Essential Mathematics

The details
Essex Pathways
Colchester Campus
Full Year
Foundation/Year Zero: Level 3
Thursday 05 October 2023
Friday 28 June 2024
26 July 2023


Requisites for this module



Key module for

BSC N325 Actuarial Science (Including Foundation Year),
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC L1G8 Economics with Mathematics (Including Foundation Year),
BENGH61P Electronic Engineering (Including Foundation Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC G104 Mathematics (Including Foundation Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1F5 Mathematics with Physics (Including Foundation Year),
BENGHP41 Communications Engineering (Including Foundation Year),
BSC I1GF Data Science and Analytics (Including Foundation Year),
BENGH618 Robotic Engineering (Including Foundation Year),
BENGH733 Mechatronic Systems (Including Foundation Year),
BENGH172 Neural Engineering with Psychology (Including Foundation Year)

Module description

The module covers the mathematical skills needed to proceed to any degree course where knowledge of mathematics to A-level standard is required. The syllabus initially covers some basic mathematics of number work, Equations and Curve Sketching to ensure that all students have acquired basic skills before proceeding on to more advanced topics.

The syllabus then expands to cover Trigonometry, Calculus, Further Algebra and Series, with lectures developing in range and content. The associated work in classes will help students develop Mathematical problem-solving skills and apply them to problems in other relevant subject areas such as economics, financial maths and engineering.

Module aims

The aims of this module are:

  • To provide students from a wide range of educational backgrounds with a broad understanding of basic and essential mathematical skills.

  • To demonstrate how Essential Mathematics knowledge can be applied in various practical applications, e.g., economics, finance and engineering contexts.

  • To give students the opportunity to engage actively with activities and class worksheets provided during lectures and classes.

  • To develop the ability to acquire knowledge and skills from lectures, textbooks and class work exercises, and from the application of theory to a range of problems.

  • To enable students to develop their problem-solving skills by using relevant and appropriate mathematical techniques.

Module learning outcomes

By the end of this module, students will be expected to be able to:

  1. Use and understand basic arithmetic and algebra in problem-solving.

  2. Solve linear single and simultaneous equations; linear inequality and regions; quadratic equations; functions.

  3. Sketch linear and quadratic curves; formulas; rules of logarithm.

  4. Understand and use differentiation; gradients of curves; equations of tangent and normal.

  5. Solve and sketch cubic, log, exponential and trigonometric equations, functions and trigonometric identities.

  6. Understand and use Integration; rules of integration; area under the curve.

  7. Understand sequences and series; arithmetic and geometric series; solve and sketch Modulus equations and functions.

Skills for your professional life (Transferable Skills)

By the end of this module, students will have practised the following transferable skills:

  1. Advanced numerical skills: this is extremely useful in any areas of Mathematics, Engineering, or in less Mathematical subjects such as Economics, etc.

  2. b) Algebra: essential in all areas where Mathematics is an inherent part, such as Mechanics, Electronics, and similar subjects. Algebra is the core skill in all numerical fields of study and work.

  3. Calculus: is the crown of advanced Mathematics in Mathematical sciences, as well as Applied Mathematical fields such as Electronics, modelling such as climate modelling, and of course pure Mathematics if you intend to pursue your studies in this area.

  4. Visualization and Graphs: extremely important skills in both pure and applied Mathematical subjects such as Electronic Engineering, Mechanics and indeed in all quantitative fields of studies and professional practice.

  5. IT skills: by practising on the NUMBAS platform and using open-source tools such as Geogebra, you will learn how to use technology to enhance your learning and increase your efficiency and productivity in your workplace.

  6. Logical approach: doing advanced topics in Mathematics helps you develop additional skills in planning, analysing, and learning methodical and logical approaches to problem-solving. These skills are transferrable to many areas of your future studies and work.

Module information


  • Essential arithmetic and number work.

  • Algebra: algebraic expressions; solution of linear, simultaneous, quadratic and cubic equations; logarithms; inequalities; trigonometric ratios and functions for any angle.

  • Graphical representation of functions and inequalities; curve sketching; graphical solution of equations; Tangents and Normals.

  • Calculus: differentiation and integration of linear, trigonometric, logarithmic and exponential functions, including the function of a function, products and quotients; second derivative; turning points; applications of differentiation; methods of integration; definite integration; areas under curves.

  • Trigonometry and trigonometric identities.

  • Sequences and series: arithmetic and geometric progressions; summation and convergence of a series; binomial theorem.

Learning and teaching methods

This module will be delivered via:

  • One 1-hour lecture per week.
  • One 2-hour class per week.
  • One 1-hour lab session using NUMBAS per week.

Teaching and learning on Essex Pathways modules offers students the ability to develop the foundation knowledge, skills, and competencies to study at the undergraduate level, through a curriculum that is purposely designed to provide an exceptional learning experience. All teaching, learning and assessment materials will be available via Moodle in a consistent and user-friendly manner.

All lecture notes, classwork exercises and Lab exercises are placed on Moodle prior to the teaching events for easy student access. Lecture notes will be supported by audio input for each lecture slide to make it easier to follow the topics on the slide. Students are expected to complete the lab exercises in labs and/or in their own individual study time. Support for this is provided via email and through academic support hours.


This module does not appear to have a published bibliography for this year.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   IA112 In-person, Open Book (restricted) Test 1     33% 
Coursework   IA112 In-person, Open Book (restricted) Test 2     50% 
Coursework   IA112 - Lab Exercises    17% 
Exam  Main exam: In-Person, Open Book (Restricted), 150 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 150 minutes during September (Reassessment Period) 

Additional coursework information

Formative assessment

  • Students engage in class activities, and lab exercises using NUMBAS, throughout the year. Students get feedback in all class and lab sessions, as well as via emails and one-to-one meetings where necessary.

Summative assessment

  • In-person, open book (restricted) test 1 (1.5 hours) - This will be given in week 8 and will cover only topics covered in the first 6 weeks of term 1 (weeks 2-7).
  • In-person, open book (restricted) test 2 (2 hours) - This is a comprehensive test and will be given in week 22. The test will cover all topics up to and including the topics in week 21.
  • Lab exercises – consists of lab exercises throughout the terms. You get this mark if you complete the tasks in the lab.
  • In-person, open book (restricted) 2.5 hrs exam - the exam covers all topics as specified in the syllabus; examples are calculus, the essential part of these topics such as equations, graphs, logarithms, the application of calculus, inequalities, simultaneous equations and topics in sequences and series.

Reassessment strategy

  • Failed exam - Resit the exam which is re-aggregated with the existing coursework mark to create a new module mark.
  • Failed coursework - Resit the exam which counts as coursework and is then re-aggregated with the existing exam mark to create a new module mark.
  • Failed exam and coursework - Resit the exam which will count as 100% exam mark. The exam will cover all the learning outcomes.

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
60% 40%


Coursework Exam
60% 40%
Module supervisor and teaching staff
Dr Mano Golipour-Koujali, email: mgoli@essex.ac.uk.
Dr Mano Golipour-Koujali
Kate Smith - catsmith@essex.ac.uk



External examiner

Dr Austin Tomlinson
University of Birmingham
Available via Moodle
Of 160 hours, 154 (96.3%) hours available to students:
0 hours not recorded due to service coverage or fault;
6 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information
Essex Pathways

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