M34 - Maths Lessons, Homework and Revision Site

L62M Lessons & Blog

Week 13 - 19 July

Tuesday Live On-line Lesson 10am

Binomial - Partial Fractions

Video of second half (sorry - forgot to press record at start)

Lesson Notes

Suggested Homework to self mark

Exercise 4B on Page 100, Q6, Q8

Solutions to Exercise 4B

Exercise 4C on Pages 102-103, Q1, Q3

Solutions to Exercise 4C

To round off Chapter 4, I suggest you do at least half of the Mixed Exercise over the summer holiday and mark as you go.

Mixed Exercise Solutions

Finally, let me wish you all the best for next year and remind you to email me today if you would like to work with me to do some consolidation work over the summer holidays.



Mr Smith

Week 06 - 12 July

Monday Recorded Lesson

Binomial Expansion of (a +bx)^n

Video (12:04)

Lesson Notes

Homework:  Please complete all parts of Exercise 4B Q1 on Page 99.

Email me your solutions by Friday 10 July.

Week 29 Jun - 05 Jul

Monday Lesson Live 7pm

Binomial Expansion For Negative And Fractional Powers

Video recording of lesson

Lesson Notes

Homework Exercise 4A Q1a,d  Q2a,d  Q3a,d

Email to me before next live lesson on Thursday at 7pm


Thursday Lesson:

Binomial Expansion (1 + x)^n Continued

Video (10:37)

Please watch video and then complete the remainder of Exercise 4A Q4-Q9.

Self-mark from Exercise 4A Solutions


Week 22 - 28 June

Thursday Lesson Live 7pm

Algebraic Division

Lesson Notes and Homework

Next online lesson on Monday 29 June at 7pm

Week 08 - 14 June

1.3 Partial Fractions

Intro to Partial Fractions (6:50)

Lesson Notes

Now turn to Exercise 1D on Page 11. Complete all the other parts of Q1 together with Q2 and Q3.

Mark your work from Exercise 1D Solutions


An Example With Three Partial Fractions

Three Partial Fractions (6:18)

Lesson Notes

Now turn to Exercise 1D on Page 11.  Complete Q4, Q6a, Q6c, Q7a, Q7b.

Note the hint for Q7 - for both parts you will need to factorise the denominators into linear factors.

Mark your work from Exercise 1D Solutions


Repeated Factors In Partial Fractions

Repeated Factors (8:44)

Lesson Notes

Now turn to Exercise 1E on Page 13.  Complete Q1, Q3, Q5, Q7.

Mark your work from Exercise 1E Solutions



Please complete these three questions and email to me by Tuesday 16 June.

Week 01 - 07 June

Chapter 1 Algebraic Methods

1.1 Proof

The first topic of this chapter is Mathematical Proof and, in particular, Proof by Contradiction.

This is an area of Mathematics where precise language is essential. 

The other topic required for the first exercise in this chapter is Negation Statements.

Have a read through these Worked Examples of Negation Statements published by the University of Toronto.

As you will see, such statements are not necessarily obvious.


Proof by Contradiction (8:58)

Lesson Notes

Complete Exercise 1A on Pages 4 and 5 of the textbook

Do the whole exercise marking one question at a time from Exercise 1A Solutions


Formal Proofs


The A-level syllabus states that there are two formal proofs you could possibly be required to reproduce in your exam:

The Number of Primes is Infinite (1:53):

Transcript of Video


The Square Root of 2 is Irrational (6:16):

Transcript of Video

These two proofs are also presented on Page 3 of the textbook.

Both proofs should be committed to memory.


1.2 Algebraic Fractions

Algebraic Fractions (7:33)

Lesson Notes

Now select a range of questions to do from Exercises 1B and 1C on Pages 6 to 8 of the textbook.

Mark from the solutions below:

Exercise 1B Solutions

Exercise 1C Solutions

Year 13 Starts Here ^

Week 18 - 24 May

AS Statistics & Mechanics 2018

I have emailed the AS Statistics & Mechanics 2018 paper to you.

Please complete and return to me by Friday 22 May for marking.

