Functions and Calculus | Strand 5 Junior Cert Higher Maths | Alison

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Strand 5 Junior Certificate Ordinary Level Functions and Calculus - Revised

Gain a better understanding of functions and calculus including the rules of differentiation, average speed, and more.

Free Course
This free online Junior Certificate course teaches you Ordinary Level Functions and Calculus. A function is a relation between a set of inputs and a set of outputs, where every input has at most one output. The course will teach you how to plot quadratic graphs, match equations and sketches, sketch a parabola using the square, look into the concept of the Trapezoidal Rule, and more. Start your learning journey, today!
  • Duration

    1.5-3 Hours
  • Assessment

  • Certification

  • Responsive






View course modules


This course first teaches the rules of differentiation which includes product rule, quotient rule, and chain rule. You will learn the use of differentiation to find the slope of a tangent to a curve at a specified point. This is then extended to the study of increasing and decreasing functions. You will also learn how to determine the local maxima and local minima turning points of a curve.

You will then study average speed, which is the rate of change of distance. This course also teaches the use of slope to determine the nature of a function. You will learn the concept of numerical integration and how to use the Trapezoidal Rule to find the area under specific curves. With the help of video presentations, you will then be guided through the process of completing the square and sketching the full method.

Functions and calculus are used in real life to help us understand rates of increase and decrease. Upon the completion of this course, you will be able to solve problems involving the maximum speed reached by car and the highest point reached by a firework or rocket. You will also learn that a Trapezoidal Rule is a numerical approach to finding definite integrals where no other method is possible. So, check out the course and gain a better understanding of functions and calculus, today.

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Learning Outcomes

Having completed this course you will be able to:

  • Examine how to work with functions to plot graphs, including quadratic graphs, cubic graphs and exponential graphs 
  • Recognise basic differentiation of functions
  • Determine the local maxima and local minima turning points of a curve
  • Recognise the rate of change of distance
  • Demonstrate how to use a slope to determine the nature of a function
  • Identify how to use the Trapezoidal Rule to find area


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:

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