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Foundation Mathematics

Module titleFoundation Mathematics
Module codeINT0007
Academic year2021/2
Module staff

Joaquin Navarrete Navarro (Lecturer)

Duration: Term123
Duration: Weeks


Number students taking module (anticipated)


Description - summary of the module content

Module description

Knowledge of mathematics underpins most disciplines, especially engineering and business studies. In this module you will learn how to describe, understand and represent situations both graphically and algebraically and draw conclusions from these. You will learn how to manipulate and solve different types of equations to find unknown values, how to make decisions and how to find the best decision from a set of different possibilities. You will learn computing techniques to apply to various situations and use on-line learning material.
This is not a course for beginners:- students taking this course should already have good knowledge of mathematics which will be checked at the beginning of the course.

Module aims - intentions of the module

This module aims to provide a foundation in mathematics for students who intend to follow a degree programme in the area of Business, Computer Science, Engineering, Psychology, Science or other related disciplines. Students will be expected to manage their time successfully in order to complete a series of coursework and other tasks.

Intended Learning Outcomes (ILOs)

ILO: Module-specific skills

On successfully completing the module you will be able to...

  • 1. Demonstrate an understanding of standard mathematical notation and techniques
  • 2. Use mathematical methods to solve simple problems requiring the use of algebraic formulae
  • 3. Demonstrate an understanding of the basic principles of the calculus
  • 4. Apply mathematics to a wide range of real life problems
  • 5. Demonstrate understanding of basic mathematical principles

ILO: Discipline-specific skills

On successfully completing the module you will be able to...

  • 6. Use mathematical software confidently, where relevant, to investigate solutions to mathematical problems
  • 7. Use the results of calculations to make predictions and give answers to appropriate accuracy

ILO: Personal and key skills

On successfully completing the module you will be able to...

  • 8. Analyse, interpret and illustrate data using a variety of techniques including graphical presentations

Syllabus plan

Syllabus plan

  1. Familiarity with the terms: natural number, integer, rational number, irrational number, real number, fractions, modulus. Decimal places and significant figures. Scientific notation.
  2. Linear Programming.
  3. Coordinate Geometry in two dimensions. The equation of a straight line. Gradient of the line joining two given points. Parallel lines. Perpendicular lines.
  4. The exponential and logarithmic functions and their graphs. Laws of logarithms. Use of logarithms to solve ax = b and to transform a given relationship to linear form so determining unknown constants from gradient and intercept. Use of Excel to draw these functions.
  5. Sequences and series. S notation. Arithmetic progression. Geometric progression. Compound Interest.
  6. Differentiation. Introduction. Notations: dy/dxandf¢(x). Differentiation as rate of change, gradients of curves. Differentiation of xn, tangents and normals to the curve, maximum and minimum values.
  7. Integration as the reverse process of differentiation. Indefinite and definite integration of standard functions. Application of integration to finding plane areas. 
  8. Numerical determination of integrals using the trapezium rule.
  9. Numerical solution of equations. Location of roots of f(x)=0 by considering change of sign and simple iterative methods. Use of spreadsheets (Excel) to determine solution of equations.
  10. Statistics. Representation of data; histograms, cumulative frequency curves, box plots. Measures of location; mean, median and mode, moving averages. Measures of dispersion; variance, standard deviation, range and interquartile range. Scatter diagrams. Trend lines. Using Excel to represent data.
  11. Probability. The concept of a random event and its probability. Venn diagrams and tree diagrams. Addition Law. Mutually exclusive events. Multiplication law and conditional probability. Independent events.
  12. Normal Distribution.

Learning and teaching

Learning activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching ActivitiesGuided independent studyPlacement / study abroad

Details of learning activities and teaching methods

CategoryHours of study timeDescription
Scheduled Learning and Teaching activities60Small group lessons, including lectures, examples, practice and use of computing techniques (synchronous).
Guided Independent Study140Study of written notes, practise examples, using resources supplied on ELE and other online learning material.


Formative assessment

Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
Practice online final exam quiz2 hours1-8Verbal and answers on ELE

Summative assessment (% of credit)

CourseworkWritten examsPractical exams

Details of summative assessment

Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Coursework assignments30Several (usually 5) online Computer Marked Assessments each taking approximately 3 hours1-8On-line feedback
Final Examination702 hour online quiz1-8Written feedback on formally submitted request


Details of re-assessment (where required by referral or deferral)

Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
Final ExaminationExamination; 2 hour online quiz1-8Next assessment period

Re-assessment notes

Deferral – if you miss an assessment for reasons judged legitimate by the Mitigation Committee, the applicable assessment will normally be deferred. See ‘Details of reassessment’ for the form that assessment usually takes. When deferral occurs there is ordinarily no change to the overall weighting of that assessment.

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to take a re-sit exam. Only your performance in this exam will count towards your final module grade. A grade of 40% will be awarded if the examination is passed.


Indicative learning resources - Basic reading

Hanrahan, V., Mathews, J., Porkess, R. & Secker, P. (2004). MEI AS Pure Mathematics C1 and C2: MEI Structured Mathematics (3rd Ed.). London: Hodder Murray.

Eccles, A., Francis, B., Graham, A.,& Porkess, R. (2004). MEI Statistics 1: MEI Structured Mathematics (3rd Ed.). London: Hodder Murray.

Berry, C., Hanrahan, V., Porkess, R., Secker, P.(2004). MEI A2 Pure Mathematics C3 and C4: MEI Structured Mathematics (3rd Ed.). London: Hodder Murray.

Indicative learning resources - Web based and electronic resources

ELE – 

Module has an active ELE page

Indicative learning resources - Other resources

Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J. & Wilkins, D. (2004). Core Mathematics 1: Heinemann Modular Mathematics. Oxford: Heinemann Educational.
Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J., Staley, G. & Wilkins, D. (2004). Core Mathematics 2: Heinemann Modular Mathematics. Oxford: Heinemann Educational.
Attwood, G., Dyer, G. & Skipworth, G. (1994). Statistics 1: Heinemann Modular Mathematics. Oxford: Heinemann Educational.

Key words search

Mathematics, Foundation Mathematics,

Credit value20
Module ECTS


Module pre-requisites


Module co-requisites


NQF level (module)


Available as distance learning?


Origin date


Last revision date