There will be no work set over half-term week.

Week 11 - 17 May

AS Pure Maths 2018

I have emailed the AS Pure Maths 2018 paper to you.

Please complete and return to me by Thursday 14 May for marking.

Week 27 Apr - 03 May

EOC Stats and Mech Paper

This paper was due in by Monday 27 April.


Specimen Papers - Pure and Applied

The next pair of papers you will self-mark and submit your scores by email.

Please submit your Pure result by Sunday 3 May and your Applied result by Wednesday 6 May.

You can access Question Papers, Mark Schemes, Solutions and Video Solutions to the Pure Paper here

On Wednesday 6 May I will issue you with your first real exam paper which I will mark.

Week 20 - 26 April

Maximising Area For A Fixed Perimeter

Here are 4 questions for you to work through where you are required to use calculus to maximise a shape's area for a fixed perimeter.

For the first 3 questions video solutions are provided. Attempt one question at a time then mark it by watching the associated video and look to improve your notation as you progress. Finally attempt Question 4 and email me your solution by next Tuesday 21 April.

Area Perimeter Questions

Question 1 Solution ( 3:16)


Question 2 Solution (2:53)


Question 3 Solution (5:03)

AS Mathematics Grade Boundaries

Grade Boundaries for AS Maths 2018 and 2019

Year MaximumABCDE


Week 23 - 29 March

First Mock Exam

Please complete Q1 - Q9 inclusive (50 marks) and email your solutions to me by Sunday 29 March

EOC AS Pure Questions

Please complete Q10 - Q17 inclusive (50 marks) and email your solutions to me by Thursday 02 April

Week 10 - 16 February

Wednesday Lesson:

Exponentials Intro

Lesson Notes


Thursday Lesson:

Exponential Modelling and Logs Intro

Lesson Notes and Homework

Week 03 - 09 February

Monday Lesson:

Hypothesis Testing 3 & Probability

Lesson Notes and Homework


Tuesday Lesson:


Lesson Notes and Homework

Week 27 Jan - 02 Feb

Wednesday Lesson:

Hypothesis Testing 1

Lesson Notes


Thursday Lesson:

Hypothesis Testing 2

Lesson Notes and Homework

Mark Schemes

CLASSWIZ Calculator - Binomial Distribution

Binomial Distribution 1 (2:08)


Binomial Distribution 2 (4:44)

Week 20 - 26 January

Monday Lesson:

Probability Trees

Lesson Notes

Homework Exercise

Homework Exercise Solutions


Tuesday Lesson:

Intro to Binomial Distribution

Lesson Notes and Homework

Week 13 - 19 January

Wednesday Lesson:

Trigonometry Topic Test

Please sit individually in class to complete this topic test.

You may use your textbooks and notes but not each other. If necessary finish it at home to hand in on Thursday.


Thursday Lesson:

Mr Smith  absent

Cover Work

Probability Trees - Exercise 5D

Venn Diagrams - Finish Exercise 5B

Week 06 - 12 January

Monday Lesson:

Intro to Venn Diagrams and Probability

Lesson Notes


Tuesday Lesson:

Venn Diagrams

Lesson Notes

Week 16 - 22 December

Wednesday Lesson:

Trigonometry - Mixed Exercise 10

Lesson Notes

Homework - Finish even numbers

Solutions to Mixed Exercise 10

Thursday Lesson:

Trigonometry - Mixed Exercise 9

Lesson Notes

Homework - Finish even numbers

Solutions to Mixed Exercise 9

Week 09 - 15 December

Monday Lesson:

Trig Identities and CAST Diagram

Lesson Notes and Homework


Tuesday Lesson:

Trig Equations and Problems

Lesson Notes

Homework 2nd and 3rd questions from Problems 2008-10

Week 02 - 08 December

Wednesday Lesson:

Intro to Trigonometry

Lesson Notes

Thursday Lesson:

Trig Problems

Lesson Notes


C2 Jan 07 Question 11     Solution

C2 Jan 08 Question 11     Solution

Mark schemes are at end of question papers

Week 25 Nov - 01 Dec

Monday Lesson:

