This module covers the basic areas of mathematics. The high tutorial content encourages the learner to complete problem sheets and so lay a strong foundation for other more advanced areas of mathematics.
Arithmetic: Integers, powers and indices, fractions and decimals, fractional powers and logarithms.
Basic Algebra: Manipulation of symbols, formulae and equations, factorisation, inequalities.
Straight Lines: Different forms of the equation of a straight line, intersection of two lines, linear inequalities.
Quadratics: The quadratic curve, quadratic equations and roots, completing the square, applications.
Further Algebra: Arithmetic and geometric progressions, sigma notation, polynomials, remainder and factor theorems, partial fractions.
The Binomial Theorem: Factorial notation, combinations, the expansion of \((1+x)^n, n \in \mathrm{N}\), the General Binomial Theorem.
Trigonometry: The unit circle, radian measure, trigonometric functions and their graphs, relationships between angles, compound angles, cosine and sine rules, solution of triangles, changing products to sums and sums to products.
Complex Numbers: The imaginary unit i, addition, multiplication and division of complex numbers, geometric representation, conjugate and modulus, polar form. De Moivre’s theorem. Roots of a complex number. Complex polynomials, the remainder and factor theorems. The fundamental theorem of algebra.
Functions: Domain, codomain, range. One-one, onto and bijections. Composition of functions. Inverse functions including trigonometric functions.
Induction. Prove simple results by induction.
Lectures supported by problem-solving sessions and the use of mathematical software packages.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |