Practice Problems
This page contains question sheets which are sent out to new students by many colleges before they arrive to start their undergraduate degree. These questions make suitable bridging material for students with single A-level Mathematics as they begin university - the material is partly revision, partly new material. All 11 sheets cover material relevant to the Mathematics, Mathematics & Statistics and Maths and Philosophy courses; sheets 8, 9 and 10 are not relevant to the Mathematics and Computer Science degree.
For each sheet the subject matter is briefly described, and there is some recommended reading material; the chapter numbers refer to the fourth edition of D.W.Jordan and P.Smith's book Mathematical Techniques, published by Oxford University Press in 2008.
- Questions:
- Sheet 1: Standard Functions and Techniques, PDF
Reading: §§ 1.3, 1.6-1.8, 1.10-1.16 - Sheet 2: Differentiation, PDF
Reading: Chapter 2 - Sheet 3: Further Differentiation, PDF
Reading: §§ 3.1-3.5, 3.9-3.10 - Sheet 4: Applications of Differentiation, PDF
Reading: §§ 4.1-4.4 - Sheet 5: Taylor Series, PDF
Reading: §§ 5.1-5.4 - Sheet 6: Complex Numbers, PDF
Reading: Chapter 6 - Sheet 7: Matrices, PDF
Reading: Chapter 7 - Sheet 8: Vectors, PDF
Reading: §§ 9.1-9.4, 9.6 - Sheet 9: The Scalar 'Dot' Product, PDF
Reading: §§ 10.1-10.3, 10.9 - Sheet 10: The Vector 'Cross' Product, PDF
Reading: §§ 11.1-11.2 - Sheet 11: Integration, PDF
Reading: §§ 14.1-15.4, 15.8 - All the above 11 sheets as one file: PDF
- All the above 11 sheets as one webpage: Questions
- Sheet 1: Standard Functions and Techniques, PDF
- More challenging Questions:
- Induction 1: PDF
Reading: R.B.J.T. Allenby Numbers and Proof, Chapter 7 - Induction 2: PDF
Reading: R.B.J.T. Allenby Numbers and Proof, Chapter 7 - Algebra 1: PDF
Reading: No pre-requisites - Algebra 2: PDF
Reading: Chapters 7 and 8 - Calculus 1 - Curve Sketching: PDF
Reading: §§ 4.1-4.4 - Calculus 2 - Numerical Methods and Estimation: PDF
Reading: §4.6, §5.2 - Calculus 3 - Techniques of Integration: PDF
Reading: §§17.5-17.7 - Calculus 4 - Differential Equations: PDF
Reading: §§ 22.3-22.4, Chapter 18 - Calculus 5 - Further Differential Equations: PDF
Reading: Chapter 19, §22.5 - Complex Numbers: PDF
Reading: Chapter 6 - Geometry: PDF
Reading: §10.1, §10.9, §11.1, §16.1 - The second 11 sheets as one file: PDF
- The second 11 sheets as one webpage: More challenging Questions
- Induction 1: PDF
- Further Sheets on Applied Mathematics (for Mathematics, Mathematics & Statistics students)
- Dynamics 1 - Basic Definitions. Newton's Second Law PDF
- Dynamics 2 - Oscillations and Further Examples. PDF
- These two sheets as one webpage: Further Sheets