + 2 x dan g : x → . Cari fungsi gubahan gf dan nilai gf(−4). 3 [1 mark] [1 markah] Answer: x Given f(x) = −x + 2 and g(x) = . 3 x Diberi f(x) = −x + 2 dan g(x) = . 3 gf(x) = g(f(x)) = g(−x + 2) −x + 2 = 3 −(−4) + 2 gf(−4) = 3 =2

USAHA +DOA+TAWAKAL

FOKUS A+

25 The functions of f and g are defined as f : x → −x + 7 and x g : x → − . Find the composite function of gf and the 6 value of gf(−5). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −x + 7 x dan g : x → − . Cari fungsi gubahan gf dan nilai 6 gf(−5). [1 mark] [1 markah] Answer: Jawapan:

26 The functions of f and g are defined as f : x → −x − 1 and x g : x → − . Find the composite function of fg and the 9 value of fg(−6). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −x − 1 x dan g : x → − . Cari fungsi gubahan fg dan nilai 9 fg(−6). [1 mark] [1 markah] Answer: x Given f(x) = −x − 1 and g(x) = − . 9 x Diberi f(x) = −x − 1 dan g(x) = − . 9 fg(x) = f(g(x)) x =f − 9 x =− − −1 9 1 = x−1 9 1 fg(−6) = (−6) − 1 9 5 =− 3

26 The functions of f and g are defined as f : x → −x − 8 and x g : x → . Find the composite function of fg and the 3 value of fg(−2). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −x − 8 x dan g : x → . Cari fungsi gubahan fg dan nilai fg(−2). 3 [1 mark] [1 markah] Answer: Jawapan:

( ) ( )

27 The functions of f and g are defined as f : x → x + 8 and g : x → x2 − 7. Find the composite function of gf and fg. Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x + 8 dan g : x → x2 − 7. Cari fungsi gubahan gf dan fg. [1 mark] [1 markah] Answer:
Given f(x) = x + 8 and g(x) = x2 − 7. Diberi f(x) = x + 8 dan g(x) = x2 − 7. gf(x) = g(f(x)) = g(x + 8) = (x + 8)2 − 7 = (x2 + 16x + 64) − 7 = x2 + 16x + 57 fg(x) = f(g(x)) = f(x2 − 7) = (x2 − 7) + 8 = x2 + 1

27 The functions of f and g are defined as f : x → x − 5 and g : x → x2 − 3. Find the composite function of gf and fg. Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x − 5 dan g : x → x2 − 3. Cari fungsi gubahan gf dan fg. [1 mark] [1 markah] Answer: Jawapan:

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MATHS Catch
SPM 2012
28 The functions of f and g are defined as f : x → 2x + 1 and g : x → −x2 − 7. Find the composite function of gf and the value of gf(−2). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 2x + 1 dan g : x → −x2 − 7. Cari fungsi gubahan gf dan nilai gf(−2). [1 mark] [1 markah] Answer:
Given f(x) = 2x + 1 and g(x) = −x2 − 7. Diberi f(x) = 2x + 1 dan g(x) = −x2 − 7. gf(x) = g(f(x)) = g(2x + 1) = −(2x + 1)2 − 7 = −(4x2 + 4x + 1) − 7 = −4x2 − 4x − 8 gf(−2) = −4(−2)2 − 4(−2) − 8 = −16

USAHA +DOA+TAWAKAL

FOKUS A+

28 The functions of f and g are defined as f : x → −2x − 3 and g : x → 5x2 − 4. Find the composite function of gf and the value of gf(3). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → −2x − 3 dan g : x → 5x2 − 4. Cari fungsi gubahan gf dan nilai gf(3). [1 mark] [1 markah] Answer: Jawapan:

29

The functions of f and g are defined as f : x → x→ 4 − 9x , x ≠ 0. Find the function g. x

5 and gf : x

29

The functions of f and g are defined as f : x → x→ −8x − 6 , x ≠ 0. Find the function g. x

7 and gf : x

Fungsi-fungsi f dan g ditakrifkan sebagai f : x → gf : x → 4 − 9x , x ≠ 0. Cari fungsi g. x

5 dan x

Fungsi-fungsi f dan g ditakrifkan sebagai f : x → gf : x → −8x − 6 , x ≠ 0. Cari fungsi g. x

