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SFY0018 : Foundation Mathematics

  • Offered for Year: 2023/24
  • Module Leader(s): Dr John Appleby
  • Lecturer: Dr Nicola Hewett
  • Owning School: Engineering
  • Teaching Location: Newcastle City Campus

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 20
Semester 2 Credit Value: 10
ECTS Credits: 15.0
European Credit Transfer System


To revise and develop mastery of the basic elements of elementary algebra, geometry and trigonometry.
To provide an introduction to standard functions; differential and integral calculus, including fundamental ideas and standard methods with some simple applications; basic knowledge of complex numbers and series.

Outline Of Syllabus

Basic algebra notation and manipulation; formulae, equations and graphs; equations of the straight line and circle; simple trigonometry.
Gradient of line and curve; differentiation from first principles; standard derivatives and simple applications; rules of differentiation (product rule, quotient rule, chain rule); higher derivatives, maxima and minima, curve sketching.
Functions. Domain and range; composite functions, standard functions (exponential, logarithmic, harmonic) and their graphs; inverse functions; derivatives.
Integration of areas; trapezium rule; indefinite and definite integrals; methods of integration (substitution, by parts, partial fractions).
Complex numbers: algebra; quadratic and cubic equations; modulus-argument form.
Finite arithmetic series; finite and infinite geometric series; binomial expansion.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion140:0040:00Testing - written exams and CBA tests.
Scheduled Learning And Teaching ActivitiesLecture501:0050:00In person lectures/tutorials. Exposition, motivation and Q&A
Structured Guided LearningLecture materials600:3030:00Viewing video lectures. Additional exposition/reinforcement
Guided Independent StudyDirected research and reading120:0020:00Preparation before starting. All new stage 0 & 1 in Engineering
Guided Independent StudyIndependent study1130:00130:00Private study - exercises (some CBA). Practice and self-testing
Guided Independent StudyIndependent study130:0030:00Private study - use of notes. Understanding 'lectures'.
Teaching Rationale And Relationship

Pre-sessional preparatory material will be made available to all new Stage 1 and Stage 0 students, consisting of videos, PDF resources, links, and on-line computer-based testing, encouraging students to revise material not studied for several months and to identify and address gaps or lack of fluency. Pre-recorded videos will be used in conjunction with ‘printed’ material and live lectures to introduce each topic and worked examples. Tutorials time (integrated with lectures) will be used in addition for motivation and to develop the tutor/student relationship. Computer-based exercises and tests will help students to check and improve their skills. Exercise sheets are for practice of methods and reinforcement of understanding and applications.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination601A30Synoptic assessment of whole semester, ability to write logically.
Written Examination1202A50Synoptic assessment of whole module.
Other Assessment
Description Semester When Set Percentage Comment
Computer assessment1M10Essential to maintain progress in a hierarchical subject, taken within 24-hour window. 2 short CBA Tests.
Computer assessment2M10Essential to maintain progress in a hierarchical subject, taken within 24-hour window. 2 short CBA Tests.
Assessment Rationale And Relationship

To encourage regular study and reflection in this hierarchical subject (with competing pressures of Engineering coursework), regular computer-based (CBA) tests will be set on questions already practised to achieve mastery of methods and skills. Written (invigilated) exams at the end of each semester will ensure retention and ability in writing mathematics systematically.

Reading Lists