Core Mathematics II module (MA12001)

Core Mathematics II develops the tools that allow mathematics to represent shape, position, motion, and change with precision. These ideas are central to pure mathematics and essential for modelling the real world, from geometry and physical systems to data-driven problems. 

Building on Core Mathematics I, you will move deeper into calculus by studying integration. You will learn how integration connects to area and total change, giving you tools that are essential for modelling changing quantities in mathematics, physics, and beyond. You will also be introduced to differential equations, which are used to describe how systems evolve, from abstract mathematical models to real physical processes.  

Alongside calculus, you will explore vectors, matrices, and geometry in two and three dimensions. These ideas give you a powerful way to describe space, solve systems of equations, and represent mathematical relationships. You will strengthen your logical reasoning and quantitative problem-solving skills, preparing you for advanced study and future careers. 

What you will learn

In this module, you will learn:

• study integral calculus and its connection to area and accumulation 
• evaluate definite and indefinite integrals 
• solve introductory differential equations 
• explore vectors, matrices, and geometry in two and three dimensions 
• study points, lines, planes, and spheres 
• solve systems of linear equations using algebraic methods. 

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

• use integration to solve mathematical and applied problems 
• interpret and solve simple differential equations 
• apply vectors and matrices to geometric problems 
• solve systems of linear equations confidently 
• use calculus, algebra, and geometry to analyse problems in later study 
• apply mathematical reasoning with precision and confidence. 

Assignments / assessment

• Coursework (40%) 
• Final, written exam (60%) 

Teaching methods / timetable

You will learn through a combination of lectures and tutorials designed to build confidence and problem-solving ability. 

Lectures introduce the key ideas, methods, and worked examples, supported by clear online lecture notes. 

In tutorials, you will apply these ideas by solving problems individually and in groups, with guidance and feedback from lecturers.