Fundamental Algebra and Calculus module (MA11002)

Strong university mathematics begins with confidence in the fundamentals. In this module, you will strengthen the algebra, functions, trigonometry, vectors, differentiation, and integration skills that underpin later study in mathematics, physics, and other quantitative subjects. 

You will develop fluency with the essential techniques used to solve mathematical problems clearly and accurately. This includes manipulating algebraic expressions, working with functions and graphs, solving equations and inequalities, using trigonometry, and applying vectors in two and three dimensions. 

You will also build your understanding of calculus. You will learn how derivatives describe rates of change, and how integration connects to antiderivatives, giving you a foundation for later work in calculus, modelling, mechanics, and mathematical methods. 

This module is designed to support your transition into university-level study. You will practise choosing appropriate methods, setting out solutions clearly, and developing the logical thinking needed for more advanced modules. These skills are valuable throughout your degree and in careers that rely on problem-solving and quantitative reasoning. 

What you will learn

In this module, you will: 

• strengthen your algebraic manipulation and equation-solving skills 
• work with functions, graphs, domains, and ranges 
• solve linear, quadratic, simultaneous, and simple trigonometric equations 
• use trigonometry and vectors to solve geometric problems 
• study differentiation and rates of change 
• explore integration as the reverse process of differentiation

By the end of this module, you will be able to: 

• simplify algebraic expressions and rearrange formulae 
• analyse functions and interpret their graphs 
• solve equations and inequalities using appropriate methods 
• carry out calculations with vectors in two and three dimensions 
• calculate derivatives and antiderivatives of standard functions 
• present mathematical solutions clearly and logically 

Assignments / assessment

• Class tests (50%) 
• Final, written exam (50%) 

Teaching methods / timetable

You will learn through: 

• interactive sessions, combining clear explanation of key ideas with time to practise solving problems 
• lecture notes available before class, so you can prepare in advance and focus on understanding during sessions 
• discussion of the week’s key ideas, helping you connect methods, examples, and problem-solving techniques 
• worked examples and guided practice, showing how mathematical methods are applied step by step 
• individual and group problem-solving, helping you build confidence, independence, and mathematical communication skills 
• regular support from lecturers and peers, giving you opportunities to ask questions, test your understanding, and improve your problem-solving ability