U61M Lessons & Blog

Week 20 - 26 May

Monday Lesson:

Small Angle Approximations

Lesson Notes

Tuesday Lesson:

Review Mech & Stats Mock Papers

Wednesday Lesson:

Sequences and Series

Lesson Notes

Week 13 - 19 May

Monday Lesson:

Integration by Parts

Lesson Notes

Wednesday Extra Lesson:

APs and GPs

Week 29 Apr - 05 May

Monday Lesson:

Normal Distribution and Hypothesis Testing

Questions and Mark Schemes

Lesson Notes

Week 22 - 28 April

Tuesday Lesson:

Review of Moments

Lesson Notes 1

Lesson Notes 2

Wednesday Lesson:

Review of Inclined Planes

Lesson Notes

Extra Lessons

Due to Easter Monday falling outside the normal two week Easter holiday and the early May bank holiday, we will miss two lessons. This leaves only 9 lessons before your first exam. I plan to replace these lost lessons with two Week 1 Wednesday Period 5 lessons when almost all of you are free.

They will be on Wednesday 1 May and Wednesday 15 May.

Reminder of June 2018 Grade Boundaries

The grade boundaries for the new Edexcel A-level Maths exams taken in June 2018 were as follows:

 Qualification A* A B C D E A-Level Maths (300) 229 184 155 126 98 70 76% 61% 52% 42% 33% 23%

There is of course no guarantee that these will be a good guide to the grade boundaries for the 2019 exams.

Reminder of June 2019 Exam Dates

The dates for the 2019 A-Level Maths Exams are as follows:

 Paper Code Date Session Pure Mathematics 1 9MA0 01 Wed 05 Jun 19 AM Pure Mathematics 2 9MA0 02 Wed 12 Jun 19 AM Statistics & Mechanics 9MA0 03 Fri    14 Jun 19 PM

Each exam lasts 2 hours and is marked out of 100.

Week 01 - 07 April

Monday Lesson:

Review - Projectiles and Moments

Lesson Notes

Week 25 - 31 March

Monday Lesson:

3D Vectors

Lesson Notes

Tuesday Lesson:

Vectors - Exercise 7D

Lesson Notes

Wednesday Lesson:

Trapezium Rule

Lesson Notes

Trapezium Rule MEI Exam Questions

Week 11 - 17 March

Monday Lesson:

Binomial Distribution

Lesson Notes

Tuesday Lesson:

Binomial - Normal Approx - Hyp Testing

Lesson Notes

Wednesday Lesson:

Normal - Hypothesis Testing

Lesson Notes

MEI Questions

Week 04 - 10 March

Monday Lesson:

Correlation and Hypothesis Testing

Lesson Notes

Wednesday Extra Lesson:

The Large Data Set

Excel Statistical Functions (6:25):

Classwiz Calculator - Binomial Distribution

Two short video clips to teach you how to use the Binomial Distribution functions on your calculator:

Binomial Distribution 1 (2:08)

Binomial Distribution 2 (4:45)

Week 25 Feb - 03 Mar

Monday Lesson:

Coding Polynomials and Exponentials to give Linear Relationships

Lesson Notes

Tuesday Lesson:

Regression Lines and Coding

Lesson Notes

Wednesday Lesson:

Regression and Measuring Correlation

Lesson Notes

Statistics Formulae - Exam Formulae Booklet Probability Formulae - Exam Formulae Booklet Correlation Coefficients - Exam Formulae Booklet Week 11 - 17 February

Monday Lesson:

Review of AS Statistics

Populations and Samples - What you need to know!

Mastering Statistics

The Large Data Set

Weather Data from 5 UK and 3 Overseas weather stations for May-Oct 1987 and May-Oct 2015.

Locations of Weather Stations CLASSWIZ Calculator

Statistical Calculations on the fx-991EX CLASSWIZ Calculator

Week 04 - 10 February

Monday Lesson:

Motion in Two (or Three) Dimensions

Tuesday Lesson:

Moments - Including Ladders Against Walls

Wednesday Lesson:

Mastering Mechanics

 Mech 1 Jan 05 - Omit Q1, Q6 Solutions Mark Scheme

View this as an opportunity to consolidate your knowledge of Mechanics topics that were introduced earlier in the course. Questions on topics that have been moved to Further Maths have been identified for you to omit.

