The course is designed to develop student’s key knowledge, understanding, skills and application of mathematics in subject-related contexts appropriate for entry to a degree course at any one of the NCUK Partner Universities.

**Linear Equations**

The equation of a line, parallel and perpendicular

lines. Solving pairs of simultaneous equations using

elimination, substitution and graphical methods.

**Simple probability**

Define probability, use sample space diagrams to

help calculate probabilities. Combining probabilities

and using tree diagrams. (Knowledge of conditional

probability is not expected in this module).

**Quadratic Equations, inequalities and Remainder Theorem**

Quadratic Functions: Factorising, completing the

square and using the quadratic formula.

Remainder Theorem: Simple algebraic division; use

of the factor theorem and the remainder theorem.

Graphs of quadratic and cubic functions.

Geometrical interpretation of algebraic solutions of

equations.

Inequalities: Manipulating inequalities, solving linear

and quadratic equations and inequalities.

**Binomial Expansions, Sequences and Series**

Binomial expansions: Pascal’s triangle, factorials,

binomial expansion (positive integer powers,

binomial coefficient notation, evaluation of specific

terms)

Sequences and series: Sequences, series, sigma

notation. Finite Arithmetic Progressions (AP) and

series including sum. Geometric Progressions (GP)

and series including sum. Convergence and

divergence of geometric series.

**Indices, Exponential and Logarithmic Functions**

Laws of Indices for all rational exponents.

Exponential function: Exponential function and its

graph, introduction to rates of growth, solution of

equations involving exponential functions.

Logarithmic function: Rules and manipulation of

logarithms, logarithmic function and its graph,

relationship between exponential/logarithm

functions, solution of equations involving either

exponential or logarithmic functions.

**Trigonometric Functions**

Angles (degree/radian measure). Trigonometric

ratios, trigonometric functions (sine, cosine, tangent)

and their graphs.

Calculus - differentiation

Principles: Gradients of tangents and normals to

curves, limit form, polynomial rules (inc. First

Principles). Derivatives of simple functions

(exponential, log, trigonometric. The trigonometric

functions are sin x, cos x and tan x only.) Use of

Formula Booklet (see Appendix C).

Generic applications: Using derivatives to help sketch

curves. Equations of tangents and normals. Maxima,

minima and points of inflexion which are stationary

points. Use of the second derivative.

Calculus - integration

Principles: Inverse of differentiation, standard

integrals (monomial, trigonometric, exponential),

indefinite and definite integration. (The trigonometric

functions are sin x and cos x only).

Area under a curve.

- Mathematics for Business, Science, and TechnologySteven T. Karris

2007 - Fundamentals of Actuarial MathematicsS. David Promislow

2014 - Business Ratios and Formulas : A Comprehensive GuideSteven M. Bragg
- Basic Business Math : A Life-Skills ApproachRichard P. Truchon and Tony Hicks

1997 - Financial MathematicsA. Lenin Jothi

2009 - An Introduction to The Mathematics of FinanceA. H. Pollard

2015