Numbers and Shapes | Free Math course | Alison

Strand 3 Leaving Certificate Higher Level Numbers and Shapes - Revised

This free online maths course looks at Numbers and Shapes, a central topic in the Leaving Certificate Paper.

Series and Sequences
Free Course
This free online course on Numbers and Shapes is designed to support to any student studying project maths in their Leaving Cert. However, it will be helpful to anyone studying maths in this area. This 'Numbers and Shapes' topic can be seen in paper 1 of the Project Maths Course in the Irish curriculum. By completing this course, you will have covered all of the essential concepts of the topic.
  • Duration

    3-4 Hours
  • Assessment

  • Certification

  • Responsive






View course modules


The concepts of number patterns are the basic building blocks that make up arithmetic and algebra. We cannot escape the use of numbers in our day to day lives. We use watches and clocks to count through the hours and minutes. We count out money for our bills and play the lottery by choosing six numbers.

The application of Geometric and Arithmetic series in finance is looked at through loan repayments and investments. The use of APR (annual percentage rate) and AER (annual equivelant rate) when calculating repayments is looked at. Students are then introduced to complex numbers and shown how to subtract, add, divide and multiply complex numbers.

Complex numbers represent the flow of current in circuits and they are also used in many other areas of electronics. We use numbers to measure the area and perimeter of various shapes (triangles, circles, hexagons and rectangles) and we also use them to work out the volumes of solids like cylinders, spheres, cones and hemi-spheres.

Start Course Now


Numbers Part 1

Numbers Part 2

Arithmetic - Financial Maths - Part 1

Arithmetic - Financial Maths - Part 2

Length, Area and Volume

Complex Numbers

Course assessment

Learning Outcomes

Having completed this course you will be able to:

  • Identify how to write numbers in the standard form or scientific notation
  • Discuss how to work with indices
  • Calculate the equation for a quadratic number pattern
  • Define the meaning of i and what imaginary number are
  • Identify how to change the base of a logarithm
  • Define what both an Arithmetic series and a Geometric series are
  • Identify how to apply and use proof by Induction and proof by contradiction
  • Discuss what percentage profit is and the differences between mark-up and margin profit
  • Calculate the interest on a loan or investment
  • Calculate the depreciation of value on items
  • Identify the two methods for calculate the annual percentage rate
  • Calculate the income tax, universal social charge, and PRSI on your paycheck
  • Discuss working out the present value formula both for future values and present values


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

Alison offers 3 types of Certificates for completed Certificate courses:

Digital Certificate - a downloadable Certificate in PDF format, immediately available to you when you complete your purchase
Certificate - a physical version of your officially branded and security-marked Certificate, posted to you with FREE shipping
Framed Certificate - a physical version of your officially branded and security-marked Certificate in a stylish frame, posted to you with FREE shipping

All Certificates are available to purchase through the Alison Shop. For more information on purchasing Alison Certificates, please visit our FAQs. If you decide not to purchase your Alison Certificate, 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 Certificate pricing, please visit our Pricing Page.



    You have received a new notification

    Click here to view them all