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.

**Curricular information is subject to change***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 | |
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Assessment Breakdown |
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Formal Examination | 70 |

Other Assessment(s) | 30 |