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Sample Tests

These sample tests give an approximate idea of the style and level of question you might be asked in your UPC entrance tests.

Click below to access online tests for UPCSE:  

Click below to access online sample tests for UPCH

> Mathematics

This subject module is recommended for students wishing to continue studying their undergraduate degrees at UCL on the following degree programmes: Economics BSc, Economics and Finance BSc, Mathematics BSc, Mathematics with Economics BSc, Statistics BSc, Statistics, Economics and Finance BSc, Arts and Sciences BASc amongst others.

UPCH Maths


This course provides key mathematical knowledge and skills for higher education.

It has two main aims: the academic aim is to study a selection of the topics usually covered in A-level mathematics and further mathematics to a very high academic standard, both broadening and deepening the student’s knowledge.

In addition, the course aims to prepare the students with the skills necessary for successful study at a British university, namely to prepare them for a more independent, self-motivated, questioning way of study. The method and reasoning behind the correct answers will be emphasized.

Content and skills

You should be familiar with the topics of algebra, trigonometry and geometry, as taught at secondary schools in general.

Topics covered include:

  • Algebra (3 weeks): quadratic eqns and their roots, sum and product of roots, remainder theorem, factor theorem, binomial theorem for all real powers, applications, hyperbolic functions, partial fractions;
  • Series (3 weeks):arithmetic and geometric series, ratio, comparison, limit-comparison and n-th term tests for convergence, Taylor series and Maclaurin series;
  • Proof (1 week): methods and language of proof, proof by induction; - Matrices (2 weeks): matrix arithmetic, simultaneous equations, solving systems by row reduction, inverses, inverses and systems of equations;
  • Differentiation (4-5 weeks): first principles, differentiating polynomial, trig, exponential, log, inverse trig and hyperbolic trig functions, product, quotient and chain rule, implicit diff, curve sketching and extrema;
  • Integration (4-5 weeks): Techniques (substitution, trig and hyberbolic trig substitution, parts), area, volume, basic differential eqns;
  • Complex numbers (2 weeks): imaginary numbers, arithmetic, complex roots, Argand diagrams, modulus-argument form, de Moivre's theorem;
  • Statistics (4-5 weeks); descriptive stats, basic probability, permutations and combinations, binomial and poisson probability.


Course structure

The course is organised by lectures and tutorials. In addition to the end of term tests and final exam, you will have to hand in regular coursework throughout the year.

Page last modified on 07 feb 13 11:28 by Martin L White