Essential Mathematics

The details
Essex Pathways
Colchester Campus
Full Year
Foundation/Year Zero: Level 3
Thursday 03 October 2019
Friday 26 June 2020
17 April 2019


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),
BENGHP41 Communications Engineering (Including Foundation Year),
BSC I1GF Data Science and Analytics (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, Ordinary Differential Equations, 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 be apply them to problems in other relevant subject areas such as economics, financial maths and engineering.

Module aims

- 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, from text books 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

On successful completion of the module students are 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; equation of tangent and normal.
5. Solve and sketch cubic, log, exponential and trigonometric equations and functions; 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

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 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


Formative assessment:
At the beginning of the Autumn Term students undergo a diagnostic test. Two weeks before each test there is a formative mock test followed by feedback.

Summative assessment:
Coursework is comprised of:
- In-class test 1 (25%)
- In-class test 2 (62.5%)
- Participation mark (12.5%) – consists of lab exercises throughout the terms.

2.5 hours exam during Summer Examination period.

Reassessment strategy
Failed Exam:
Resit the exam which is re-aggregated with existing coursework mark to create a new module aggregate.

Failed Coursework:
Resit the exam which counts as coursework and is then re-aggregated with the existing exam mark to create a new module aggregate.

Failed Exam and Coursework:
Resit the exam which will count as 100% exam mark. The exam will cover all the learning outcomes.

Learning and teaching methods

The module runs over 22 weeks and is delivered via one-hour lecture, one-hour maths lab, and a two-hour class. The activities and class worksheets have a range of questions from basic level to more advanced level. Some questions also extend to the applications in economics, finance and engineering to allow students to have an experience using Maths skills in various contexts. All lecture notes and exercises are placed on Moodle for easy student access. Listen Again is also used as part of learning support in which students can reviews the recordings at a later date.


  • Bostock, L.; Chandler, S. (2000) Core maths for advanced level, Cheltenham: Stanley Thornes.

The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   IA112 Test 1     25% 
Coursework   IA112 Test 2     62.5% 
Coursework   Participation    12.5% 
Exam  150 minutes during Summer (Main Period) (Main) 

Overall assessment

Coursework Exam
40% 60%


Coursework Exam
40% 60%
Module supervisor and teaching staff
Dr Mano Golipour-Koujali, email: mgoli@essex.ac.uk.
Dr Mano Golipour-Koujali
Kate Smith (catsmith@essex.ac.uk or 01206 874564)



External examiner

No external examiner information available for this module.
Available via Moodle
Of 224 hours, 148 (66.1%) hours available to students:
76 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Essex Pathways

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