BSc/MChem Chemistry with an Integrated Foundation Year

The Foundation Year Bursary  is available to UK students who are registered on an undergraduate foundation year here and who has had a full financial assessment carried out by Student Finance.

Details of country-specific funding available to international students can be found within our  International country profiles .

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability, therefore, we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships please visit our  undergraduate student finance pages  and the Department funding pages that you intend to progress to after successfully completing the Foundation Year.

The course unit unit aims to provide a basic course in calculus and algebra to students in Foundation studies with AS-level mathematics or equivalent.

On completion of this unit successful students will be able to:

1 - Express a (proper or improper) rational function in terms of simpler (partial) fractions. Isolate parts of a non-rational expression

which can be turned into partial fractions form.

2 - Find information (e.g. centres, crossing-points) from the equations of straight lines and circles. On the basis of information relevant to straight-lines and circles, find the equations of straight-lines and circles.

3 - Combine, as a single trigonometric ratio multiplied by a constant, two or more expressions of the form a \cos x or b \sin x.

4 - Convert the coordinates of a point from plane-polar to cartesian (rectangular) coordinates or from cartesian to plane-polar coordinates.

5 - Carry out simple differentiation and (indefinite and definite) integration using tables of derivative and integrals.

6 - Use differentiation to locate and to classify (maximum, minimum or point of inflection) stationary points and to find the maximum or minimum value that a given function takes on a given interval.

7 - Carry out differentiation of functions using the product, quotient and chain (function of a function) rules. Carry out differentiation using implicit, logarithmic and parametric differentiation.

8 - Sketch simple curves seen previously. Sketch curves on the basis of their relation with curves sketched previously or on the basis of specific values of the function. Sketch a curve using locations of axis-crossings, stationary points and asymptotes. Sketch curves for different values of a parameter.

9 - Use definite integration to find the areas between curves or between curves and the axes.

10 - Evaluate integrals using integration by parts, integration by substitution or by re-arrangement e.g. integration using partial fractions.

11 - Write down terms in a series based on the formula for a general term. Find possible general forms for a series based on a small number of terms. Find information (specific terms, sums of terms)

on the basis of other information for arithmetic and geometric series. Expand a function of the form $(a + x)^n$ as a binomial series for negative or non-integer values of n. Determine whether a (simple) series will converge or diverge.

12 - Write down the series expansion of a function around a given point as a Maclaurin or Taylor series.

13 - Determine physical behaviour of a system by means of an derivative, integral or other quantity.

Rational Functions and Partial Fractions (3 lectures)

• Simple Rational Functions (including distinction of proper / improper)
• Forms for Partial Fractions
• Techniques for finding partial fraction coefficients
• Limitations of partial fractions (combination with non-rational functions etc)

Geometry and Trigonometry (3 lectures)

• Straight Lines and Conic Sections
• Combining Trigonometric Ratios ( a cos x + b sin x = r cos (x - \alpha) etc)
• Polar Coordinates of points

Differentiation (4 lectures)

• Reminder of simple differentiation
• Stationary Points
• Product, quotient and chain rules
• Implicit, logarithmic and parametric differentiation

Curve Sketching (4 lectures)

• Some simple curves e.g. trig, exponentials,
• Functions of the form f(ax+b)
• Curve sketching by using function values
• Curve sketching using axis-crossings, stationary points and asymptotes
• Curves and a parameter.

Integration (4 lectures)

• Reminder of simple indefinite and definite integration
• Integration and areas under / between curves
• Integration by parts
• Integration by substitution
• Integration by partial fractions

Sequences and Series (4 lectures)

• The notation of series
• Arithmetic and Geometric Series
• The role of convergence
• Binomial Series
• Maclaurin and Taylor Series

Quizzes during tutorials in weeks 5, 7, 9, 11. Weighting within unit 20%

Diagnostic Followup: (week 3). Weighting within unit 10%

Examination. Weighting within unit 70%

CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)

BOSTOCK, L., & CHANDLER, S. 1981. Mathematics - the core course for A-level. Thornes, Cheltenham. (ISBN0859503062)

BOSTOCK, L., CHANDLER, S., & ROURKE, C. 1982. Further pure mathematics. Thornes, Cheltenham. (ISBN0859501035)

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates