Tuesday and Wednesday Lessons – Further Trigonometry and Further Trigonometric Identities (Chap 6 & 7 from C3)

LEARNING OBJECTVIE: Revision of Chap 6 & Chap 7 of C3

Chapter Six

1. The functions secant θ ,cosecant θ and cotangent θ
   
   1. Ex 6A Type Questions
      
2. Graphs of Sec θ, Cosec θ, cot θ
   
   1. Ex 6B type Questions
      
3. Simplify Expressions, prove identities and solve equations involving Sec θ, Cosec θ, cot θ
   
   1. Ex 6C type questions
      
4. Know and use the identities 1+ tan²θ≡ sec²θ and 1+ cot²θ≡ cosec²θ
   
   1. Ex 6D Type Questions
      
5. Use inverse trig functions arcsinx, arcosx and arctan x and their graphs
   
   1. Ex 6E Type Questions
      

Chapter 7

1. Addition Formulae
   
   1. Ex 7A
      
2. Double Angle Formulae
   
   1. Ex 7B
      
3. Using Double angle formula to solve more equations, and prove more identities
   
   1. Ex 7C
      
4. Write expression of the form a cos θ + b sin θ, where a and b are constants, as a sine function only or a cosine function only
   
   1. Ex 7D
      
5. Express sums and differences of sines and cosines as products of sines and/or cosines by using the 'factor formulae'
   
   1. Ex 7E
      
6. 
   

Revision of Trig

Tues 6th Dec – Revision – Numerical Methods

LEARNING OBJECTIVE: To Revise all topics in Numerical Methods Chapter

SUCCESS CRITERIA: You Will be able to get full marks on numerical methods questions in C3 exam paper

LESSON:

Section 1 – Sketch / plot the graph to find where routes are:

See where the solution of the equation changes sign

Doesn't Work When:

1. There is a discontinuity
   
2. There are two roots between tow values
   

Mymaths Lesson

Section 2: rearranging formula and then using an iterative method

Use screen 5 from this MyMthas Lesson

Work Through Mixed Exercises page 55 of C3 Text Book

 

Tues 29th Nov – Revision of Exponential and Log Functions

LEARNING OBJECTIVE: To revise rules of logs to use when solving exponential and log functions as well as sketching exponential and log functions

SUCCESS CRITERIA: You will be able to solve C3 log and exponential questions

RULES OF LOGS

Work through this Logs/Exponential revision lesson

Work through Ex 3c page 41

Weds 23rd Nov – review of D1 Topics via mock exam paper

LEARNING OBJECTIVE: To refine exam technique by checking marks scheme against your own answers

SUCCESS CRITERIA: You gain higher marks in next mock exam paper

LESSON: Finish going through exam paper questions – Q 5, 6 & 7

If any time left students to choose their weakest topic and find an exam type questions from mixed exercises at the end of the appropriate chapter to have a go at.

 

Tues Nov 22nd – Review of Mock exam – Revision of Prims and Kruskals Algorithms

LEARNING OBJECTIVE: To develop deeper understanding of topics from results of mock exam Results

SUCCESS CRITERIA: You will understand where you lost marks in the recent exam paper test.

Give papers back

Look at results analysis. Work through Exam questions – explaining mistakes / errors. AT question 3 do some indepth revision of Prims and Kruskals Algorithms Using text book

Kruskals Definition on Page 41

Prims Definition on page 45

Have a go at 1, 2 and 6 on page 58, 59 and 60 of text book

Check answers

Weds 16th Nov – Consolidation of Matching – Corrections from Homework -

LEARNING OBJECTIVE: Review Matching homeworks – compare with requirements for Exam questions

SUCCESS CRITERIA: You will be aware of what to include in an A* Exam question on Matching's.

