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