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Strand 5 Higher Level Functions and Calculus Free Course

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  • Description
  • Outcome
  • Certification
  • Functions was 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 ‘anti-differentiation’ 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 ‘anti-derivative’ 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 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( 4 )
  • Module 1: Functions
    • 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(x-a)
    • Translating of functions using f(x)+a
    • Sketching functions in x direction
    • Sketching functions in the y direction
    • The Discriminant
    • Inverse and bijective functions
  • Module 2: Calculus - Differentiation
    • 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
    • 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
  • Module 3: Calculus - Integration
    • 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
  • Strand 5 Higher Level Functions and Calculus Assessment
    • Strand 5 Higher Level Functions and Calculus Assessment
  • Resource: Examination Material Archive
Topics List ( 1 )
Strand 5 Higher Level Functions and Calculus Assessment
You must score 80% or more to pass this assessment.
Course Features
  • Duration

    3-4 Hours

  • Publisher

    Advance Learning

  • Video


  • Audio


  • Assessment


  • Certification


  • Price


  • Reward

    50 Pts

  • Responsive


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