Notes on logic and proof for students preparing for TMUA Paper 2. End-of-chapter exercises are provided: one version of the notes contains the answers and the other one doesn’t. TMUA is the Test of Mathematics for University Admission, required for various Economics/Computer Science/Mathematics undergraduate university courses. The text was written by me (based on the official TMUA Notes on Logic and Proof); some of the questions were written using Google Gemini and then edited/corrected/quality checked by myself. This is a second draft with a few new bits that weren’t in the first draft. I am aware that there is abundant room for these notes to be improved, and I welcome feedback. Comments, suggestions for improvement and corrections are welcome.

MCQs (and answers) for students to match an appropriate graph to a given formula, suitable for students preparing for the TMUA entrance exam. (Note that one question uses the base for natural logarithms, e, which is not in the syllabus for TMUA, but some students may have come across this, so I have left the question in.) The questions were originally written primarily as preparation for the (now defunct) MAT entrance exam, but the skills needed here are, I believe, relevant to TMUA preparation. Comments, corrections and suggestions for improvement welcome.

Given a function and its domain, students find the range of the function, the the inverse function and the domain and range of the inverse function. A grid with lots of examples for students to complete. Some extension questions too. Answers given. The bog-standard questions and answers were generated by our AI overlords, but were checked by this human underling. Extension questions are my responsibility. Comments and suggestions for improvement welcome.

A slide showing logically equivalent statements, including: if A then B; A is sufficient for B; B is necessary for A; if not B then not A; and the dreaded A only if B. Potentially useful for students preparing for TMUA Paper 2. A good plan is often to reword a knotty mathematical statement into a more easily comprehensible form. TMUA is the Test of Mathematics for University Admission, required for various Economics/Computer Science/Mathematics undergraduate university courses. Comments, suggestions for improvement and corrections are welcome.

Two MCQ review tests for students preparing for TMUA, on: necessary and sufficient conditions; counterexamples; contrapositive; converse; quantifiers and negation; logically equivalent statements. Answers are provided. TMUA is the Test of Mathematics for University Admission, required for various Economics/Computer Science/Mathematics undergraduate university courses. Questions were written using Google Gemini and then edited/corrected/quality checked by myself. Comments, suggestions for improvement and corrections are welcome.

MCQs based on logic component of TMUA : necessary and sufficient conditions; counterexamples; contrapositive; converse; quantifiers and negation; logically equivalent statements. Answers are provided. TMUA is the Test of Mathematics for University Admission, required for various Economics/Computer Science/Mathematics undergraduate university courses. Questions were written using Google Gemini and then edited/quality checked by myself. Comments, suggestions for improvement and corrections are welcome.

Students choose an appropriate integration technique for each integral in a list. Some of the integrals allow more than one method. Year 13 A level Maths. This resource is based on a similar MEI resource at http://mei.org.uk/app/uploads/2021/09/30-integration-res.pdf but allows students to develop their intuition about integration methods over a greater number of examples. Comments and suggestions for improvement welcome.

A summary of integration techniques for algebraic fractions and a grid of integrals on which to practise. Students choose an appropriate integration technique for each integral in a list. Some of the integrals allow more than one method. Year 13 A level Maths. Allows students to develop their intuition about integration methods for algebraic fractions. Comments and suggestions for improvement welcome.

A summary of the formulae that are not provided in the exam, according to the AQA and Edexcel A level Mathematics specifications.

Students solve equations involving indices. This resource develops fluency with negative and fractional indices. Suitable for GCSE/A level Maths students. Comments and suggestions for improvement welcome.

Students write the logs of various numbers in terms of the logs of two given integers. Develops fluency with logs. Suitable for A level Maths students. Comments and suggestions for improvement welcome.