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Strand 5 Leaving Certificate Higher Level Functions and Calculus - Revised

This course covers functions, differentiation calculus, the trapezoidal rule and more as part of Project Maths.

Publisher: Advance Learning
This free online course will teach you about higher level functions and calculus, including quadratic, cubic and exponential graphs. You will learn how to plot graphs, sketch parabolas and translate functions. You will also examine differentiation and integral calculus. This course is the final strand in Phase 3 of the Project Maths Leaving Certificate series but anyone can sign up to do it because it is open to all.
Strand 5 Leaving Certificate Higher Level Functions and Calculus - Revised
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This course begins by teaching you how to plot quadratic, reciprocal and exponential graphs from a table of values. You will learn how to match equations and sketches, and look into the sketching of a parabola using completion of the square. Completing the square is the process where you change the form of the equation so that the left side is a perfect square trinomial. You will study the full method of completing the square, as well as learn about matching quadratic and exponential functions and graphs.

You will then look into the translation of functions using F(X-A). This course will teach you how to sketch functions in the X direction and in the Y-direction. You will study the discriminant, which is the part of the quadratic formula underneath the square root symbol b²-4ac and states whether there are two solutions, one solution, or no solutions to an equation. You will also cover inverse and bijective functions as well as differential calculus and integration calculus.

Functions and differentiation are used in real life to help us understand rates of increase and decrease. On the completion of this course, you will have a clearer understanding of the rules of differentiation, the basic integration of algebraic, trigonometrical, and exponential functions, the use of integration to find an area, and the trapezoidal rule.

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