LESSON:

Review of Homework. Take note of the following

1. Must include the alternate paths you have considered
   
2. Must include new matching's
   
3. Must include any intermediate positions in ,matching's (Eg if more than two pairs of unmatched)
   
4. Must include the final complete matching or best matching plus a reason why complete matching not possible
   
5. Use homework questions to demo above
   
6. If any time left then start working through Examination Style paper on page 173 of text book (Photocopy masters provided for questions 1, 4, 5, 7, and 8
   

FRIDAY LESSON: Sit a past paper in exam conditions during the lesson

Friday Nov 11th (P1 & P2) – Work through a D1 Past Paper

LEARNING OBJECTIVE: Revise D1 Topics for January Exam

SUCCESS CRITERIA: You will be able to solve D1 exam Questions

LESSON: Hand out D1 Jan 2009 Exam Paper

Use Mark Scheme as and When Necessary

Whilst students are working meet with them individually to give current grades and set some targets in their planner

Weds Nov 9th – D1 Revision – Go Thorugh Test 2 / Exam questions

LEARNING
OBJECTIVE: TO Review Test 2 results – revising Critical Path Analysis, Rout Inspection Problem, & Linear Programming

SUCCESS
CRITERIA: You Will Be able to solve exam type questions on these topics

LESSON: Work through Test papers questions by question pointing out errors and how to ensure max marks in exam.

If Time Have a go at these questions:

Question 6 page 75

Question 5 page 111

Question 1 Page 145

Fri Nov 4th P2 & 3 – The Maximum Matching Algorithm and Test reviewing Chap 4, 5 & 6

LEARNING OBJECTIVE: Discover how to model a problem using a bipartite graph and solve problems using the maximum matching algorithm

SUCCESS CRITERIA: You will be able to solve matching problems using the maximum matching algorithm

LESSON:

Continue exploring matchin with This lesson on the maximum matching algorithm.

Homework Ex 7a and 7b using the templates provided

Period 3 Test on Chapters 4, 5 & 6

Weds Nov 2nd – Bipartite Graphs - Matchings

LEARNING OBJECTIVE: Discover how to model a problem using a bipartite graph and solve problems using the maximum matching algorithm

SUCCESS CRITERIA: You will be able to solve matching problems using the maximum matching algorithm

LESSON:

Quick reminder of What a Bipartite graph is using screens 3 & 4 of this Lesson. Use the examples to show how to find some possible matchings

You Should now be able to answer the three questions in Exercise 7a (Photocopy masters are available)

Explore finding matchings using this Lesson – using the example screens and problems with students.

If time allows continue with This lesson exploring the maximum matching algorithm

PLENARY: Checking understanding of students – preparation for Fridays lesson – Period 1 more on Matching with a chance to have a go at some questions. Period 2 – Test on Chapters 4 5 & 6

Fri Oct 21 – Solving Linear Programming Problems

LEARNING OBJECTIVE: To Understand how to use a mix of graphing techniques and algebra to solve linear programming problems

SUCCESS CRITERIA You will be able to solve Linear Programming Problems

LESSON 1: Work through this MyMaths Lesson to show how to find the minimum or maximum point from the Object Line and then use Simultaneous equations to work out exact values and the final Maximum or minimum values.

You should now be able to solve Ex 6B

LESSON: 2 Work through this second Lesson which looks at The Vertex method and consides integer solutions

You should now be able to solve Ex 6c and 6D

Homework: 6a, 6b, 6c, 6d plus Q8 page 164, q 18 page 167 and q 21 page 169

 

Weds Oct 19th – Intro to Linear Programming – Formulating the Problems

LEARNING OBJECTIVE: To Discover and practice formulating a wordy problem into Variables, Constraints and an objective function

SUCCESS CRITERIA: You will be able to extract the necessary information from a problem to formulate a problem into a linear programming problem

LESSON: Work through this Lesson, using the examples with students working out their own solutions and checking them onscreen

PLENARY: Checking understanding through checking their solutions to problems.

