# 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