7 dan x

[1 mark] [1 markah] Answer:
5 4 − 9x Given f(x) = and gf(x) = . x x 5 4 − 9x Diberi f(x) = dan gf(x) = . x x gf(x) = g(f(x)) 5 = g( ) x 5 Let y = x 5 So, x = y 5 4−9 y g(y) = 5 y 5  y = 4 − 9 y  5  4 = y−9 5 4 Therefore, g : x → x − 9 5

[1 mark] [1 markah] Answer: Jawapan:

()

()()

30 The functions of f and g are defined as f : x → 7x − 1 and x+8 g:x→ , x ≠ 8. Find the composite function of gf x−8 and fg. Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 7x − 1 x+8 dan g : x → , x ≠ 8. Cari fungsi gubahan gf dan fg. x−8 [1 mark] [1 markah] Answer:
Diberi f(x) = 7x − 1 dan g(x) = gf(x) = g(f(x)) = g(7x − 1) x+8 . x−8

30 The functions of f and g are defined as f : x → 9x + 5 and x−1 g:x→ , x ≠ 5. Find the composite function of gf x−5 and fg. Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 9x + 5 x−1 dan g : x → , x ≠ 5. Cari fungsi gubahan gf dan fg. x−5 [1 mark] [1 markah] Answer: Jawapan:

15
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MATHS Catch
SPM 2012

USAHA +DOA+TAWAKAL

FOKUS A+
=

(7x − 1) + 8 (7x − 1) − 8 7x + 7 = ,x≠9 7x − 9 fg(x) = f(g(x)) x+8 =f x−8 x+8 =7 −1 x−8 7(x + 8) − (x − 8) = x−8 6x + 64 = ,x≠8 x−8

( ) ( )

31 The functions of f and g are defined as f : x → x + 5 and x+7 g:x→ , x ≠ k. Find x+8 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x + 5 x+7 dan g : x → , x ≠ k. Cari x+8 (a) the value of k nilai k (b) the composite function f2 fungsi gubahan f2 (c) the composite function gf fungsi gubahan gf [1 mark] [1 markah] Answer:
(a) x + 8 = 0 x = −8 ∴k = −8 (b) f2 = f(f(x)) = f(x + 5) = (x + 5) + 5 = x + 10 (c) gf(x) = g(f(x)) = g(x + 5) (x + 5) + 7 = (x + 5) + 8 x + 12 = , x ≠ −13 x + 13

31 The functions of f and g are defined as f : x → x + 7 and x−3 g:x→ , x ≠ k. Find x+9 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x + 7 x−3 dan g : x → , x ≠ k. Cari x+9 (a) the value of k nilai k (b) the composite function f2 fungsi gubahan f2 (c) the composite function gf fungsi gubahan gf [1 mark] [1 markah] Answer: Jawapan:

32 The functions of f and g are defined as f : x → 9x + 6 and fg : x → −6x − 5. Find the function g. Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 9x + 6 dan fg : x → −6x − 5. Cari fungsi g. [1 mark] [1 markah] Answer:
Diberi f(x) = 9x + 6 dan fg(x) = −6x − 5. fg(x) = f(g(x)) = 9g(x) + 6 9g(x) + 6 = −6x − 5 −6x − 11 g(x) = 9 −6x − 11 ∴g:x→ 9

32 The functions of f and g are defined as f : x → 9 − 8x and fg : x → 4x + 3. Find the function g. Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 9 − 8x dan fg : x → 4x + 3. Cari fungsi g. [1 mark] [1 markah] Answer: Jawapan:

33 The functions of f and g are defined as f : x → x − 1 and g : x → 1 − 9x. Find the composite function of gf and the value of gf(3). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x − 1 dan g : x → 1 − 9x. Cari fungsi gubahan gf dan nilai gf(3). Answer:
Given f(x) = x − 1 and g(x) = 1 − 9x.

