This page gathers all the University maths: lessons, worksheets, quizzes and tests on 14 topics for pupils aged 18-19 (Higher education (undergraduate)). They also help you prepare for the University mathematics.
Everything for University Year 1 maths is split by type, so you can go straight to what you need: lessons, worksheets, multiple choice questions, quizzes, tests or starters. Each card opens the full list of topics.
- Lessons
Notes and worked examples - Worksheets
Printable PDF with answers - Multiple choice
Ten questions per topic - Quizzes
Quick checks with instant results - Tests
Marked out of 20 - Starters
Mental maths warm-ups
About University maths
In University maths, the topics are grouped into 5 strands: Foundations (1), Calculus and analysis (6), Linear algebra (4), Probability and statistics (2), Discrete mathematics (1). First, choose a topic in the list, then open its page. Every topic has a lesson, a worksheet with a separate answer page, multiple choice questions, a quiz, a test and starters. Also, most pages have a PDF, so you can print them for homework or revision.
Finally, when a topic feels easy, move on to the next one, because each topic builds on the one before. Because every topic page links to the others, you can switch from learning to practising in one click. Meanwhile, the sidebar shows the other year groups, so you can go back or move ahead. In addition, the answers always sit on their own page; therefore you can try first and check later.
Topics in University maths
- Logic, sets and proof techniques – Write proofs using direct, contrapositive, contradiction and induction.
- Functions, limits and continuity – Use the epsilon-delta definition of limit and the intermediate value theorem.
- Differentiation and its applications – Differentiate, apply mean value theorem and Taylor expansion.
- Integration and the fundamental theorem of calculus – Use integration techniques and the fundamental theorem of calculus.
- Sequences and series convergence – Test convergence of series and find radius of convergence.
- Vectors and systems of linear equations – Solve linear systems by row reduction.
- Matrices and determinants – Calculate with matrices, determinants and inverses.
- Vector spaces and linear maps – Understand span, independence, basis and kernel/image.
- Eigenvalues and eigenvectors – Find eigenvalues, eigenvectors and diagonalise matrices.
- Multivariable calculus – Use partial derivatives, optimisation and double integrals.
- Differential equations – Solve separable, linear and constant-coefficient differential equations.
- Probability and random variables – Calculate expectation, variance and use binomial, Poisson and normal distributions.
- Statistical inference – Build confidence intervals and carry out hypothesis tests.
- Number theory and discrete mathematics – Use modular arithmetic, combinatorics and basic graph theory.