HOMEWORK: Ex 6A page 119

Fri Oct 14th - Scheduling

LEARNING OBJECTIVE: Understand and use GANTT charts to enable a project to be scheduled in the most efficient way possible

SUCCESS CRITERIA: You will be able to allocate workers to a project in order to complete the project in the minimum time with the minimum number of works. You will also be able to adjust the GANTT chart and schedule should any critical activities not complete on time.

LESSON: Work through this Mymaths Lesson to develop the ideas of scheduling.

Use the printouts of the network on screen 5, and the Gantt charts on screen 6 & 7 to help students answer questions

Now Work through Ex 5H Page 108

HOMEWORK: Ex 5F, 5G, 5H Plus q 4 & 5 from Mixed Exercise page 111

Weds Oct 12th – Gantt (Cascade Charts)

LEARNING OBJECTIVE: To show how the activities for a project can be depicted as a cascade / GANTT chart

SUCCESS CRITERIA: You will be able to draw a GANTT chart from an activity network

RESOURCES NEEDED: A4 Graph Paper for each student

LESSON: Look at GANTT Charts From This Mymaths Lesson Screen 6 onwards

Work through to end of The Lesson then try Ex 5F page 103. Before end of lesson ensure we have looked at Example 12 on Page 104.

You should now be able to answer all questions in Ex 5G

HOMEWORK: 5F and 5G completed for Next Friday.

Weds Oct 12th Simultaneous Equations - Substitution

LEARNING OBJECTIVE: To discover how to use an alternative method (Substitution) to solve a simultaneous equation problem

SUCCESS CRITERIA: You will be able to solve simultaneous equation problems using any method we have covered.

STARTER: Screen 5 from this MyMaths Lesson

LESSON: Video 1,

Example Solve x - y =12 and 3x + 2y = 46

Solve Ex 19L

Q7 2x + y = 4, and x – y = 5

Q 15 x – 5y = 15 and 3x – 7y = 17

Q1 page 425 (briefly looked at yesterday) solve on IWB

Work through Ex 19M page 425.

PLENARY: Checking answers – look at Q ?? From Practice Paper 2. Can you solve it now?

Fri Oct 7th – Critical Path Analysis-Continued – Forward / Backward Pass, Early and Late events

LEARNING OBJECTIVE: Discover how to find Eaeliest and Late times using forward and backward passes. Use this information to find the critical events.

SUCCESS CRITERIA: You will be able to find earliest and latest times at the completion of events and use this to find the critical events.

LESSON Use this Lesson to show how to make a forward pass to find earliest time sand a backward pass to find late times

You should now be able to answer all questions in ex 5C

Use this lesson to Determine Critical Activities and the critical path(s)

You should now be able to complete Ex 5D

This Weeks Homework Ex 5A,5B,5C and 5D

Weds OCT 5th – Critical Path Analysis

LEARNING OBJECTIVE: To Understand how to use networks to show the flow of activities within a project

SUCCESS CRITERIA: You Will. Understand and be able to use dependency diagrams and be able to represent related activies of a project as a connected network

KEYWORDS: Dependency Diagram, Dummies, Source Node, Sink Node (Tail Node), Forward Pass, Backward Pass, Early Event, Late Event

LESSON: Work through this Lesson with students, using last three screens as examples for students to work through.

Now use this lesson to show the use of Dummies, again use last three screens to give students lots of practice

Ex 4A can now be completed, first exercise towards this weeks homework.

Friday 30th Sep – Eulerian Trails and the Route Inspection Problem

LEARNING OBJECTIVE: To discover what the following terms mean –Eulerian, semi Eulerian and Traversable and solve problems like the 'The Chinese Postman Problem"

SUCCESS CRITERIA: You will be able to solve Chinese Postman Type Problems

LESSON: Discover what is meant by Traversable, Eulerian and Semi-Eulerian Using this Lesson

Exercise 4A

 

Chinese Postman Problem – Work thorugh this lesson, then this lesson

 

Exercise 4B to Complete

 