33 The functions of f and g are defined as f : x → x − 3 and g : x → 8x + 2. Find the composite function of gf and the value of gf(−4). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → x − 3 dan g : x → 8x + 2. Cari fungsi gubahan gf dan nilai gf(−4). Answer:

16
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MATHS Catch
SPM 2012

USAHA +DOA+TAWAKAL

FOKUS A+ gf(x) = g(f(x)) = g(x − 1) = 1 − 9(x − 1) = −9x + 10 gf(3) = −9(3) + 10 = −17

34 Given the function f : x → ax + b and the composite function f2 : x → 25x + 36, where a and b are constants and a > 0, find the values of a and b. Diberi fungsi f : x → ax + b dan fungsi gubahan f2 : x → 25x + 36, di mana a dan b ialah pemalar dan a > 0, cari nilai a dan b. [1 mark] [1 markah] Answer: f2(x) = a(ax + b) + b = a2b + ab + b 2 a = 25 a=5 ab+ b = 36 6b = 36 b=6

34 Given the function f : x → ax + b and the composite function f2 : x → 16x + 10, where a and b are constants and a > 0, find the values of a and b. Diberi fungsi f : x → ax + b dan fungsi gubahan f2 : x → 16x + 10, di mana a dan b ialah pemalar dan a > 0, cari nilai a dan b. [1 mark] [1 markah] Answer: Jawapan:

35 The fuction f is defined as f : x → 7x − 9. Find Fungsi f ditakrifkan sebagai f : x → 7x − 9. Cari (a) f−1(5) (b) f−1(x) [1 mark] [1 markah] Answer:
(a) Let f−1(5) = k So f(k) = 5 7k − 9 = 5 k=2 Therefore, f−1(5) = 2 (b) Let f−1(x) = y So f(y) = x 7y − 9 = x 7y = x + 9 x+9 y= 7 x+9 Therefore, f−1(x) = 7

35 The fuction f is defined as f : x → 3x − 5. Find Fungsi f ditakrifkan sebagai f : x → 3x − 5. Cari (a) f−1(1) (b) f−1(x) [1 mark] [1 markah] Answer: Jawapan:

36 The fuctions f and g are defined as f : x → 3x + 3 and g : x → −5x − 1. Find gf−1(x). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 3x + 3 dan g : x → −5x − 1. Cari gf−1(x). [1 mark] Answer:
Let f−1(x) = y So f(y) = x 3y + 3 = x x−3 y= 3

36 The fuctions f and g are defined as f : x → 2 − 5x and g : x → 2x − 4. Find gf−1(x). Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 2 − 5x dan g : x → 2x − 4. Cari gf−1(x). [1 mark] Answer:

Therefore f−1(x) = gf−1(x) = g(f−1(x)) x−3 = g( ) 3 x−3 = −5( )−1 3 12 − 5x = 3

x−3 3

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MATHS Catch
SPM 2012

USAHA +DOA+TAWAKAL

FOKUS A+
KERTAS 2 INPUT
1

OUTPUT
1

[Pelajari dan kaji dahulu soalan dibahagian ini] −1 2 The fuctions f and g are defined as f : x → ,x≠ 3x − 2 3 and g : x → −8x. Find −1 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 3x − 2 2 , x ≠ dan g : x → −8x. Cari 3 (a) f−1(x) [2 marks] [2 markah] (b) f−1g(x) [2 marks] [2 markah] (c) gf−1(x) [2 marks] [2 markah]

[Selesaikan Semua Soalan dibahagian Ini] −1 The fuctions f and g are defined as f : x → , x ≠ −4 2x + 8 and g : x → −2x. Find −1 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 2x + 8 , x ≠ −4 dan g : x → −2x. Cari (a) f−1(x) [2 marks] [2 markah] (b) f−1g(x) [2 marks] [2 markah] (c) gf−1(x) [2 marks] [2 markah]

(a) Let f−1(x) = y So f(y) = x −1 =x 3y − 2 −1 = x(3y − 2) −1 = 3xy − 2x 2x − 1 = 3xy 2x − 1 y= 3x Therefore f−1(x) = 2x − 1 ,x≠0 3x

(b) f−1g(x) = f−1(g(x)) = f−1(−8x) 2(−8x) − 1 = 3(−8x) −16x − 1 = ,x≠0 −24x −1 −1 (c) gf (x) = g(f (x)) 2x − 1 = g( ) 3x 2x − 1 = −8( ) 3x 8 − 16x = ,x≠0 3x

