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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
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Functions - Learning Outcomes
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Plotting Quadratic Graphs From Table of Values
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Plotting Cubic Graphs From Table of Values
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Plotting Reciprocal Graphs From Table of Values
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Plotting Exponential Graphs From Table of Values
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Matching Equations and Sketches
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Matching Functions and Graphs – Quadratic / Exponential
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Translation of Functions Using f(x-a)
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Translating Functions Using f(x)+a
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Stretching Functions in x Direction
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Stretching Functions in The y Direction
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The Discriminant
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Functions - Lesson Summary
Calculus - Differentiation
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Calculus - Differentiation - Learning Outcomes
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Basic Differentiation of y = x^n
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Differentiation of Polynomials
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Equation of a Tangent
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Equation of a Normal
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General Differentiation of x^n
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Second Derivative
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Differentiation of Tangents
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Using Different Variables
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Differentiating Products and Quotients
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The Chain Rule
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The Product Rule
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The Quotient Rule
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Applications of Differentiation 1 (Displacement / Velocity / Acceleration)
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Applications of Differentiation 2 (Voltage / Current)
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Differentiation and Turning Points
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Maximum Volume of Box
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Differentiation and Matching Graphs
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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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