Week 28 Jan - 03 Feb

Monday Lesson:

Review of Mock Performance

Week 21 - 27 January

Mock Exams Week

Monday Lesson:

Projectiles Revision

Week 14 - 20 January

Monday Lesson:

Vectors in Kinematics and Statics Problems

Problems

Solutions

Week 07 - 13 January

Monday Lesson:

General Binomial Expansion

Lesson Notes

Tuesday Lesson:

Recurrence Relations - Iterative Sequences

Lesson Notes

Wednesday Lesson:

Review of Projectiles

Lesson Notes

Homework Questions

Homework Solutions

Mock Exam Preparation

Year 13 Pure Maths Mock - Jan 2019 (2 Hours)

 Question Topic Marks 1 Geometric Progression 5 2 Differentiation From First Principles 5 3 Functions 13 4 Calculus Associated with Cubic 10 5 Rcos (theta - alpha) Methods 11 6 Parametric Equations 5 7 Modulus Function 6 8 Simultaneous Eqns / Discriminant 5 9 Differentiation / Iteration 9 10 Equation of a Circle 9 11 Arithmetic Progression 5 12 Implicit Differentiation 7 13 Trigonometric Equations 10 100

Year 13 Mechanics & Statistics Mock - Jan 2019 (1 Hour)

 Question Topic Marks 1 Venn Diagram - Probability 11 2 Normal Distribution 8 3 SUVAT in 2-Dimensions 4 4 Dynamics on an Inclined Plane 11 5 Projectiles 14 48

Week 10 -16 December

Monday Lesson:

Static Rigid Bodies

Lesson Notes

Tuesday Lesson:

Dynamics on Inclined Plane

Lesson Notes

Sequences and Series

Wednesday Lesson:

Arithmetic Progressions

Lesson Notes

TheMathsTeacher Arithmetic Progression Notes

TheMathsTeacher Arithmetic Progression Exercise

Week 03 - 09 December

Monday Lesson:

Static Friction on Inclined Slope

Week 26 Nov - 02 Dec

Intro to Friction

Monday Lesson:

Intro to Friction

IT Problem - No Lesson Notes

Tuesday Lesson:

Resolving Forces

IT Problem - No Lesson Notes

Wednesday Lesson:

Resolving Forces on Inclined Plane

IT Problem - No Lesson Notes

Week 19 - 25 November

Monday Lesson:

Inverse Functions

Lesson Notes

Week 12 - 18 November

Monday Lesson:

Moments - Tilting

Lesson Notes

Tuesday Lesson:

Functions

Lesson Notes

Wednesday Lesson:

Modulus Function

Lesson Notes

Week 5 - 11 November

Monday Lesson:

Review of Normal Distribution Assessment

Lesson Notes

Week 29 Oct - 4 Nov

Moments

Monday Lesson:

In Mr Smith's absence please read the introduction to the Chapter on Moments and attempt Exercise 4A.

Tuesday Lesson:

In Mr Smith's absence continue reading about moments and attempt Exercise 4B.

Exercise 4B Solutions

Wednesday Lesson Objective:

To be able to use moments to calculate forces in equilibrium situations.

Lesson Notes

Week 15 - 21 October

Approximate Binomial With Normal

Monday Lesson:

Lesson Notes

Week 08 - 14 October

Introduction to Normal Distribution

Monday Lesson Objective:

To be able to use a Classwiz calculator to perform calculations associated with use of the Normal Distribution.

Lesson Notes

Tuesday Lesson Objective:

To be able to calculate parameters of Normal Distribution

Lesson Notes

Wednesday Lesson Objective:

To be able to:

• Approximate the Binomial with the Normal
• Apply a continuity correction

Lesson Notes

A-Level Maths Marking Guidance 2018

Here is the advice provided to Edexcel A-Level Maths markers for the June 2018 Pure Mathematics papers. You will find it useful when using official mark schemes to self-mark questions you do from past papers.

A-Level Maths Marking Guidance 2018

Classwiz Calculator - Normal Distribution

Three short video clips to teach you how to use the Normal Distribution functions on your calculator:

Normal Distribution 1 (1:18)

Normal Distribution 2 (1:51)

Normal Distribution 3 (1:37)

Week 01 - 07 October

Monday Lesson:

Working through Exercises 2D and 2E

Lesson Notes

Week 24 - 30 September

Conditional Probability

Monday Lesson Objective:

To be able to use set notation within Venn diagrams.

Exercise 2A

Lesson Notes

Tuesday Lesson Objective:

To be able to state the formulae for:

• Independent events
• Conditional probability

Lesson Notes

Wednesday Lesson

Two-Way Tables and Venn Diagrams

Lesson Notes

Algebraic Division

Lesson Objective:

To be able to divide polynomials by both linear and quadratic expressions.