2

The fuctions f and g are defined as f : x → 4 − and g : x → 2x. Find 5

2 ,x≠ 5x + 4

2

The fuctions f and g are defined as f : x → 2 − and g : x → 4x. Find 3

2 ,x≠ 3x + 2

Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 4 , x ≠ − dan g : x → 2x. Cari 5 −1 (a) f (x)

2 5x + 4

Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 2 , x ≠ − dan g : x → 4x. Cari 3 −1 (a) f (x)

2 3x + 2

[2 marks] [2 markah] (b) f−1g(x) [2 marks] [2 markah] (c) gf−1(x) [2 marks] [2 markah] (c) gf−1(x) (b) f−1g(x)

[2 marks] [2 markah] [2 marks] [2 markah] [2 marks] [2 markah]

18
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MATHS Catch
SPM 2012

USAHA +DOA+TAWAKAL

FOKUS A+
(a) Let f−1(x) = y So f(y) = x 2 =x 5y + 4 2 = x(5y + 4) 2 = 5xy + 4x 2 − 4x = 5xy 2 − 4x y= 5x Therefore f−1(x) = (b) f−1g(x) = f−1(g(x)) = f−1(2x) 2 − 4(2x) = 5(2x) 1 − 4x = ,x≠0 5x −1 (c) gf (x) = g(f−1(x)) 2 − 4x = g( ) 5x 2 − 4x = 2( ) 5x 4 − 8x = ,x≠0 5x 2 − 4x ,x≠0 5x

3

The fuctions f and g are defined as f : x → 3 − and g : x → 5x. Find 4

−3 ,x≠ 4x + 3

3

The fuctions f and g are defined as f : x → and g : x → 5x. Find

4 3 ,x≠ 3 − 5x 5 4 3 − 5x

−3 Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 4x + 3 3 , x ≠ − dan g : x → 5x. Cari 4 (a) f−1(x) [2 marks] [2 markah] (b) f−1g(x) [2 marks] −1 (c) gf (x) [2 marks]
(a) Let f−1(x) = y So f(y) = x −3 =x 4y + 3 −3 = x(4y + 3) −3 = 4xy + 3x −3x − 3 = 4xy −3x − 3 y= 4x Therefore f−1(x) = −3x − 3 ,x≠0 4x

Fungsi-fungsi f dan g ditakrifkan sebagai f : x → 3 , x ≠ dan g : x → 5x. Cari 5 (a) f−1(x)

[2 marks] [2 markah] (b) f−1g(x) [2 marks] [2 markah] (c) gf−1(x) [2 marks] [2 markah]

(b) f−1g(x) = f−1(g(x)) = f−1(5x) −3(5x) − 3 = 4(5x) −15x − 3 = ,x≠0 20x (c) gf−1(x) = g(f−1(x)) −3x − 3 = g( ) 4x −3x − 3 = 5( ) 4x −15x − 15 = ,x≠0 4x

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MATHS Catch
SPM 2012

USAHA +DOA+TAWAKAL

FOKUS A+
4 The functions f and g are defined as f : x → 5 and g : x → 4x. Find 3 (a) f−1(x)

x−8 ,x≠ 5 − 3x

4

The fuctions f and g are defined as f : x → and g : x → −8x. Find (a) f−1(x)

x−2 2 ,x≠ 7x − 2 7

[2 marks] (b) f−1g(x) [2 marks] (c) gf−1(x) [2 marks]
(a) Let f−1(x) = y So f(y) = x y−8 =x 5 − 3y y − 8 = x(5 − 3y) y − 8 = −3xy + 5x y + 3xy = 5x + 8 y(3x + 1) = 5x + 8 5x + 8 y= 3x + 1 Therefore, f−1(x) = (c) gf (x) = g(f (x)) 5x + 8 = g( ) 3x + 1 5x + 8 = 4( ) 3x + 1 20x + 32 1 = ,x≠− 3x + 1 3
−1 −1

[2 marks] [2 markah] (b) f−1g(x) [2 marks] [2 markah] (c) gf−1(x) [2 marks] [2 markah]

5x + 8 1 ,x≠− 3x + 1 3

(b) f−1g(x) = f−1(g(x)) = f−1(4x) 5(4x) + 8 = 3(4x) + 1 20x + 8 1 = ,x≠− 12x + 1 12