PLENARY: Checking answers to questions in class

Tues 27th Sep – Exam Revision – Indices and Standard Index Form

LEARNING OBJECTIVE: TO revise Indices Laws and Standard Index Form
SUCCESS CRITERIA: You will be able to answer indices and Standard Index form Exam questions

Practice Paper – unit 2 Higher - Set 1

STARTER:

Answer at least three of these algebra questions:

Expand and simplify the following

6 – 4(3X – 5)	(3X + 3)(5X – 4)	3(

Fri 23rd Sep – Dijkstra’s Algorithm

LEARNING OBVJECTIVE: TO Assimilate the steps in Dijkstra's algorithm and apply them to solve real life problems

SUCCESS CRITERIA: You will be able to use Dijkstra's algorithm to find solutions to 'Shortest Path' problems on Distance Network.

LESSON 1: Work through the first three screens of this Lesson. Use the printouts of screens 4, 5 6 and 7 to give students an opportunity to try applying the algorithm themselves step by step, using the onscreen verision as checks to their progress.

Use screen 8 to Summarise the first stages of using Dijkstr'a Algorithm

PLENARIES: Checking their progress with onscreen working of the problems set.

LESSON: 2

Work through the second stages of Dijkstra's algorithm, so we can find the route of the shortest path.

PLENARIES: Checking their progress with onscreen working of the problems set.

HOMEWORK: Ex 3b, 3c and 3d = Revision on First three chapters for test next Weds

Weds 21st Sep – Prim’s Algorithm and Dijkstra’s Algorithm

LEARNING OBJECTVIE: To apply Prims algorithm to find minimum spanning tree AND Dijkstra's algorithm for finding the shortest path between two vertices in a network.

SUCCES CRITERIA: You Will be able to apply both algorithms to networks to solve problems.

LESSON: PRIMS Algorithm 1, Prims Algorthim 2

Exercise 3B and 3C to be completed for Homework

PLENARY: Check on understanding of both ways of applying Prims Algorithm

Weds Sep 13th – Graphs and Networks

LEARNING OBJECTIVE: Understand Graph and network terminology, model a situation using a graph, understand how to represent a graph using a matrix. Be able to use Kruskals algorithm to find a minimum spanning tree.

SUCCES CRITERIA: You Should:

1. Know how networks and graphs can be used to create mathematical models
   
2. Know some basic knowledge of graph theory terminology
   
3. Know some special types of graphs
   
4. Understand how graphs and networks can be represented by matrices.
   
5. Understand what a minimum spanning tree is and use Kruskals algorithm to find one.
   

LESSON: Quickly take students through pages 26 to 35 of text book. Then in Friday's lesson and homework do Ex 2a and 2b.

If you need more explanations work through these MyMaths Lessons at Home

Intro to Graphs, Types of Graph
Defining Graphs, Modelling with Graphs

MyMthas Lesson on Kruskals Algorithm

Homework Ex 3A - using Kruskals Algorithm

Tues Sep 13th Data Collection methods

LEARNING OBJECTIVE: You are going to look at good questionnaire design

SUCCESS CRITERIA: You will understand how to avoid biased, embarrassing and leading questions when designing a questionnaire

STARTER: Arrange the numbers

LESSON: Work through the first two screens of this Mymaths Lesson

Now Try and work through these questions

PLENARY: Discussion on answers to questions and correct answers

Friday 9th Sep – Quick Sort Middle Item Algorithm, Binary Search and Bin Packing Algorithms

LEARNING OBJECTIVE: to discover and practice the following algorithms: Quick Sort Middle item, Binary Search, Bin Packing - First Fit, First Fit Decreasing and Full Bin

Success criteria: You will be able to apply all the algorithms efficiently .

