This module covers basic algebra, trigonometry, complex numbers, the Binomial Theorem, graphical methods, introductory differential and integral calculus in one variable, Simpson’s Rule and basic probability and statistics.
- Preliminaries: Use of calculator. Volumes and surface areas, Number systems, Binary and decimal representations.
- Algebra: Transposition and substitution of formulae. Powers, roots and logarithms. Solution of simple, simultaneous and quadratic equations, functions.
- Graphical Methods: The straight line. Graphs of parabolas, cubic curves, logarithmic and exponential curves. Determination of laws by transformation of non-linear data to linear form.
- Trigonometry: Degree and radian measure. Sine and cosine rule. Application in two and three dimensions.
- Binomial Expansion: Integral and rational powers. Applications.
- Complex Numbers: Sums, products and quotients. Cartesian and Polar form. De Moivre’s Theorem.
- Differential Calculus: Derivatives of elementary functions of one variable. Sums, products, quotients and composite functions. Maximum and minimum values of functions. Points of inflexion.
- Integral Calculus: Definite and indefinite integrals of elementary functions in one variable. Solution of integrals by substitution. Numerical integration using Simpson’s rule.
- Statistics: Presentation of data. Discrete and continuous data. Measures of central tendency and dispersion. Cumulative frequency.
- Basic Probability: Addition Law. Multiplication Law for independent events. Mutually exclusive events. Conditional probability.