5

The functions f and g are defined as f : x → 3 − and g : x → 5x. Find 2 (a) f−1(x)

x+1 ,x≠ 2x + 3

5

The fuctions f and g are defined as f : x → 1 − and g : x → 5x. Find 5 (a) f−1(x)

x+3 ,x≠ 5x + 1

[2 marks] (b) f−1g(x) [2 marks] (c) gf−1(x) [2 marks]
(a) Let f−1(x) = y So f(y) = x y+1 =x 2y + 3 y + 1 = x(2y + 3) y + 1 = 2xy + 3x y − 2xy = 3x − 1 y(1 − 2x) = 3x − 1 3x − 1 y= 1 − 2x Therefore, f−1(x) = 3x − 1 1 ,x≠ 1 − 2x 2 (c) gf−1(x) = g(f−1(x)) 3x − 1 = g( ) 1 − 2x 3x − 1 = 5( ) 1 − 2x 15x − 5 1 = ,x≠ 1 − 2x 2

[2 marks] [2 markah] (b) f−1g(x) [2 marks] [2 markah] (c) gf−1(x) [2 marks]

(b) f−1g(x) = f−1(g(x)) = f−1(5x) 3(5x) − 1 = 1 − 2(5x) 15x − 1 1 = ,x≠ 1 − 10x 10

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...“English should not become official” America is a country filled with many people with different language trying to get along. We live in a society made up and founded by immigrants. Looking at our society today, English shouldn’t become the official language of the U.S because, first of all it is unfair for others living here who have English as a second language or can speak little English. Second of all, it will limit certain people when it comes to finding a job because not everybody is capable of speaking, reading, or writing the English language correctly. Finally, it violates the terms our country was built on. If English becomes the official language of the U.S, people with English as a second language or with little English are put at a disadvantage. It’s a fact that our society is largely made of immigrants. Moreover, children who will be born in the U.S won’t be able to learn their parent’s native language. So it wouldn’t make any sense from the government to limit them because the government will need bilingual people. We take pride in our diversity, so when we limit our diversity, we put people here at a disadvantage. Additionally, there are certain people who don’t dedicate themselves to learn the English language. The reason is because they get employed by businesses that practice the same language. For instance, lots of Spanish immigrants only get to work in the Spanish community. Spanish is very much used in the United States, because they don’t develop any...

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English

...ourselves by only speaking English?” Will Hutton clarity how he think it´s important for the individual person and the English people to learn more than the language, which are their native language. He talk about how it´s important to speak a foreign language, especially to save the Britain´s future economic. By comparing England and America where he see same “xenophobia” culture, he indicate why American can have their attitude to foreign language while they can´t, like it´s saying in the text. In addition will Hutton see this as a lost interest in other countries from the youth, he discuss how that fact establish this unwillingness. The second text by David Hughes “Do we really need foreign language skills to flourish?” David Hughes thinks that the fluency in foreign language is a benefit for anyone, but he doesn´t see the importance in that, when the rest of the world is learning English. When David Hughes went to the Far East, he heard English spoken everywhere, and as he wrote it in the text. The third text by Susan Purcell “Saying Britons ´don’t do´ languages is a fallacy” explain why the discussion about the English language skills is far more nuances. Susan Purcell is comparing the text to the EU-countries with England. She is talking about how the other European Union countries compare their language and how English is the mandatory first foreign language in 13 of the EU´s member states. Over 90 % of children in European countries ‘schools learn English, like is saying in...

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...English should continue to be the official language of India. English is used as the official language in India. Yes • English is one such language that is understood by people from different castes and states, and therefore deserves to be the official language of India. • If any other language is tried to make the official language, all the regional parties will start the battle of making the state level as official language of India. • If Hindi is given priority then it will create differences among the people who don’t speak it making them feel as second class citizens. • Region C forms an important part of India that got agitated when PM Modi used Hindi for its diplomatic talks.  • The use of English language is as per the requirement of being a part of globalization and there is nothing wrong in it. No • Forget about all the different castes and religions as Indians have their own national language that is Hindi, and that should only be the official language of India. • It is the duty of the government to take the measures so that people all over in India can read, write and speak in Hindi.  • Already Indian has adopted the western culture in many ways. If it continues there will be no personal or rather say national identity of India. • In this case, India should learn something from Pakistan who made the Urdu as their official language after the division of country. • The small little steps are the ways that will make sure that the...