Quick Sort middle Item

Binary Search

Bi Packing – First Fit, Bin Packing Full Bin

Bin Packing First Fit Decreasing

Homework Ex A,B,C D,E from Chapter 1

Hanson (and Sam?) Work through Q1 to 7 pages 77 and 78 of old D1 text Book

Weds Sep 7th – Check on Chapter 1 of D1

Learning
Objective: To ensure summer holiday preparation has been completed for Chapter 1 – Algorithms from module D1

SUCCESS
Criteria: You will be able to answer exam style questions on Sorting Algorithms, Bin Packing Algorithms and binary Search Algorithms

STARTER: Logon to Laptop, discuss Algorithms Chapter from D1 and AS results

LESSON: Complete all MyMaths homework tasks and / or Questions 1 to 7 from review exercises pages 77 – 79

If any Students NOT completed work over summer they have an opportunity in this weeks lessons to 'catch up'

PLENARY: Discussion on 'where students are' Plan of work for next two weeks to ensure both Chapter 1 and Chapter 2 are completed by September 23^rd.

Fri 8th July – Revision of Chapters 1,3 & 4 – Periods 2 & 3

Fri 8th July – Revision of Chapters 1,3 & 4 – Periods 2 & 3

Laptops are booked for these two lessons and will be in Maths Room 1 waiting. Please leave them in Maths Room 1 at the end of the lesson after students have replaced them all tidily.

LEARNING OBJECTIVE: You will use the skills and knowledge learned over the last month to complete online tasks

SUCCESS CRITERIA: You will gain 80% plus in all 7 online tasks

LESSON: Collect a laptop and logon to Mymaths where I have set 7 online tasks covering the work we have done in Chapters 1,3 & 4.

If you do not get 80% plus (A green traffic Light) you must repeat the task until you do.

Should there be any issues using laptops then complete the list of exercises below:

Chapter 1 – Mixed Exercise page 10 & 11 Ex 1E

Chapter 3 Mixed Exercises page 41 – 43 Ex 3C

Chapter 4 Mixed Exercise page55 – 57 Ex 4Cin the time allocated start working

Should you complete all that within the time start working on the review exercise on pages 58 – 62, which review the whole first half of the C3 course

PLENARY: The online tasks give feedback regards correct answers whenever a student clicks on the 'mark' button or moves onto another page of tasks.

Weds 6th – Revision of Chapters 1,3 & 4 – Periods 2

Weds 6^th July – Revision of Chapters 1,3 & 4 – Periods 2

Laptops are booked for this lesson and will be in Maths Room 1 waiting. Please leave them in Maths Room 1 at the end of the lesson after students have replaced them all tidily.

LEARNING OBJECTIVE: You will use the skills and knowledge learned over the last month to complete online tasks

SUCCESS CRITERIA: You will gain 80% plus in all 7 online tasks

LESSON: Collect a laptop and logon to Mymaths where I have set 7 online tasks covering the work we have done in Chapters 1,3 & 4.

If you do not get 80% plus (A green traffic Light) you must repeat the task until you do.

Should there be any issues using laptops then complete the list of exercises below:

Chapter 1 – Mixed Exercise page 10 & 11 Ex 1E

Chapter 3 Mixed Exercises page 41 – 43 Ex 3C

Chapter 4 Mixed Exercise page55 – 57 Ex 4Cin the time allocated start working

Should you complete all that within the time start working on the review exercise on pages 58 – 62, which review the whole first half of the C3 course

PLENARY: The online tasks give feedback regards correct answers whenever a student clicks on the 'mark' button or moves onto another page of tasks.

Weds 29th June – Revision of Chapters 1, 3 & 4

LEARNING OBJECTIVE: You will use the skills and knowledge learned over the last month to solve problems

SUCCESS CRITERIA: You will be able to answer all Questions in Mixed exercises in Chap 1,3 & 4

In The last few lessons of this term (6 Lessons in total) you have to complete the following

Chapter 1 – Mixed Exercise page 10 & 11 Ex 1E

Chapter 3 Mixed Exercises page 41 – 43 Ex 3C

Chapter 4 Mixed Exercise page55 – 57 Ex 4Cin the time allocated start working

Plus all Mymaths Homework tasks I have set.

