Calculus

This unit takes students on the journey in to Calculus by building on work they have done in modelling. From the basic principles through to optimisation and beyond for HL students. Conceptually challenging but very rewarding, these topics are a great insight in to the potential of mathematics for solving applied problems.

What is here?

Here are the sub pages for this section. Each of them leads you to slide galleries to offer explanation, teaching activities and practice exercises and exam style questions.

SL Scheme - Calculus

The new Mathematics: Applications and Interpretation syllabus is out and published on the IB website. Log in to your MyIB account and head to this link . It is a new course with a new name and renewed...

SL Calculus Concept

This is the first of three sections on differential calculus. This is significant branch of mathematics with lots of applications. It builds very nicely on other concepts in the course and those you are...

SL Integration + Trapezium rule

Welcome to integration! A lot of fun is in store! It helps to remember that this topic, along with differentiation, is the best description humans have yet invented for measuring, describing and calculating...

SL Optimisation

In this section we look at how calculus is used to find the local maximum and minimum values of functions and, as such, how that is used to optimise. This is done both in the abstract and in context but...

SL Tangents & Normals

In this unit we look at find the equations of tangents and normals to curves, increasing and decreasing functions and the second derivative. All this builds on the fundamental notion that calculus tells...

HL Euler's Method

There is no "general solution” for all differential equations. As such, they are classified by whether they are “linear” or “non-linear”, the “methods” that can be used to solve them etc....

HL Phase Portraits

Phase Portraits - What are they? What's the link to Eigen vectors and values?The concept of Eigen values and vectors grew out of the study, around the 1740s/50s, by the French mathematician, d'Alembert,...

HL Slope Fields

Conceptual overview: 'Slope fields' as an introduction to differential equations - what are they?Instead of starting with "data", plotting it, and finding which functions have a similar shape e.g. maximums,...

Concepts

This is a brief outline of the concepts on which this topic is based

2103PRLN


Selected Pages

free

SL Scheme - Calculus 11 September 2021

The new Mathematics: Applications and Interpretation syllabus is out and published on the IB website. Log in to your MyIB...
more

free

SL Integration + Trapezium rule 25 June 2021

Welcome to integration! A lot of fun is in store! It helps to remember that this topic, along with differentiation, is the...
more

HL Chain, Product, Quotient rules(5.9) 12 September 2021

On this page you can find the a set of IB style questions for this topic that covers 65 marks over the range of difficulty...
more

Lotka Volterra 5 September 2021

Biologists studying a single species, call it X in isolation, like a bacteria in a Petri dish, have observed that in the...
more

HL 2nd Order Differential Eq(5.18) 18 August 2021

On this page you can find a video introduction to 2nd order differential equations, created by James Tanton (training available...
more

HL Coupled Diff Eq & Phase Portraits(5.17) 18 August 2021

On this page you can find a set of videos, created by James Tanton (training available here), for topics AHL 5.17 that provide...
more

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