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...COMPULSORY SUBJECT ENGLISH (801) Aims (English Language) To develop the ability to: • • • derive, infer and critically assess information through listening. express oneself by speaking individually, or in a discussion. read with comprehension drawing information directly or by inference from the text, through an understanding of grammar and structure, vocabulary and idiom. employ a variety of skills in writing : within a framework, using argument or imagination or note making and summarizing. • • use the English language for the purpose of study and social and cultural interaction. speak and write clearly and to the purpose, using appropriate grammar, vocabulary and idiom. Aims (Prescribed Texts) 1. To enjoy and appreciate literature through a critical study of selected literary works. 2. Through the study of literature: • • • approach an understanding of humanity. develop an interest in the thought and culture of the peoples of the world. develop the power of expression and a sense of aesthetic values. • CLASSES XI & XII There will be two papers as follows: Paper 1: English Language (3 hours) – 100 marks Paper 2: Prescribed Textbooks (3 hours) – 100 marks Paper 1: English Language (3 hours) Question One: A composition on one of a number of subjects. ...30 Marks Question Two: Directed writing (an article, a book/film review, speech and report writing or personal profile) based on suggested points...20 Marks Question Three: Short-answer questions to test grammar, structure...

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...Assignment 1: The Story of English "A English Speaking World" English as a world language has developed through different periods of time and in different places. English was and is still spoken in great numbers in countries across the world. English has branched out into different dialects, with slang included especially in the American form of English. English also bears a sort of social class, where those who speak English have a certain upper class appearance. It also creates a common language which helps business, economies and people connect better. It has become a dominant language and serves as a lingua franca for the world. The popularity of English has allowed the world to communicate at a higher efficiency when compared to a world with no dominate language. But his plan did not work and India along with China has seen an ever increasing number of people learning and speaking English. The popularity and necessity of English is seen in India government systems and everyday life. India's civil system is predominantly in English rather than Hindi. Out of 137 typist at a civil court, only one types in Hindi while the rest in English. This is necessary for smooth transactions to occur in India's systems, which we have seen from examples in class. Without a lingua franca, communication between India's different regions would be very difficult. In India there are 14 different variations of Hindi, with English as a common language miscommunication is less...

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...Anyone who reads Old and Middle English literary texts will be familiar with the mid-brown volumes of the EETS, with the symbol of Alfred's jewel embossed on the front cover. Most of the works attributed to King Alfred or to Aelfric, along with some of those by bishop Wulfstan and much anonymous prose and verse from the pre-Conquest period, are to be found within the Society's three series; all of the surviving medieval drama, most of the Middle English romances, much religious and secular prose and verse including the English works of John Gower, Thomas Hoccleve and most of Caxton's prints all find their place in the publications. Without EETS editions, study of medieval English texts would hardly be possible. As its name states, EETS was begun as a 'club', and it retains certain features of that even now. It has no physical location, or even office, no paid staff or editors, but books in the Original Series are published in the first place to satisfy subscriptions paid by individuals or institutions. This means that there is need for a regular sequence of new editions, normally one or two per year; achieving that sequence can pose problems for the Editorial Secretary, who may have too few or too many texts ready for publication at any one time. Details on a separate sheet explain how individual (but not institutional) members can choose to take certain back volumes in place of the newly published volumes against their subscriptions. On the same sheet are given details about...

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...Pronunciation Schwa Schwa is the most common sound in the English language. It occurs only in unstressed syllables and getting it correct helps spoken English to sound more natural and fluent. Any vowel letter can be pronounced as schwa and the pronunciation of a vowel letter can change depending on whether the syllable in which it occurs is stressed or not. The phonemic symbol for schwa is: /e/ Following are two exercises to help students develop their awareness of schwa. The audio examples from the exercises can be downloaded from www.bbclearninglish.com Pronunciation Schwa Exercise 1 Look at the words below and decide where in the word the schwa sound occurs. Underline and/or write the schwa symbol over the correct part of the word. The first one has been done for you. Hint: One word has two examples of schwa. All the others have only one. docto r banana difficult to mo rro w s u mme r le ve l prote ct survive pupil the atre me a s u re w izard Pronunciation Schwa © BBC Learning English bbclearningenglish.com Pronunciation Schwa Exercise 2 In this exercise, look at these sentences and decide where the schwa sound occurs. It may occur more than once in each sentence. The minimum number of schwas in a sentence is 1, the maximum 7. 1. It’s for y ou /e/ 2. 3. 4. 5. 6. 7. It tak es a lot of time How about a cup of tea? What are y ou doing tonight? What time will y ou arriv e at V ictoria? I was going...

