Skip to main content


SFY0018 : Foundation Mathematics

  • Offered for Year: 2022/23
  • Module Leader(s): Dr John Appleby
  • Lecturer: Dr Kate Henderson
  • Owning School: Engineering
  • Teaching Location: Newcastle City Campus
Semester 1 Credit Value: 20
Semester 2 Credit Value: 10
ECTS Credits: 15.0


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 completion130:0030:00Testing - CBA and some written.
Guided Independent StudyAssessment preparation and completion120:0020:00Preparation before starting All new stage 0&1 in Engineering
Structured Guided LearningLecture materials600:3030:00Viewing video lectures Main form of exposition
Scheduled Learning And Teaching ActivitiesSmall group teaching201:0020:00In person lectures. Motivation.
Guided Independent StudyIndependent study1150:00150:00Private study - exercises CBA. Practice and self-testing
Guided Independent StudyIndependent study130:0030:00Private study - use of notes. Understanding lectures.
Scheduled Learning And Teaching ActivitiesScheduled on-line contact time201:0020:00Online tutorial Q&A for student questions.
Teaching Rationale And Relationship

NB This rationale is for the special circumstances of the Covid-19 crisis, during which in-person contact will be limited at least until January 2021.
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 to introduce each topic and worked examples, in place of normal lectures. In-person classroom time (in suitable groups) will be used in addition for motivation and to develop the tutor/student relationship. Live (synchronous) on-line tutorials will be used to address student queries, with on-screen mathematical work. Computer-based exercises and tests will help students to check and improve their skills. Bookable ‘office hour’ personal tutorials will support students on demand. Exercise sheets are for practice of methods and reinforcement of understanding and applications.

Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

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

Description Length Semester When Set Percentage Comment
Written Examination602A20Ensure ability to write mathematics
Other Assessment
Description Semester When Set Percentage Comment
Written exercise1M20Regular CBA testing 20 mins Essential to maintain progress in a hierarchical subject
Written exercise1M30Final CBA test 1 1 hour typical Incentive study and check progress
Written exercise2A30Final CBA test 2 1 hour typical Incentive study and check progress
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, with multiple attempts, to achieve mastery of methods and skills. End of Semester CBA tests will assess overall knowledge, and a final written (take-home) exam will ensure ability in writing mathematics systematically.

Reading Lists