Lesson Notes

Lesson Recap (4:23)

Transcript of Video

Support:

TheMathsTeacher.com

Algebraic Multiplication & Division (13 mins)

Video Lesson Notes

Partial Fractions

Lesson Objective:

To be able to decompose rational algebraic fractions into partial fractions.

Denominators of the rational fractions will be limited to having linear factors or repeated linear factors.

It may be necessary to factorise the denominator to obtain the required linear factors.

Lesson Recap 1 - Linear Factors (6:17)

Transcript of Video

Lesson Recap 2 - Repeated Linear Factors (6:03)

Transcript of Video

Algebraic Fractions

Lesson Objective:

To be able to manipulate and simplify algebraic fractions.

Lesson Recap 1 (4:33)

Transcript of Video

Lesson Recap 2 (2:56)

Transcript of Video

Year 13 Parents' Evening

Year 13 Parents' Evening will be held on Thursday 13 December 2018 from 4pm - 7pm.

The grade boundaries for the new Edexcel AS Maths and A-level Maths exams taken in May/June 2018 were as follows:

 Qualification A* A B C D E AS Maths (160) N/A 105 90 75 61 47 66% 56% 47% 38% 29% A-Level Maths (300) 229 184 155 126 98 70 76% 61% 52% 42% 33% 23%

There is of course no guarantee that these will be a good guide to the grade boundaries for the 2019 exams.

A-Level Exam Dates Summer 2019

The dates for the 2019 A-Level Maths Exams are as follows:

 Paper Code Date Session Pure Mathematics 1 9MA0 01 Wed 05 Jun 19 AM Pure Mathematics 2 9MA0 02 Wed 12 Jun 19 AM Statistics & Mechanics 9MA0 03 Fri    14 Jun 19 PM

Each exam lasts 2 hours and is marked out of 100.

The above dates are now final and will not be changed.

U61M Homework

Differentiation - Rates of Change

Rates of change questions normally involve three variables: Time t and two others such as Volume and Length. When a question asks you to find a rate of change it means find the derivative with respect to time.

Rates of Change Example (4:16)

Transcript of Video

Rates of Change 2008-14 Questions

Rates of Change 2008-14 Mark Schemes

Rates of Change 2008-14 Solutions

General Motion Examples

Constant Acceleration - SUVAT in 2 Dimensions (6:46)

Transcript of Video

Variable Acceleration - Calculus (7:03)

Transcript of Video

General Motion

The general motion questions on past Edexcel papers often involve the concept of impulse which is no longer on the syllabus. The following 10 MEI questions are perhaps a better guide as to the type of question we can expect on this topic.

General Motion MEI 2005-09 Questions

General Motion MEI 2005-09 Mark Schemes

General Motion MEI 2005-09 Solutions

Solutions to Mock Statistics & Mechanics

Here are the question paper, mark scheme and solutions you sat on Wednesday 3 April.

Question Paper

Mark Scheme

Solutions

Solutions To Mock Pure 1

Here are the question paper, mark scheme and solutions you sat on Wednesday 27 March.

Go through your own solutions to see where you need to improve or expand your knowledge.

Question Paper

Mark Scheme

Solutions

Optional Connected Particles Homework

Here is a substantial 54 mark homework on Edexcel Connected Particle Exam Questions. My Year 12 class are doing it this week. If you would like to sharpen up your knowledge and skills in this area you could complete it and hand in next Monday. I would mark it and return it to you on Tuesday.

Edexcel Connected Particle Exam Questions

This homework is optional since you are already working on Stats 1 papers this week.

Edexcel Connected Particle Solutions

Binomial Hypothesis Testing

Hypothesis Tester

Mastering Statistics

Once we have completed the 8 Mechanics 1 papers we will concentrate on Statistics 1 papers to consolidate knowledge of topics introduced earlier in the course.

 Statistics 1 Jan 2005 Solutions Mark Scheme Statistics 1 Jun 2005 Solutions Mark Scheme Statistics 1 Jan 2006 Solutions Mark Scheme Statistics 1 Jun 2006 Solutions Mark Scheme Statistics 1 Jan 2007 Solutions Mark Scheme Statistics 1 Jun 2007 Solutions Mark Scheme Statistics 1 Jan 2008 Solutions Mark Scheme Statistics 1 Jun 2008 Solutions Mark Scheme

Some questions have been annotated 'No longer on Syllabus'. Miss those questions out.