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...JEJEMON research paper by John Andrew Samonte * by diyubaku, Oct 10, 2010, 10:42:48 PM * Journals / Personal iii Table of Contents Title Page............................................................................................i Acknowledgement......................................................................ii Table of Contens......................................................................................iii Chapter I....................................................................................1 Introduction and Background of the story.........................1 Significance of the Study..................................................3 Scope and Limitations......................................................5 Chapter II................................................................................... Research Problem.................................................................................8 Effects..................................................................................................10                                                                                                                                                                          ii Acknowledgement  “You learn to speak by speaking, to study by studying, to run by running, to work by working; in just the same way, you learn to love by loving.” I  would  like  to  express my sincerest thanks to those special persons  who  made  my  life  so meaningful...

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...Mat Clark – IELTS Speaking LỜI NÓI ĐẦU Chào các bạn, xuất phát từ nhu cầu bản thân muốn học môn speaking cho bài thi tiếng anh IELTS, chúng tôi nhận thấy cuốn sách này có giá trị rất tốt cho việc tham khảo. Tuy nhiên, các bản sách điện tử đang tràn lan trên mạng Internet hiện nay có chất lượng rất thấp, kèm theo đó là việc có thêm tiếng Trung dẫn tới lãng phí về giấy in, tiền bạc, thời gian. Hiện nay, cuốn này này đã được một nhà xuất bản tại Việt Nam mua lại bản quyền từ tác giả Mat Clark, và đã xuất bản tại Việt Nam, chúng tôi khuyên các bạn nên mua cuốn sách này để sử dụng, nhằm tôn trọng giá trị của cuốn sách này, cũng như tôn trọng tác quyền của tác giả cũng như nhà xuất bản. Chúng tôi gõ lại cuốn sách này nhằm mục đích duy nhất là để học tập, nghiên cứu, không hề mang bất cứ mục đích kinh doanh nào. Mọi hành động thương mại liên quan tới bản gõ lại này là không hề liên quan tới chúng tôi. Mong các bạn tôn trọng tác giả và tôn trọng ý muốn của chúng tôi. Trong quá trình gõ và biên tập, do trình độ không chuyên, không thể tránh khỏi có sai sót. Xin cảm ơn, chúc các bạn học tốt. 1 Mat Clark – IELTS Speaking IELTS SPEAKING – MAT CLARK Preface During my 5 years as an IELTS examiner in China, I have seen thousands of Chinese IELTS candidates perform OK in the speaking interview. Most people would agree that an OK score in speaking is 5 or 6. Many students now realize that a score of 5 or 6 for speaking is not enough for their study requirements...

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...survey with a questionnaire divided into two sections, first one is for the English teachers and another one is for the students, it's...

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...I Acknowledgement For many of us, the state of education in a country speaks volumes. Where English is spoken and taught as a second language, fluency is deemed a basic requirement for proper communication and propagation of ideas and connotes success. Does this fluency actually translate to a country's economic success and overall standing in the world of nations? The reason why we came up with this topic is to test the capability of a certain number of people when it comes to proficiency in English, not just to test but to give some idea what is the importance of being proficient in English and how can it help us. English language is and has always been one of the most popular languages spoken, written & followed all over the globe. No matter in which part of the world you choose to go, command over this language enables you to communicate with others regardless of what their national language would be. Therefore it becomes not only important but compulsory to master this art & implement it in the real life. This course is designed to clear concepts, renew basics and to professionally prepare you for real life communication at all levels. · Background of the study English has been considered as international language and also for studying use English as official language. Proficiency in English includes capability to read and understand the language and the way words are pronounced as well as the sense in which word are used (though variations in usage is identified...

