# Strand 5 Higher Level Functions and Calculus

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• 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 ‘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 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