BEng/MEng Mechanical Engineering 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 aims to: provide a basic course in calculus and algebra to students in the Foundation Year with no post-GCSE mathematics.

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

1 - Define the exponential function and apply the rules of indices to simplify algebraic expressions.

2 - Use the definition of the logarithm, together with its rules, to solve logarithmic equations.

3 - Find the roots, degree, leading term and coefficients of a polynomial.

4 - Identify and solve quadratic equations using the quadratic formula.

5 - Determine the equation of a line given its gradient and a point through which it passes.

6 - Calculate the gradient of a line given: (a) two points it passes through; (b) the gradient of a line to which it is parallel/perpendicular.

7 - Find the coordinates of the intersection points of two curves.

8 - Write down the equation of a tangent to a curve at a point.

9 - Given two points in the plane, determine the equation of a circle centred at one point and passing through the other.

10 - Define the domain of a function and calculate its inverse.

11 - Determine and simplify the composition of two functions.

12 - Convert angles between degrees and radians.

13 - Using the unit circle, recall the definition of the trigonometric functions, and apply this to determine the values of these functions at commonly-encountered angles.

14 - Find the size of an angle using the inverse trigonometric functions together with geometric reasoning.

15 - Use trigonometric identities to determine all angles and side-lengths in a right-angled triangle, given a side-length and one other piece of information (side-length or angle).

16 - Use the chain/product/quotient rules to differentiate the composition/product/quotient of two functions.

17 - Apply the rules for differentiation to determine the coordinates of, and classify, the stationary points of a given function.

18 - Use integration to find the area between two curves.

Functions (3 lectures)

• Definition of a function
• Indices
• Standard functions (polynomial, exponentials, logarithms etc.)

Solution of Equations (2-3 lectures)

• Accuracy and Rounding
• Linear, Quadratic and other polynomial equations

Trigonometry (4 lectures)

• Circular measure
• Trigonometric functions
• Inverse Trig Functions
• Trigonometric Identities

Coordinate Geometry (3-4 lectures)

• Straight lines,
• circles,
• points of intersection,
• slopes and gradients

Differentiation (3 lectures)

• Definition
• Derivatives of standard functions
• Product rule
• Quotient Rule
• Chain Rule

Stationary points (2 lectures)

• Maxima and Minima
• Curve Sketching

Integration (4 lectures)

• Derivatives and anti-derivatives
• Indefinite integration, specific integrals, use of tables

Definite integrals and areas under / between curves.

Coursework 1 (week 5); Weighting within unit 10%

Coursework 2 (week 10); Weighting within unit 10%

Computer assignments; Weighting within unit 10%

End of semester 1 examination; Weighting within unit 70%

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

BOOTH, D. 1998. Foundation Mathematics (3rd ed.). Addison-Wesley, Harlow. (ISBN0201342944)

BOSTOCK, L., & CHANDLER, S. 1994. Core Maths for A-level (2nd ed.). Thornes, Cheltenham. (ISBN9780748717798)

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