Module Directory

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 and 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 calculus, further algebra, and trigonometry, with lectures developing in range and content. The associated work in classes will help students develop mathematical problem-solving skills and to apply them to problems in relevant subject areas such as mathematics and engineering.

 The module aims are:

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


2. To demonstrate how Essential Mathematics knowledge can be applied in various practical applications.


3. To develop the ability to acquire knowledge and skills from lectures, textbooks, class worksheets, and lab exercises, as well as from the application of theory to a range of problems where appropriate.


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

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 inequalities and regions of inequality; quadratic equations; functions.


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


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


5. Solve and sketch polynomial and non-polynomial equations and functions, learn about trigonometric functions and identities.


6. Understand and use integration; rules of integration including integration by substitution and integration by parts; area under a curve.

Skills for your professional life (Transferable Skills)

By completing this module, you will be to transfer your skills in numerous areas as follows:

a) Advanced numerical skills: this is extremely useful in any areas of Mathematics or Engineering

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

c) Calculus: widely used in Mathematical sciences, as well as Applied Mathematical fields such as Electronics

d) Visualization and Graphs: extremely important skills in both pure and applied Mathematical subjects such as Electronic Engineering, Mechanics, and in most quantitative fields of study and professional practice.

e) IT skills: by practicing on NUMBAS platform and using tools such as Desmos or Geogebra, you will learn how to use technology to enhance your learning and increase your efficiency and productivity in your workplace.

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

Syllabus

Essential arithmetic and number work

Algebraic expressions; solution of linear, simultaneous, quadratic and cubic equations; logarithms; inequalities;

Graphical representation of functions and inequalities; curve sketching; graphical solution of equations; tangents and normals.

Calculus: differentiation and integration of polynomial, trigonometric, logarithmic, and exponential functions, including function of a function, products and quotients; second derivative; turning points; applications of differentiation; methods of integration including integration by substitution (reverse of the chain rule) and integration by parts (reverse of the product rule); definite integration; areas under curves.

Trigonometry, trigonometric ratios and functions, and trigonometric identities.

Teaching and learning on Essex Pathways modules offers students the ability to develop the foundation knowledge, skills, and competences to study at 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.

The module is delivered via 1 x 1-hour lecture, 1 x 2-hour class and 1 x 1-hour lab sessionAll lecture notes, classwork exercises and Lab exercises are placed on Moodle prior to the teaching events for easy students’ access. Lecture notes will be available in PowerPoint format. Lectures and class activities are also available on Listen Again website (see the module guide on Moodle).