Strand 5 Leaving Certificate Higher Level Functions and Calculus  Revised
Gain a better understanding of the concepts of function, differentiation calculus, Trapezoidal rule, and more.
Description
This course begins by teaching you how to plot quadratic graphs, reciprocal graphs, 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(XA). This course will teach you how to sketch functions in the X direction and in the Ydirection. You will study the discriminant, which is the part of the quadratic formula underneath the square root symbol b²4ac 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. Upon 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. So, check out the course and easily learn the applications of calculus in the real world, today.
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

Sketching Parabola Using Completing The Square

Completing The Square and Sketching The Full Method

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

Inverse and Bijective Functions

Functions  Lesson Summary
Calculus  Differentiation  Part 1

Calculus  Differentiation  Part 1  Learning Outcomes

Basic Differentiation of y = x^n

Differentiation of Polynomials

Equation of a Tangent

Equation of a Normal

Harder Questions on Normals

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

Calculus  Differentiation  Part 1  Lesson Summary
Calculus  Differentiation  Part 2

Calculus  Differentiation  Part 2  Learning Outcomes

Differentiation of Logarithms

Differentiation of y = sinx

Differentiation of y = cosx

Differentiation and Rates of Change

Rate of Change Example 1

Rate of Change Example 2

Differentiation and Turning Points

Differentiation and Matching Graphs

Applications of Differentiation 1 (Displacement/Velocity/Acceleration)

Applications of Differentiation 2 (Voltage/Current)

Maximum Volume of Box

Exploring Relationships Between Graphs of Cubic Functions and Their Differentials

Exploring Relationships Between Graphs of Trigonometric Functions and Their Differentials

Exploring Relationships Between Graphs of Exponential Functions and Their Differentials

Inverse Functions Differentiated

Calculus  Differentiation  Part 2  Lesson Summary
Calculus  Integration

Calculus  Integration  Learning Outcomes

Basic Integration

The Integral Sign

Harder Integration

Definite Integration

Area Between Lines

Basic Differential Equations

Integration of Trig Functions (y=cos4x)

Integration of Exponentials

Introducing the Trapezoidal Rule

Trapezoidal Rule Into Integration

Finding the Area Between a Quadratic Function and a Straight Line

Calculus  Integration  Lesson Summary
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 or stretch a function along either the x or y axis
 Identify an inverse function and a bijective function
 Recognise how to calculate the gradient of a curve
 Calculate the differentiation of several different types of formulas and equations
 Identify the chain rule, the product rule and the quotient rule
 Calculate the turning points of a curve
 Use differentiation to calculate the displacement, velocity and acceleration, of an object
 Discuss the relationships between different equations/functions and their differentials
 Discuss what basic integration is and calculate it
 Define and calculate definite integration
 Calculate the area under a curve with integration
Certification
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 securitymarked Certificate, posted to you with FREE shipping
Framed Certificate  a physical version of your officially branded and securitymarked 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.