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Differentiating functions defined implicitly

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Lesson 9.6: Differentiating functions defined implicitly

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Differentiating trigonometric functions

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Differentiation using the quotient rule

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Lesson 9.4: Differentiation using the quotient rule

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Differentiation using the product rule

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Lesson 9.3: Differentiation using the product rule

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Differentiation using the chain rule (part 2)

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Lesson 9.2B: Differentiation using the chain rule (Part 2 of 2)

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Differentiation using the chain rule (part 1)

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Lesson 9.2A: Differentiation using the chain rule (Part 1 of 2)

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Differentiating sin x, cos x, e^x and others from first principles

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Lesson 9.1: Differentiate sin x, cos x, e^x and others from first principles

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Prove from first principles the derivative of ln x.

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Lesson 9.1*: Prove from first principles that the derivative of ln x is 1/x

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Exploring the properties of functions and their inverses

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Lesson 3.4: Finding inverse functions using graphical and algebraic methods

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Learn how to compose two or more functions to form a composite function.

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Lesson 3.3: Composite functions (Chapter 3: Functions)

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Understanding domain and range

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An introduction to the modulus function and its key properties.

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Find the nth term of an arithmetic sequence.

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Lesson 1, Chapter 4.1: Sequences & Series

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Lesson 1: The Binomial Expansion (Year 2, Pure Mathematics)

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Lesson 1: The Binomial Expansion (Year 2, Pure Mathematics)

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Expand (1 + x)n for any rational constant n and determine the range of validity.

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Lesson 1, Chapter 2.1: The Binomial Expansion

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Lesson 2: The Binomial Expansion (Ch. 2.2)

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Lesson 2: The Binomial Expansion (Ch. 2.2)

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Use the binomial expansion to find approximations to irrational numbers.

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Lesson 2, Chapter 2.2: The Binomial Expansion

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Prove and apply the formula for the sum of n terms of an arithmetic series.

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Lesson 2, Chapter 4.2: Sequences & Series

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Lesson 3: The Binomial Expansion (Ch. 2.3)

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Lesson 3: The Binomial Expansion (Ch. 2.3)

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Expansions of the form (a + bx)n where n is a rational number (+/-)

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Lesson 3, Chapter 2.3: The Binomial Expansion

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Classifying sequences and an introduction to geometric sequences.

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Lesson 3, Chapter 4.3: Sequences & Series

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Please use the form to submit your request for worked solutions to any of the exercises in the notes, concept checks, unit reviews or spaced retrieval practice papers.

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Lesson 4: The Binomial Expansion (Ch. 2.4)

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Lesson 4: The Binomial Expansion (Ch. 2.4)

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Finding expansions of partial fractions.

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Lesson 4, Chapter 2.4: The Binomial Expansion

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Construct implication statements in one or both directions.

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Lesson 2 Introduction: Eight Logic Puzzles

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Lesson 2 Introduction: Eight Logic Puzzles

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Try these problems before attempting any of the content from Lesson 2

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Summary of "representatives for elements of number sets"

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Summary of "representatives for elements of number sets"

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This is a supporting list of algebraic representations of natural numbers, integers, rationals, irrationals and real numbers for simple proofs.

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Lesson 1: Numbers, Propositions & Implications

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Lesson 1: Numbers, Propositions & Implications

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Here we discuss the fundamental properties of distinct sets of numbers and their use in mathematical proof.

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Chapter IA - Introduction to Methods of Proof

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Lesson 8: "Differential Equations" Online Instruction Video

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Lesson 8: "Differential Equations" Online Instruction Video

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This lesson focuses on separation of variables only. No other method is required in this course.

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An introduction to solving "first order differential equations" using separation of variables.

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Attempt these questions before watching the instructional video for Lesson 8. <Prior knowledge is assumed.>

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Lesson 8: Preparation Task (Year 2 Integration)

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Complete online instructional video. <Please attempt the 'Preparation Task' and print out the notes before viewing this lesson.>

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This function is mentioned in Lesson 7: The Trapezium Rule. It is not a requirement for the course, but it is interesting nontheless.

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The Error Function & The Impossible Integral of e^(-x^2)

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Notes to accompany the online instruction videos. Please print, fill out and archive for future reference.

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Attempt the questions presented in this video before viewing Lesson 7: The Trapezium Rule.

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Lesson 6: Finding Areas Using Integration Techniques

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Lesson 6: Finding Areas Using Integration Techniques

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Includes revision of integration techniques for definite integrals and their application in finding areas. (Prior knowledge is assumed.)

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Lesson 6: "Finding Areas using Integration"

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Lesson 6: Finding Areas Using Integration Techniques Notes

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Lesson 6: Finding Areas Using Integration Techniques Notes

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Preparation task, concept, proof and worked examples.

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Review of some recent integration techniques. We can apply these to evaluate areas between curves later.

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Preparation Task for Lesson 6: 'Finding Areas Using Integration Techniques.'

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Lesson 5: "Integration with Partial Fraction Decomposition" online video

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Lesson 5: "Integration with Partial Fraction Decomposition" online video

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Use this video in conjunction with the notes.

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Attempt the questions after watching the online video and filling-in the notes. <Solutions to all concept checks are available on request.>

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Lesson 5: "Integration with Partial Fraction Decomposition" Notes

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Lesson 5: "Integration with Partial Fraction Decomposition" Notes

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Available for printing and to accompany the online video for Lesson 5, Ch.XI Integration.

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4 primer questions for the upcoming instruction video: "Lesson 5: Integration with partial fraction decomposition." <Video and notes to follow shortly.>

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This "Concept Check" will enable you to test your own understanding of integration by parts.

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Accompanying notes to the video of the same name. <Please print off before watching!>

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The fourth lesson in a series introducing 'integration by parts'.