Other questions are on correlation and regression. If you are supplied with tabulated bivariate data you can attempt these on your calculator. However, if you are given summary statistics for the data you can either miss the question out or, better still, use the formulae below to attempt the questions to increase your insight into correlation and regression. Mech 1 January 2009

You should all have a paper copy of the Mech 1 January 2009 paper. Please complete and hand in first lesson back on Monday 25 February. In case you lose your hard copy here is one you can download:

Mech 1 January 2009 Question Paper  Omit Q3 which is no longer on the syllabus.

Have a good break.

Mastering Mechanics

Two Papers Per Week For A Month

 Mech 1 Jan 05 - Omit Q1,6 Solutions Mark Scheme Mech 1 Jun 05 - Omit Q2 Solutions Mark Scheme Mech 1 Jan 06 - Omit Q2 Solutions Mark Scheme Mech 1 Jun 06 - Omit Q2 Solutions Mark Scheme Mech 1 Jan 07 - Omit Q4 Solutions Mark Scheme Mech 1 Jun 07 - Omit Q2 Solutions Mark Scheme Mech 1 Jan 08 - Omit Q2 Solutions Mark Scheme Mech 1 Jun 08 - Omit Q1 Solutions Mark Scheme Mech 1 Jan 09 - Omit Q3 Solutions Mark Scheme

View this as an opportunity to consolidate your knowledge of Mechanics topics that were introduced earlier in the course. Questions on topics that have been moved to Further Maths have been identified for you to omit.

Aim to complete two papers per week for the next four weeks. Once this work is complete we will do a Mech 1 paper under exam conditions.

Review of Mock Exams

Please complete the following and hand in during Mr Herring's lesson on Thursday:

AP, GP and Modulus Function questions if you scored less than full m,arks on them.

Any Statistics or Mechanics question for which you scored less than 70% of the marks.

General Binomial Expansion

Valid for expressions of the form (1 + x)n where n is negative, fractional or both.

It must be 1 at the front of the bracket and the validity depends on having |x| < 1

General Binomial Questions

General Binomial Solutions

General Binomial Mark Schemes

This topic is not on the January mock exam.

Mock Exam Preparation - Points of Inflection

This is the final element of the support for mock exam preparation. The question concerned is 'Calculus Associated with a Cubic'.

Though most of the marks are for problem solving with standard calculus for polynomials the first 3 marks are concerned with a general point of inflection. This has not been examined on our old MEI syllabus and I can find no mention of it in our new textbooks. I have recorded a 10 minute lesson which will hopefully help you get to grips with it.

Points of Inflection (9:39)

TheMathsTeacher Differentiation of Polynomials Notes

Points of Inflection Notes

Mock Exam Preparation - 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

Mock Exam Preparation - Iteration

Here is an Iteration Question with the mark scheme, together with a video solution:

Equation of Iteration Example (5:44)

Equation of Iteration Example Solution

Further Practice:

Iteration Questions

Iteration Solutions

Iteration Mark Schemes

Mock Exam Preparation - Functions

This is a very important topic. Historically, it has been heavily examined by Edexcel. For example, on the June 2013 Core 3 paper there were two questions on Functions accounting for 18 of the 75 marks on the paper. Further down this web page you completed Functions questions from 2008-10 (blog entry dated 21 Nov 18). The questions supplied here are taken from 2011-13 papers.

Here is a Functions Question with the mark scheme, together with a video solution:

Functions Example (7:54)

Functions Example Solution

Further Practice:

Functions (2011-13) Questions

Functions (2011-13) Solutions

Functions (2011-13) Mark Schemes

Mock Exam Preparation - Equation of a Circle

Here is an Equation of a Circle Question with the mark scheme, together with a video solution:

Equation of Circle Example (5:23)

Equation of Circle Example Solution

Further Practice:

Circle Questions

Circle Solutions

Mock Exam Preparation - Modulus Function

Here are two Modulus Function Questions with the mark scheme, together with a video solution:

Modulus Function Examples (5:00)

Modulus Function Examples Solutions

Further Practice:

Modulus Function Questions

Modulus Function Solutions

Mock Exam Preparation - Normal Distribution

Here is a Normal Distribution Question with the mark scheme, together with a video solution:

Normal Distribution Example (7:49)

Further Practice:

Normal Distribution Questions

Normal Distribution Solutions

Normal Distribution Mark Schemes

Mock Exam Preparation - Parametric Equations

Parametric Equations questions often involve differentiation, integration and eliminating the parameter to obtain the cartesian equation of the curve. You have not yet covered the necessary integration techniques, so your exam question will not require integration. The further practice questions involve integration techniques which will be necessary for your final exam. For now you can practise the non-integration parts of these questions.

