M34 - Maths Lessons, Homework and Revision Site

Blog posts : "L62M"

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

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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.

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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


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Week 22 - 28 June

Thursday Lesson Live 7pm

Algebraic Division

Lesson Notes and Homework

Next online lesson on Monday 29 June at 7pm

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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.

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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

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Year 13 Starts Here ^

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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.

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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.

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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.

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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)

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AS Mathematics Grade Boundaries

Grade Boundaries for AS Maths 2018 and 2019

Year MaximumABCDE


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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

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Week 10 - 16 February

Wednesday Lesson:

Exponentials Intro

Lesson Notes


Thursday Lesson:

Exponential Modelling and Logs Intro

Lesson Notes and Homework

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Week 03 - 09 February

Monday Lesson:

Hypothesis Testing 3 & Probability

Lesson Notes and Homework


Tuesday Lesson:


Lesson Notes and Homework

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Week 27 Jan - 02 Feb

Wednesday Lesson:

Hypothesis Testing 1

Lesson Notes


Thursday Lesson:

Hypothesis Testing 2

Lesson Notes and Homework

Mark Schemes

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CLASSWIZ Calculator - Binomial Distribution

Binomial Distribution 1 (2:08)


Binomial Distribution 2 (4:44)

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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

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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

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Week 06 - 12 January

Monday Lesson:

Intro to Venn Diagrams and Probability

Lesson Notes


Tuesday Lesson:

Venn Diagrams

Lesson Notes

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