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 icon PDF
      Reading: §§ 1.3, 1.6-1.8, 1.10-1.15
    • Sheet 2: Differentiation, PDF icon PDF
      Reading: Chapter 2
    • Sheet 3: Further Differentiation, PDF icon PDF
      Reading: §§ 3.1-3.5, 3.9-3.10
    • Sheet 4: Applications of Differentiation, PDF icon PDF
      Reading: §§ 4.1-4.4
    • Sheet 5: Taylor Series, PDF icon PDF
      Reading: §§ 5.1-5.4
    • Sheet 6: Complex Numbers, PDF icon PDF
      Reading: Chapter 6
    • Sheet 7: Matrices, PDF icon PDF
      Reading: Chapter 7
    • Sheet 8: Vectors, PDF icon PDF
      Reading: §§ 9.1-9.4, 9.6
    • Sheet 9: The Scalar 'Dot' Product, PDF icon PDF
      Reading: §§ 10.1-10.3, 10.9
    • Sheet 10: The Vector 'Cross' Product, PDF icon PDF
      Reading: §§ 11.1-11.2
    • Sheet 11: Integration, PDF icon PDF
      Reading: §§ 14.1-15.4, 15.8
    • All the above 11 sheets as one file: PDF icon PDF
  • More challenging Questions:
    • Induction 1: PDF icon PDF
      Reading: R.B.J.T. Allenby Numbers and Proof, Chapter 7
    • Induction 2: PDF icon PDF
      Reading: R.B.J.T. Allenby Numbers and Proof, Chapter 7
    • Algebra 1: PDF icon PDF
      Reading: No pre-requisites
    • Algebra 2: PDF icon PDF
      Reading: Chapters 7 and 8
    • Calculus 1 - Curve Sketching: PDF icon PDF
      Reading: §§ 4.1-4.4
    • Calculus 2 - Numerical Methods and Estimation: PDF icon PDF
      Reading: §4.6, §5.2
    • Calculus 3 - Techniques of Integration: PDF icon PDF
      Reading: §§17.5-17.7
    • Calculus 4 - Differential Equations: PDF icon PDF
      Reading: §§ 22.3-22.4, Chapter 18
    • Calculus 5 - Further Differential Equations: PDF icon PDF
      Reading: Chapter 19, §22.5
    • Complex Numbers: PDF icon PDF
      Reading: Chapter 6
    • Geometry: PDF icon PDF
      Reading: §10.1, §10.9, §11.1, §16.1
    • The second 11 sheets as one file: PDF icon PDF
  • Further Sheets on Applied Mathematics (for Mathematics, Mathematics & Statistics students)
    • Dynamics 1 - Basic Definitions. Newton's Second Law PDF icon PDF
    • Dynamics 2 - Oscillations and Further Examples. PDF icon PDF