Differentiation and Functions in Mathematics

• Description
• Outcome
• Certification
• This intermediate math course continues our free online maths suite of courses. It covers rules and applications of differentiation, straight line graphs, graphing circular functions, logs and indices, the Binomial theorem, inverse functions, and factors of polynomials. This course is ideal for second-level students, anyone studying for an exam, and those interested in re-igniting their knowledge of mathematics!

• After completing this course you will be more familiar with the basic functions of differential calculus, the rules of differentiation, linear combinations of functions, quotient of two functions and much more. You will gain a good knowledge of the applications of differentiation such as maximum, minimum and equations of tangents. You will know what the polynomial function is used for and how to factorise polynomials successfully. This course will demonstrate how to use straight line and circular functions on a graph successfully.You will have a good understanding inverse functions, logarithms, index laws and the binomial theorem of Pascal's Triangle.

• All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.

Having an official Alison document is a great way to share your success. Plus it’s:

• Ideal for including in CVs, job applications and portfolios
• An indication of your ability to learn and achieve high results
• An incentive to continue to empower yourself through learning
• A tangible way of supporting the Alison mission to empower people everywhere through education.

Modules List( 9 )
• Rules of differentiation
• Basic functions
• Functions
• Rules of differentiation
• Rules for finding derivatives
• Linear combination of functions
• Product of two functions
• Quotient of two functions
• Function of a function
• Applications of differentiation
• Applications of Differentiation
• Stationary Points
• Maximum or Minimum
• Maximum/Minimum Problems
• Equations of Tangents and Normals
• Examples
• Factors of polynomials
• Factorising polynomials
• Polynomial notation and function manipulations
• Factorising polynomials
• Factorisation process for cubics
• Factorisation process for quartics
• Factor and remainder theorems
• Long division
• Synthetic division
• Factorising polynomials: example
• Straight line graphs
• Activity
• Graphs of polynomial functions: the garden activity
• Introduction
• Graphs of polynomial functions
• Graphs derived from standard graphs
• Other standard graphs
• Certain special graphs
• Transformations
• Reflections
• Dilations
• Combinations of transformations
• Important graphs
• Important graphs: Type 1
• Important graphs: type 2
• Important graphs: type 3
• Important graphs: type 4
• Graphs of inverse functions
• Graphs of polynomial functions: examples
• Graphs of circular functions
• Introduction
• Graphs of the form y=Asin(a(x+b))+B and y=Acos(a(x+b))+B
• Solution of trigonometric equations
• Graphs of the form y = tan(ax)
• Equations of the form sin(ax)=B and cos(ax)=B
• Equations of the form sin(ax)=kcos(ax)
• Inverse functions
• Inverse functions - many-to-one and one-to-many
• Inverse functions
• Further inverse functions
• Examples
• Logarithms and index laws
• Indices and logarithms
• Solution of exponential and logarithmic equations
• Examples
• The binomial theorem
• Binomial theorem – Pascal's triangle
• The binomial expansion
• The binomial expansion - examples
• Assessment
• Intermediate Mathematics 1 Assessment
Topics List ( 8 )
Rules of differentiation
Rules of differentiation This free online course covers topics related to differentiation such as the rules of differentiation and how to calculate derivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 6 )
Applications of differentiation
Applications of differentiation This free online course covers applications of differentiation such as calculating the stationary points, and the maxima and minima points. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 9 )
Factors of polynomials
Factors of polynomialsThis free online course is an introduction to the techniques used to factorise cubic and quadratic polynomials.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 19 )
Straight line graphs
Straight line graphs This free online course covers topics related to straight line graphs including graphs for polynomial functions and transformations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 6 )
Graphs of circular functions
Graphs of circular functionsThis free online course is an introduction to the equations used for graphs of circular forms.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 4 )
Inverse functions
Inverse functionsThis free online course is an introduction to inverse functions.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 3 )
Logarithms and index laws
Logarithms and index laws This free online course is an introduction to logarithms and index equations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Topics List ( 3 )
The binomial theorem
The binomial theorem This free online course is an introduction to the binomial theorem. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Assessment
Assessment
Course Features
• Duration

2-3 Hours

• Publisher

XSIQ

• Video

Yes

• Audio

Yes

• Assessment

Yes

• Certification

Yes

• Price

Free

• Reward

50 Pts

• Responsive

No