
Free Course

XSIQ

23 Hours

Assessment

Certification

Academic  Secondary  Level 1

50 Pts
Differentiation and Functions in Mathematics

Description

Outcome

Certification

This intermediate math course continues our 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 secondlevel students, anyone studying for an exam, and those interested in reigniting 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 celebrate and share your success. It is: Ideal to include with CVs, job applications and portfolios
 A way to show your ability to learn and achieve high results
Modules List( 9 )

Module
1 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.

Basic functions
Start Topic

Functions
Start Topic

Rules of differentiation
Start Topic

Rules for finding derivatives
Start Topic

Linear combination of functions
Start Topic

Product of two functions
Start Topic

Quotient of two functions
Start Topic

Function of a function
Start Topic


Module
2 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.

Applications of Differentiation
Start Topic

Stationary Points
Start Topic

Maximum or Minimum
Start Topic

Maximum/Minimum Problems
Start Topic

Equations of Tangents and Normals
Start Topic

Examples
Start Topic


Module
3 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.

Factorising polynomials
Start Topic

Polynomial notation and function manipulations
Start Topic

Factorising polynomials
Start Topic

Factorisation process for cubics
Start Topic

Factorisation process for quartics
Start Topic

Factor and remainder theorems
Start Topic

Long division
Start Topic

Synthetic division
Start Topic

Factorising polynomials: example
Start Topic


Module
4 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.

Activity
Start Topic

Graphs of polynomial functions: the garden activity
Start Topic

Introduction
Start Topic

Graphs of polynomial functions
Start Topic

Graphs derived from standard graphs
Start Topic

Other standard graphs
Start Topic

Certain special graphs
Start Topic

Transformations
Start Topic

Reflections
Start Topic

Dilations
Start Topic

Combinations of transformations
Start Topic

Addition of ordinates
Start Topic

Important graphs
Start Topic

Important graphs: Type 1
Start Topic

Important graphs: type 2
Start Topic

Important graphs: type 3
Start Topic

Important graphs: type 4
Start Topic

Graphs of inverse functions
Start Topic

Graphs of polynomial functions: examples
Start Topic


Module
5 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.

Introduction
Start Topic

Graphs of the form y=Asin(a(x+b))+B and y=Acos(a(x+b))+B
Start Topic

Solution of trigonometric equations
Start Topic

Graphs of the form y = tan(ax)
Start Topic

Equations of the form sin(ax)=B and cos(ax)=B
Start Topic

Equations of the form sin(ax)=kcos(ax)
Start Topic


Module
6 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.

Inverse functions  manytoone and onetomany
Start Topic

Inverse functions
Start Topic

Further inverse functions
Start Topic

Examples
Start Topic


Module
7 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.

Indices and logarithms
Start Topic

Solution of exponential and logarithmic equations
Start Topic

Examples
Start Topic


Module
8 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.

Binomial theorem – Pascal's triangle
Start Topic

The binomial expansion
Start Topic

The binomial expansion  examples
Start Topic


Assessment