IGCSE Additional Mathemathics

이연욱 (지은이)헤르몬하우스2023-07-05

IGCSE Additional Mathematics의 토픽들을 15개의 토픽으로 세분화하였다. IGCSE Additional Mathematics 시험에 출제될 수 있는 모든 개념과 실전시험에 나오는 모든 문 제유형들을 포함하여 실전시험에 대한 적응력을 높일 수 있도록 구성했다. 이 책을 통해서 중학교 과정의 탄탄한 수학 실력을 쌓을 수 있는 것은 물론이고 향후 공부하게 되는 IB Math나 A-Level 등의 이후 고등학교 수학에 있어서의 든든한 기초가 될 것이다.

목차

CHAPTER 1 Functions 9

1.1 Definition of a function 9

1.2 Composition functions 13

1.3 Modulus or absolute value functions 14

1.4 Inverse functions 16

1.5 Transformations 19

CHAPTER 2 Quadratics 29

2.1 Quadratic functions 29

2.2 Maximum and minimum value by completing the square 31

2.3 Solving quadratic equations 32

2.4 Solving quadratic inequalities 34

2.5 Discriminant of a quadratic equation 35

CHAPTER 3 Indices and surds 43

3.1 Simplifying expressions involving indices 43

3.2 Solving equations involving indices 45

3.3 Simplifying expressions involving surds 47

3.4 Rationalizing the denominator 48

3.5 Solving equations involving surds 49

CHAPTER 4 Factors of polynomials 57

4.1 Operations with polynomials 57

4.2 Finding zeros of a polynomial function 59

4.3 The remainder theorem 60

4.4 The factor theorem 62

4.5 Rational zeros theorem 64

4.6 Graphing cubic functions 67

4.7 Solving cubic inequalities graphically 68

CHAPTER 5 Logarithmic and exponential functions 77

5.1 Logarithms 77

5.2 Properties of logarithms 79

5.3 Solving exponential and logarithmic Equations 82

5.4 Graphs of logarithmic and exponential functions 84

5.5 Graphs of y = kenx+ a and y = k ln (ax+b) 85

CHAPTER 6 Straight-line graphs 95

6.1 Coordinate geometry 95

6.2 Finding areas of polygons using shoelace method 98

6.3 Linear law 100

CHAPTER 7 Coordinate geometry of circles 109

7.1 The standard equation of a circle 109

7.2 Intersection of a circle and a straight line 111

7.3 The equation of a tangent line to a circle 113

7.4 Intersection of two circles 114

CHAPTER 8 Trigonometry 119

8.1 Circular measure 119

8.2 Finding the exact value of the trigonometric functions 123

8.3 Graphs of trigonometric functions 128

8.4 Solving trigonometric equations 134

8.5 Proving trigonometric identities 136

8.6 Area of non-right angled triangles 138

8.7 Solving triangles using the law of sines and cosines 139

CHAPTER 9 The binomial theorem 155

9.1 The Fundamental Counting Principle 155

9.2 Permutation and combination 157

9.3 The binomial theorem 159

CHAPTER 10 Sequence and series 169

10.1 Sequence 169

10.2 Series 172

CHAPTER 11 Vectors 181

11.1 Vector notation 181

11.2 Algebraic operations on vectors 183

11.3 Vector geometry 184

11.4 Constant velocity problems 191

CHAPTER 12 Derivative functions 199

12.1 Instantaneous rate of change 199

12.2 Finding the derivative functions 202

12.3 Tangent and normal lines 204

CHAPTER 13 Differentiation rules 211

13.1 The product and quotient rules 211

13.2 The chain rule 214

13.3 The second derivative 217

CHAPTER 14 Applications of differentiation 225

14.1 Small increments and approximations 225

14.2 Related rates 228

14.3 Understanding a curve from the first and second derivatives 231

14.4 Local maximum and local minimum 233

14.5 Practical maximum and minimum problems 236

CHAPTER 15 Integration 245

15.1 Indefinite integrals 245

15.2 The U-Substitution rule 250

15.3 Definite integrals 254

15.4 Area between two curves 257

15.5 Kinematics 260