Year 2 A-level Mathematics (Template) by Mr Brockway

Lesson 4: Integration by Parts

MrPBrockway — 2020-05-07 19:37:41 UTC

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

Lesson 4 : "Integration by Parts" Notes

MrPBrockway — 2020-05-07 19:43:49 UTC

Accompanying notes to the video of the same name.

Lesson 4: Concept Check Worksheet

MrPBrockway — 2020-05-07 19:50:50 UTC

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

Lesson 5: Preparation Task

MrPBrockway — 2020-05-07 19:55:52 UTC

4 primer questions for the upcoming instruction video: "Lesson 5: Integration with partial fraction decomposition."

Lesson 5: "Integration with Partial Fraction Decomposition" Notes

MrPBrockway — 2020-05-10 15:48:10 UTC

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

Lesson 5: Concept Check Worksheet

MrPBrockway — 2020-05-10 20:00:31 UTC

Attempt the questions after watching the online video and filling-in the notes.

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

MrPBrockway — 2020-05-11 12:11:04 UTC

Use this video in conjunction with the notes.

Lesson 6: Preparation Task

MrPBrockway — 2020-05-14 08:37:03 UTC

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

Lesson 6: Finding Areas Using Integration Techniques Notes

MrPBrockway — 2020-05-18 20:35:28 UTC

Preparation task, concept, proof and worked examples.

Lesson 6: Finding Areas Using Integration Techniques

MrPBrockway — 2020-05-19 10:18:59 UTC

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

Lesson 7: Preparation Task

MrPBrockway — 2020-05-21 15:15:44 UTC

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

Lesson 7: "The Trapezium Rule" Notes

MrPBrockway — 2020-05-25 14:33:55 UTC

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

The Error Function

MrPBrockway — 2020-05-25 18:31:45 UTC

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

Lesson 7: "The Trapezium Rule"

MrPBrockway — 2020-05-25 21:18:06 UTC

Complete online instructional video.

Lesson 8: Preparation Task

MrPBrockway — 2020-05-29 06:53:59 UTC

Attempt these questions before watching the instructional video for Lesson 8.

Lesson 8: Notes

MrPBrockway — 2020-06-12 13:30:06 UTC

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

Lesson 8: "Differential Equations" Online Instruction Video

MrPBrockway — 2020-06-12 13:34:46 UTC

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

Lesson 1: Numbers, Propositions & Implications

MrPBrockway — 2020-06-12 13:40:03 UTC

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

Summary of "representatives for elements of number sets"

MrPBrockway — 2020-06-12 19:25:15 UTC

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

Lesson 2 Introduction: Eight Logic Puzzles

MrPBrockway — 2020-06-13 17:21:08 UTC

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

Card Sort Activity: Implications

MrPBrockway — 2020-06-13 18:00:09 UTC

Construct implication statements in one or both directions.

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

MrPBrockway — 2020-10-15 07:23:10 UTC

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

Lesson 1: Sequences and Series

MrPBrockway — 2020-10-15 14:19:22 UTC

Find the n^thterm of an arithmetic sequence.

How to use this padlet

MrPBrockway — 2020-10-17 18:05:31 UTC

Lesson 2: The Binomial Expansion (Ch. 2.2)

MrPBrockway — 2020-10-17 18:34:43 UTC

Use the binomial expansion to find approximations to irrational numbers.

Lesson 3: The Binomial Expansion (Ch. 2.3)

MrPBrockway — 2020-10-17 18:37:09 UTC

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

Lesson 4: The Binomial Expansion (Ch. 2.4)

MrPBrockway — 2020-10-17 18:40:48 UTC

Finding expansions of partial fractions.

Requesting solutions

MrPBrockway — 2020-10-21 08:47:45 UTC

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.

Lesson 2: Sequences & Series

MrPBrockway — 2020-10-21 10:33:41 UTC

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

Lesson 3: Sequences & Series

MrPBrockway — 2020-10-21 10:35:33 UTC

Classifying sequences and an introduction to geometric sequences.

Lesson 1: Functions

MrPBrockway — 2021-04-14 10:50:38 UTC

An introduction to the modulus function and its key properties.

Lesson 2: Functions

MrPBrockway — 2021-04-14 11:18:26 UTC

Understanding domain and range

Lesson 3: Functions

MrPBrockway — 2021-04-14 11:20:04 UTC

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

Lesson 4: Functions

MrPBrockway — 2021-04-14 11:22:23 UTC

Exploring the properties of functions and their inverses

Lesson 1 (Supplementary): Differentiation

MrPBrockway — 2021-04-14 11:25:29 UTC

Prove from first principles the derivative of ln x.

Lesson 1: Differentiation

MrPBrockway — 2021-04-14 11:27:13 UTC

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

Lesson 2A: Differentiation

MrPBrockway — 2021-04-14 11:31:55 UTC

Differentiation using the chain rule (part 1)

Lesson 2B: Differentiation

MrPBrockway — 2021-04-14 11:36:58 UTC

Differentiation using the chain rule (part 2)

Lesson 3: Differentiation

MrPBrockway — 2021-04-14 11:42:41 UTC

Differentiation using the product rule

Lesson 4: Differentiation

MrPBrockway — 2021-04-14 11:44:23 UTC

Differentiation using the quotient rule

Lesson 5: Differentiation

MrPBrockway — 2021-04-14 12:09:06 UTC

Differentiating trigonometric functions

Lesson 6: Differentiation

MrPBrockway — 2021-04-14 12:11:55 UTC

Differentiating functions defined implicitly