Here is a Parametric Equations Question with the mark scheme, together with a video solution:

Parametric Equations Example (3:18)

Further Practice:

Parametric Equations Questions

Parametric Equations Solutions

Parametric Equations Mark Schemes

Mock Exam Preparation - Quadratic Discriminant

Here is a Quadratic Discriminant Question with the mark scheme, together with a video solution:

Further Practice:

Mock Exam Preparation - Rcos(theta - alpha) Methods

Here is an Rcos(theta - alpha) Methods Question with the mark scheme, together with a video solution:

Rcos(theta - alpha) Methods Example (6:00)

Further Practice:

Rcos(theta - alpha) Methods Questions

Rcos(theta - alpha) Methods Solutions

Rcos(theta - alpha) Methods Mark Schemes

Mock Exam Preparation - Trig Identities & Equations

Here is a Summary of Trigonometric Identities you need to memorise. Do not rely on them being in the Formulae Booklet as you need to recognise them within the context of problems you are looking to solve.

Here is a Trigonometric Identity & Equation Question with the mark scheme, together with a video solution:

Trigonometric ID & Eqn Example (6:23)

Trigonometric ID & Eqn Example Solution

Further Practice:

Trig Identities & Equations 2008-10 Questions

Trig Identities & Equations 2008-10 Solutions

Trig Identities & Equations 2008-10 Mark Schemes

Mock Preparation - Vectors 2D SUVAT

Here is a Vectors 2D SUVAT Question with the mark scheme, together with a video solution which introduces the techniques involved:

Vectors 2D SUVAT Example (8:24)

Vectors 2D SUVAT Example Solution

Further Practice:

Vectors 2D SUVAT Questions

Vectors 2D SUVAT Solutions

Vectors 2D SUVAT Mark Schemes

Mock Preparation - Venn Diagram

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

Functions - Major Homework

Please complete by Monday 2 December and mark as you go.

Questions

Mark schemes

Solutions

All these questions are taken from the Revision Page

Moments

Please complete and self-mark for Monday:

Moments 2005-2007

Mark Scheme

Solutions

Video Solution Jan 2005 (5:03)

Video Solution Jun 2005 (6:51)

Past Exam Questions On Normal Distribution

For Monday 15 October, please complete Normal 2008-10 questions and self-mark using the mark schemes and my solutions.

Work For Mr Herring's Lessons

Further to my email last Friday, during lesson time for Mr Herring on Tuesday Period 2 please complete the Probability Mixed Exercise 2 on pages 34-36 of our Statistics & Mechanics Year 2 textbook.

The answers are in the back of the book but here are my full solutions.

Homework will be to revise for the Probability Topic Test which you will complete during Mr Herring's lesson on Friday Period 4.

DUE TO HOUSE MUSIC DAY, PLEASE NOW HAND IN PROBABILITY ASSESSMENT ON MONDAY 15 OCTOBER

Topic Test - Algebraic & Partial Fractions

Please complete the topic test handed out during the lesson and hand in next Monday 8 October.

This is a major piece of work that could take up to 90 minutes.

Here are the solutions.

Conditional Probability -Trees

Please finish off and self mark from back of textbook:

• Exercise 2D Q2, Q4, Q6
• Exercise 2E Q4, Q6, Q8

Venn Diagrams and Two Way Tables

For Monday please complete Exercise 2C Q8, 10, 12

Algebraic Fractions

Please complete these Algebraic Fractions questions and hand in on Wednesday. Where questions have multiple parts you should attempt only part (a).

Here are the solutions.

Set Notation in Venn Diagrams

Finish Exercise 2A Q 5-12.

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

Partial Fractions

Please complete Partial Fractions and hand in on Monday.

Here are the solutions.

Algebraic Fractions

Exercise 1B pages 6-7

Please complete Exercise 1B. Where there are multiple parts do only parts a and b.

Algebraic Multiplication & Division

In preparation for the lesson on Monday 10 September please:

Watch the 13 minute video lesson Algebraic Multiplication and Division.

Print off the lesson notes for your file.

Complete and self- mark the exercise from the solutions included.

Note that the video lessons will not play full screen on Chrome without a browser extension. They will on other browsers.

Becoming An Effective Learner

Professor Stephen Chew is a cognitive psychologist from Samford University, Birmingham, Alabama. In 2011, he recorded five short videos (each 5 - 9 minutes long) to help students become more effective learners. They contain a whole range of dos and don'ts together with practical suggestions you can adopt to improve your learning. Below are direct links to each video. As an alternative you can log on to Youtube and type in 'Stephen Chew'