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...English as Official Language of United States of America The English language is originated from the Germanic tribes language, which has its roots from England in the form of Old English also known as Anglo-Saxon and has evolved into todays Modern English as we know it. English has become one of the most spoken languages in world, and is ranked as the second most spoken language. English should be the official language of the United States of America. Considered as an international language, it is the most learned and studied language throughout the world. United States laws prohibit the use of any other languages other then English on military installation or in Department of Defense buildings when conducting official business. These are just two reason of why I believe English should be the official language of the United States. In the United States, there are approximately 300 languages other than English that are spoken at home. English should be made the official language of the United States because it will knock down the language barriers for immigrants and they will be more likely to prosper in this nation, even though this may be a difficult process to accomplish at first, for many poor immigrants. In New York City, New York there are approximately thirty-five household languages other then English. If each of these subcultures of New York City have no common language, then it would create over thirty-five separate cities unable to prosper as one. Being required...

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...English y the largest language by number of words; the Oxford English Dictionary lists 500,000 words, not including technical and scientific terms.[18][19] Contents [hide] * 1 Significance * 2 History * 3 Classification and related languages * 4 Geographical distribution * 4.1 Countries in order of total speakers * 4.2 Countries where English is a major language * 4.3 English as a global language * 4.4 Dialects and regional varieties * 4.5 Constructed varieties of English * 5 Phonology * 5.1 Vowels * 5.1.1 Notes * 5.2 Consonants * 5.2.1 Notes * 5.2.2 Voicing and aspiration * 5.3 Supra-segmental features * 5.3.1 Tone groups * 5.3.2 Characteristics of intonation—stress * 6 Grammar * 7 Vocabulary * 7.1 Number of words in English * 7.2 Word origins * 7.2.1 Dutch and Low German origins * 7.2.2 French origins * 8 Writing system * 8.1 Basic sound-letter correspondence * 8.2 Written accents * 9 Formal written English * 10 Basic and simplified versions * 11 See also * 12 References * 12.1 Notes * 12.2 Bibliography * 13 External links | [edit] Significance See also: English-speaking world and Anglosphere Modern English, sometimes described as the first global lingua franca,[20][21] is the dominant...

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...English is a West Germanic language that was first spoken in early medieval England and is now a global lingua franca.[4][5] It is spoken as a first language by the majority populations of several sovereign states, including the United Kingdom, the United States, Canada, Australia, Ireland, New Zealand and a number of Caribbean nations; and it is an official language of almost 60 sovereign states. It is the third-most-common native language in the world, after Mandarin Chinese and Spanish.[6] It is widely learned as a second language and is an official language of the European Union, many Commonwealth countries and the United Nations, as well as in many world organisations. English arose in the Anglo-Saxon kingdoms of England and what is now southeast Scotland. Following the extensive influence of England, Great Britain, and the United Kingdom from the 17th to mid-20th centuries through the British Empire, it has been widely propagated around the world.[7][8][9][10] Through the spread of American-dominated media and technology,[11] English has become the leading language of international discourse and the lingua franca in many regions.[12][13] Historically, English originated from the fusion of closely related dialects, now collectively termed Old English, which were brought to the eastern coast of Great Britain by Germanic settlers (Anglo-Saxons) by the 5th century; the word English is simply the modern spelling of englisc, the name of the Angles[14] and Saxons for their...

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...Should English be made the official language of India? Well, although English is a global language and it has somewhat become necessary to know English if one has to be successful globally, still making it our country’s official language makes little sense to me. If the whole point of changing our official language is related to the growth and success of our nation then China and its growth should make no sense to the world. The leader in BRIC nations and the nation considered next ‘SUPERPOWER’ after America doesn’t have English as their official language. They are doing great with mandarin and have very less people speaking English there. When their language is not posing a hindrance to their growth, when their GDP rate is going pretty well, when they are not thinking for changing their official language but are rather putting their heads into bigger constructive discussions then why should we? Globalization has brought the world closer and therefore to know and have tolerance for different cultures and languages is absolutely great but to forget and bring a change in our own heritage is something that according to me should not be acceptable. It’s fantastic to know English and get education in the same medium. Surely, it enhances our people to be recognized globally. It may bring them confidence and it may also aid to their growth in personality, but to look down upon one’s own culture and language is like looking down upon your parents when they are old and they need help...

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