Linear Coding of Data

Lesson Notes


Tuesday Lesson:

Representation of Data

Lesson Notes and Homework


Mixed Exercise 2 

Exercise 3A   Exercise 3B   Exercise 3C    Exercise 3D    Exercise 3E

Week 18 - 24 November

Wednesday Lesson:

Median and IQR

Lesson Notes


Thursday Lesson:

Mean and Standard Deviation

Lesson Notes and Homework


Statistics Calculations on Casio Classwiz Calculator

Entering statistical data and performing calculations (2:14)

Week 11 - 17 November

Monday Lesson:

Intro to Sampling

Populations and Samples - What you need to know!

Homework - Read Chapter 1


Tuesday Lesson:

Measures of Location And Spread

Lesson Notes

Homework - Read Chapter 2



Week 04 - 10 November

Wednesday Lesson:

Proof 2 Exercise 7D

Lesson Notes and Homework


Thursday Lesson:

Proof 3 Exercise 7E

Lesson Notes and Homework

Week 21 - 27 October

Monday Lesson:

Binomial Mixed Exercise 8

Lesson Notes and Homework


Tuesday Lesson:


Lesson Notes

Week 14 - 20 October

Wednesday Lesson:

Binomial Expansion

Lesson Notes

Homework Questions 5 to 10


Thursday Lesson:

Binomial 2

Lesson Notes and Homework

Week 07 - 13 October

Monday Lesson:

Algebraic Long Division

Lesson Notes

Video Lesson (13 mins), Notes and Exercise


Tuesday Lesson:

Factor Theorem

Lesson Notes

Video Lesson (24 mins), Notes and Exercise

Year 12 Parents' Evening

The Year 12 Parents' Evening will be held on Tuesday 23 June.

Week 30 Sep - 06 Oct

Wednesday Lesson:

Circle Exercises 6D & 6E

Lesson Notes


Thursday Lesson:

Circle Exercises 6F & Mixed Exercise 6

Lesson Notes & Homework

Mixed Exercise 6 Solutions

Week 23 - 29 September

Monday Lesson:

Intro to The Circle

Lesson Notes


Tuesday Lesson:

Circle - Midpoints and Bisectors

Lesson Notes and Homework

Week 16 - 22 September

Wednesday Lesson:

Straight Line 3

Lesson Notes


Thursday Lesson:

Straight Line 4

Lesson Notes and Homework

Mixed Exercise 5 Solutions

Week 09 - 15 September

Monday Lesson:

Cancelled for University trip


Tuesday Lesson:

Straight Line 2

Lesson Notes

Week 02 - 08 Sep

Wednesday Lesson:

Coordinate Geometry Basics

Lesson Notes


Thursday Lesson:

Straight Line 

Exercises 5A and 5B

Lesson Notes

L62M Homework

Differentiation From First Principles

Here is a short video working through an example of differentiating a polynomial term from first principles.

Differentiating f(x) = x4 (4:33)

Differentiating f(x) = x4 lesson notes

Further Practice:

Differentiating From First Principles Questions

Differentiating From First Principles Solutions

Venn Diagrams

Here are three Venn Diagram Questions you may like to attempt before watching a video solution to the first and viewing written solutions to all three.

Venn Diagram Question from Jan 2004 (6:10)

Venn Diagram Probabilites Solutions

The Venn Diagram 11 mark question is one where the diagram will require probabilities rather than raw data in the circles. Set notation will be used. Here is a comprehensive exercise of 8 questions on this topic.

Venn Diagram practice questions

Venn Diagram solutions

Venn Diagram mark scheme


Straight Line Assessment

Please complete this assessment and hand in next Monday 23 September.

Here are the Solutions.

Straight Line 2

Homework is at the bottom of the lesson notes for Tuesday 10 September.

Check your answers:

Exercise 5C      Exercise 5D      Exercise 5E     Exercise 5F

Straight Line 1

The homework for Thursday's lesson is listed at the end of the lesson notes opposite.


Check your solutions here for Exercise 5A and Exercise 5B

Coordinate Geometry Basics