AS CIE Pure Mathematics 2 Textbook
INDEX
Chapter 1: Algebra
1.1 The modulus function
1.2 Graphs of (y = |f(x)|) where (f(x)) is linear
1.3 Solving modulus inequalities
1.4 Division of polynomials
1.5 The factor theorem
1.6 The remainder theorem
End-of-chapter review exercise 1
Chapter 2: Logarithmic and Exponential Functions
2.1 Logarithms to base 10
2.2 Logarithms to base (a)
2.3 The laws of logarithms
2.4 Solving logarithmic equations
2.5 Solving exponential equations
2.6 Solving exponential inequalities
2.7 Natural logarithms
2.8 Transforming a relationship to linear form
End-of-chapter review exercise 2
Chapter 3: Trigonometry
3.1 The cosecant, secant and cotangent ratios
3.2 Compound angle formulae
3.3 Double angle formulae
3.4 Further trigonometric identities
3.5 Expressing (a\sin\theta + b\cos\theta) in the form (R\sin(\theta \pm \alpha)) or (R\cos(\theta \pm \alpha))
End-of-chapter review exercise 3
Cross-topic Review Exercise 1
Chapter 4: Differentiation
4.1 The product rule
4.2 The quotient rule
4.3 Derivatives of exponential functions
4.4 Derivatives of natural logarithmic functions
4.5 Derivatives of trigonometric functions
4.6 Implicit differentiation
4.7 Parametric differentiation
End-of-chapter review exercise 4
Chapter 5: Integration
5.1 Integration of exponential functions
5.2 Integration of (\frac{1}{ax+b})
5.3 Integration of (\sin(ax+b)), (\cos(ax+b)) and (\sec^2(ax+b))
5.4 Further integration of trigonometric functions
5.5 The trapezium rule
End-of-chapter review exercise 5
Chapter 6: Numerical Solutions of Equations
6.1 Finding a starting point
6.2 Improving your solution
6.3 Using iterative processes to solve problems involving other areas of mathematics
End-of-chapter review exercise 6
Cross-topic Review Exercise 2
Chapter 7: Further Algebra
7.1 Improper algebraic fractions
7.2 Partial fractions
7.3 Binomial expansion of ((1+x)^n) for values of (n) that are not positive integers
7.4 Binomial expansion of ((a+x)^n) for values of (n) that are not positive integers
7.5 Partial fractions and binomial expansions
End-of-chapter review exercise 7
Chapter 8: Further Calculus
8.1 Derivative of (\tan^{-1}x)
8.2 Integration of (\frac{1}{x^2+a^2})
8.3 Integration of (\frac{kf'(x)}{f(x)})
8.4 Integration by substitution
8.5 The use of partial fractions in integration
8.6 Integration by parts
8.7 Further integration
End-of-chapter review exercise 8
Cross-topic Review Exercise 3
Chapter 9: Vectors
9.1 Displacement or translation vectors
9.2 Position vectors
9.3 The scalar product
9.4 The vector equation of a line
9.5 Intersection of two lines
End-of-chapter review exercise 9
Chapter 10: Differential Equations
10.1 The technique of separating the variables
10.2 Forming a differential equation from a problem
End-of-chapter review exercise 10
Chapter 11: Complex Numbers
11.1 Imaginary numbers
11.2 Complex numbers
11.3 The complex plane
11.4 Solving equations
11.5 Loci
End-of-chapter review exercise 11