Table of Contents

• Introduction to the book
  • The language of mathematics
• Logarithms
  • Introduction
  • Definition of logarithms
  • Logarithm bases
  • Laws of logarithms
  • Logarithm law 1: \(\log_a 1 = 0\)
  • Logarithm law 2: \(\log_a a = 1\)
  • Logarithm law 3: \(\log_a (x.y) = \log_a (x) + log_a (y)\)
  • Logarithm law 4: \(\log_a \left(\frac{x}{y}\right) = \log_a (x) - \log_a (y)\)
  • Logarithm law 5: \(\log_a \left(x^b\right) = b \log_a (x)\)
  • Logarithm law 6: \(\log_a \left(\sqrt[b]{x}\right) = \frac{\log_a (x)}{b}\)
  • Solving simple log equations
  • Logarithmic applications in the real world
  • End of chapter exercises
• Sequences and series
  • Introduction
  • Arithmetic sequences
  • Geometric sequences
  • Recursive formulae for sequences
  • Series
  • Finite arithmetic series
  • Finite squared series
  • Finite geometric series
  • Infinite series
  • End of chapter exercises
• Finance
  • Introduction
  • Finding the length of the investment or loan
  • Series of payments
  • Investments and loans
  • Formula sheet
  • End of chapter exercises
• Factorising cubic polynomials
  • Introduction
  • The factor theorem
  • Factorisation of cubic polynomials
  • Solving cubic equations
  • End of chapter exercises
• Functions and graphs
  • Introduction
  • Definition of a function
  • Notation used for functions
  • Graphs of inverse functions
  • End of chapter exercises
• Differential calculus
  • Introduction
  • Limits
  • Differentiation from first principles
  • Rules of differentiation
  • Applying differentiation to draw graphs
  • Using differential calculus to solve problems
  • End of chapter exercises
• Linear programming
  • Introduction
  • Terminology
  • Linear programming and the feasible region
  • End of chapter exercises
• Geometry
  • Introduction
  • Circle geometry
  • Co-ordinate geometry
  • Transformations
  • End of chapter exercises
• Trigonometry
  • Introduction
  • Compound angle identities
  • Applications of trigonometric functions
  • Other geometries
  • Summary of the trigonometric rules and identities
  • End of chapter exercises
• Statistics
  • Introduction
  • Normal distribution
  • Extracting a sample population
  • Function fitting and regression analysis
  • End of chapter exercises
• Combinations and permutations
  • Introduction
  • Counting
  • Notation
  • Fundamental counting principle
  • Combinations
  • Permutations
  • Applications
  • End of chapter exercises