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 third edition of D.W.Jordan and P.Smith's book Mathematical Techniques, published by Oxford University Press in 2002.

• Questions:
  • Sheet 1: Standard Functions and Techniques, (PDF)
    Reading: §§ 1.3, 1.6-1.8, 1.10-1.15
  • 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)

• 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)