Strand 5 Leaving Certificate Ordinary Level Functions and Calculus  Revised
Learn more about functions and calculus in Project Maths Strand 5 Ordinary Level.
Description
Functions is the final strand in phase 3 of the ordinary level Project Maths Course. This topic provides every important link between Algebra and Numbers and then introduces students to applications of calculus in real life.
The use of differentiation to find the slope of a given tangent to a curve at a point is introduced. This then leads on to the study of decreasing and increasing functions. Functions and Differentiation are often used in real life as an aid to understanding rates of decrease and increase.
For example, students will examine problems involving the maximum speed that can be reached by a car. They will look at the highest point that can be reached by a rocket or firework. Finally, the mathematical concept of numerical integration is investigated through the use of the 'Trapezoidal Rule' to find areas under given curves.
Start Course NowModules
Functions

Functions  Learning Outcomes

Plotting Quadratic Graphs From Table of Values

Plotting Cubic Graphs From Table of Values

Plotting Reciprocal Graphs From Table of Values

Plotting Exponential Graphs From Table of Values

Matching Equations and Sketches

Matching Functions and Graphs – Quadratic / Exponential

Translation of Functions Using f(xa)

Translating Functions Using f(x)+a

Stretching Functions in x Direction

Stretching Functions in The y Direction

The Discriminant

Functions  Lesson Summary
Calculus  Differentiation

Calculus  Differentiation  Learning Outcomes

Basic Differentiation of y = x^n

Differentiation of Polynomials

Equation of a Tangent

Equation of a Normal

General Differentiation of x^n

Second Derivative

Differentiation of Tangents

Using Different Variables

Differentiating Products and Quotients

The Chain Rule

The Product Rule

The Quotient Rule

Applications of Differentiation 1 (Displacement / Velocity / Acceleration)

Applications of Differentiation 2 (Voltage / Current)

Differentiation and Turning Points

Maximum Volume of Box

Differentiation and Matching Graphs

Calculus  Differentiation  Learning Outcomes
Course assessment
Learning Outcomes
Having completed this course students will be able to
 Identify how to plot Quadratic, cubic, reciprocal and exponential graphs from a table of values
 Identify how to translate a function along either the x or y axis
 Identify how to stretch a function along either the x or y axis
 Recognise how to calculate the gradient of a curve
 Identify how to calculate the equation of a tangent and normal to a curve
 Calculate differentiation for equations/formulas with negative indices
 Calculate the second derivative of a formula/equation
 Identify how to use the chain rule to calculate the equation of a tangent
 Identify how to use the product rule to find the equation of a normal
 Identify how to use the quotient rule to calculate the turning points
 Recognize the application of differentiation for calculating displacement, velocity, acceleration, voltage and current
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