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Foundation Diploma in Mathematics - Science, Technology and Engineering

Core Maths Skills
Free Course

Learn Foundation Level maths for STEM subjects.

Description Outcome Certification View course modules

This diploma course provides students with the mathematical knowledge and skills needed to study a Science, Technology or Engineering discipline at third-level. The course consists of maths tutorial videos in which qualified maths teachers resolve problems in real-time. Furthermore, a comprehensive assessment tests students on all aspects of mathematics which are related to science, technology and engineering. This course will appeal to third-level students who are lacking confidence in their mathematical knowledge and skills. This course will also appeal to students who are re-entering formal education after a significant absence. This diploma course will help to build students’ confidence in their mathematical ability and ensure that they are prepared for third-level study. The topics covered in this course are, Introduction to Mathematics, Algebra, Equations and Functions, Calculus, Probability and Statistics, Calculus, Matrices, Trigonometry and Complex Numbers.

After completing this course students will understand and be skilled in the following mathematics topics:


  • Large Numbers in Standard Form;
  • Changing Decimals to Standard form;
  • Changing Large Numbers from Standard Form;
  • Changing Small Numbers from Standard Form;
  • Working with Indices;
  • Positive Fractional Indices - All Types;
  • Negative Fractional Indices;
  • Rearranging Simple Formulae;
  • Rearranging Simple Formulae – 2 Steps;
  • Solving Simultaneous Equations Graphically;
  • Expanding any Two Brackets;
  • Factorising Quadratics;
  • Factorising – Difference of Two Squares;
  • Equations With Linear Functions in the Denominator;
  • Quadratic Equations Both Brackets the Same Sign;
  • Quadratic Equations Brackets With Different Signs;
  • Quadratic Equations Using the Formula;
  • Use of the Discriminant;
  • Equations with Indices;
  • Logarithmic Equations;
  • Plotting Quadratic Graphs from a Table of Values;
  • Plotting Cubic Graphs from a Table of Values;
  • Plotting Reciprocal Graphs from Table of Values;
  • Basic Differentiation of Differentiation of Polynomials;
  • The Product Rule;
  • The Quotient Rule;
  • The Chain Rule;
  • Second Derivative;
  • Differentiation and Turning Points;
  • Differentiation of Logarithms;
  • Basic Integration;
  • The Integral Sign;
  • Harder Integration;
  • Definite Integration;
  • Area between lines;
  • Arrangements;
  • Arrangements and Selections;
  • The Binomial Distribution;
  • Basic Information About Matrices;
  • How to Operate With Matrices;
  • Determinants;
  • Using Matrices When Solving System of Equations;
  • Finding Angles With the Sine Ratio;
  • Finding Sides With the Sine Ratio;
  • Finding Angles With the Cosine Ratio;
  • Finding Sides With the Cosine Ratio;
  • Finding Angles With the Tangent Ratio;
  • Finding Sides With the Tangent Ratio;
  • Introducing Radians;
  • Using Radians to Find the Area of a Sector;
  • Solving Trigonometric Equations;
  • Finding a Missing Side With the Sine Rule;
  • Finding a Missing Angle With the Sine Rule;
  • Finding Areas with Trigonometry;
  • Problem Solving With the Cosine Rule;
  • The Argand Diagram and Modulus;
  • The meaning of i;
  • Manipulating Complex Numbers;
  • Writing Complex Numbers in Polar Form;
  • Complex Numbers when solving Quadratic Equations;
  • Multiplying and Dividing in Polar Form (Ex);
  • Proof of De-Moivre’s Theorem.

All Alison courses are free to enrol, study and complete. To successfully complete this Diploma course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Diploma course, you have the option to acquire official Certification, which is a great way to share your achievement with the world. Your Alison Certification is:

Ideal for sharing with potential employers - include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive to you to continue empowering yourself through lifelong learning

Alison offers 3 types of Certification for completed Diploma courses:

Digital Diploma - a downloadable Diploma in PDF format, immediately available to you when you complete your purchase
Diploma - a physical version of your officially branded and security-marked Diploma that is posted to you (with FREE standard shipping worldwide)
Framed Diploma - a physical version of your officially branded and security-marked Diploma in a stylish frame that is posted to you (with FREE standard shipping worldwide)

All Certification is available to purchase through the Alison Shop. For more information on purchasing Alison Certification, please visit our faqs. If you decide not to purchase your Alison Certification, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Certification pricing, please visit our Pricing Page.

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