
Free Course

Advance Learning

34 Hours

Assessment

Certification

Academic  Secondary  Level 2

50 Pts
Strand 5 Higher Level Functions and Calculus

Description

Outcome

Certification

Functions is the final strand to be introduced in phase 3 of the new Project Maths Course.
This topic provides an essential link between Algebra and Number and introduces the students to applications of calculus in the real world. Functions and Differentiation are used in real life to help us understand rates of increase and decrease.
For example, students will solve problems involving the maximum speed reached by a car and the rate of increase in the size of a raindrop as it falls to the ground. Integration is introduced as ‘antidifferentiation’ and students are given excellent examples to reinforce this theory. Applications of integration to find areas under curves and between curves are clearly demonstrated.
Finally, the concept of numerical integration is introduced through the use of the ‘Trapezoidal Rule’. 
Having completed this course students will be able to:
 Basic Differentiation of functions (including trig, exp and log)
 The rules of differentiation (product rule, quotient rule, chain rule)
 Determine the local maxima and local minima turning points of a curve
 Understand rate of change of distance, area and volume
 Understand the meaning of ‘antiderivative’ and Indefinite Integration
 Basic Integration of algebraic functions
 Basic Integration of Trigonometrical and Exponential functions
 How to use integration to find an area and use of the Trapezoidal Rule

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( 4 )

PROJECT MATHS STRAND 5 HIGHER LEVEL: FUNCTIONS AND...

Module
1 Functions
Learn more about functions.

Plotting quadratic graphs from table of values
Start Topic

Plotting cubic graphs from table of values
Start Topic

Plotting reciprocal graphs from table of values
Start Topic

Plotting exponential graphs from table of values
Start Topic

Matching equations and sketches
Start Topic

Sketching parabola using completing the square
Start Topic

Completing the square and sketching the full method
Start Topic

Matching functions and graphs – quadratic / exponential
Start Topic

Translation of functions using f(xa)
Start Topic

Translating of functions using f(x)+a
Start Topic

Sketching functions in x direction
Start Topic

Sketching functions in the y direction
Start Topic

The Discriminant
Start Topic

Inverse and bijective functions
Start Topic


Module
2 Calculus  Differentiation
Learn more about differentiation.

Basic differentiation of y = x^n
Start Topic

Differentiation of polynomials
Start Topic

Equation of a tangent
Start Topic

Equation of a normal
Start Topic

Harder questions on normals
Start Topic

General differentiation of x^n
Start Topic

Second derivative
Start Topic

Differentiation of tangents
Start Topic

Using different variables
Start Topic

Differentiating products and quotients
Start Topic

The Chain Rule
Start Topic

The Product Rule
Start Topic

The Quotient Rule
Start Topic

Differentiation of logarithms
Start Topic

Differentiation of y = sinx
Start Topic

Differentiation of y = cosx
Start Topic

Differentiation and rates of change
Start Topic

Rate of change  Example 1
Start Topic

Rate of change  Example 2
Start Topic

Differentiation and turning points
Start Topic

Differentiation and matching graphs
Start Topic

Applications of differentiation 1 (displacement / velocity / acceleration)
Start Topic

Applications of differentiation 2 (voltage / current)
Start Topic

Maximum volume of box
Start Topic

Exploring relationships between graphs of cubic functions and their differentials
Start Topic

Exploring relationships between graphs of trigonometric functions and their differentials
Start Topic

Exploring relationships between graphs of exponential functions and their differentials
Start Topic

Inverse functions differentiated
Start Topic


Module
3 Calculus  Integration
Learn more about integration.

Basic integration
Start Topic

The integral sign
Start Topic

Harder integration
Start Topic

Definite integration
Start Topic

Area between lines
Start Topic

Basic differential equations
Start Topic

Integration of Trig functions (y=cos4x)
Start Topic

Integration of exponentials
Start Topic

Introducing the Trapezoidal Rule
Start Topic

Trapezoidal Rule into integration
Start Topic

Finding the area between a quadratic function and a straight line
Start Topic


END OF COURSE ASSESSMENT

Strand 5 Higher Level Functions and Calculus Assessment

You must score 80% or more to pass this assessment.

Strand 5 Higher Level Functions and Calculus Assessment
Start Topic


RESOURCE

Resource: Examination Material Archive View Resource