Should you complete all that within the time start working on the review exercise on pages 58 – 62, which review the whole first half of the C3 course.

Fri June 24th – Numerical Methods –Finding roots of an equation using an iterative procedure

LEARNING OBJECTIVE: You will discover how rearranging a function can lead to an iterative formulae that can be used to quickly find the value of the root of an equation

SUCCESS CRITERIA: You will be able to state that a root of an equation lies between two values and also determine an iterative formula that will lead to a solution of an equation to a particular accuracy

STARTER: You have 15 mins to have a go at question 1 from ex 4A page 48 (Ex 4A to be completed by Next Wednesday. Show how to use Excel to build formulae and list solutions rapidly

LESSON: Work slowly through this MyMaths Lesson (leave the last screen for the plenary at the end of the second lesson.

After working on the iWB together using the MyMaths lesson and practicing putting iterative formulae into your calculator start working through Ex 4B (4B to be completed by Friday of Next Week (You will have to leave it with Mr Nathan For Me)

PLENARY: Have a look at the exam type question (Last Screen) from the MyMaths Lesson

Weds June 22nd – More work on Exponential Function

LEARNING OBJECTIVE: To Consolidate work on Exponential functions and graphs of exponential functions

SUCCESS CRITERIA: You will be able to solve problems using exponential functions and sketch and interpret graphs of exponential functions

LESSON: A chance to go through any issues from Fridays lesson and Homework set so far.

Give students an opportunity to work on Ex 3B with support

REMINDER THAT EX 1D, 3a and 3B are to be completed by Friday of this week.

In Second Half of lesson look at this MyMthas lesson (screens 1,2 & 3 only), developing a method for determining whereabouts the roots of an equation are.

If time have a go at Ex 4A q1

PLENARY: Working on Questions from Screen and support around room checking answers.

Testing E-mail to Blog

This is a test message

Mr Speight

This message has been processed by MIMESweeper for Exchange.

 

Friday Jun 17th – The inverse of The exponential function

LESSON OBJECTVIE: To Develop the ideas of e^x having an inverse function

SUCCESS CRITERIA: You will be able to solve equations using the fact that ln x is the inverse of e^x and sketch and recognise transformations of f(x) = ln x

1. Review Remainder theorem when divisor is a quadratic – Use ex 1d – parts e, & f
   
2. Give them time to work through es 3A page 35/36
   
3. Revision of Rules of Logs using Mymaths Lesson Screens 5 & 6
   
4. Intro to Log_e as the inverse of e^{x –} Use geobra Webstart to plot functions on screen
   
5. Work through Mymaths Lesson really slowly to introduce Ln function
   
6. If time start working on Ex 3B
   

    
    

  

Friday Jun 17th – The inverse of The exponential function

LESSON OBJECTVIE: To Develop the ideas of e^x having an inverse function

SUCCESS CRITERIA: You will be able to solve equations using the fact that ln x is the inverse of e^x and sketch and recognise transformations of f(x) = ln x

1. Review Remainder theoreom when divisor is a quadratic – Use ex 1d – parts e, & f
   
2. Give them time to work through es 3A page 35/36
   
3. Revision of Rules of Logs using Mymaths Lesson Screens 5 & 6
   
4. Intro to Log_e as the inverse of e^{x –} Use geobra Webstart to plot functions on screen
   
5. Work thorugh Mymthas Lesson really slowly to
   

    

Functions

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Weds 15th June – Introduction to exponential functions and “the exponential function”

LEARNING OBJECTIVE: TO understand what is meant by an exponential function and the exponential function

SUCCESS CRITERIA: You will be able to sketch simple transformations of the graph of y =e^x

LESSON: First go over division by a quadratic, cubic, quartic etc... and explain why the remainder could be a linear, quadratic cubic – to sort out the confusion from Fridays Lesson

Encourage a revisit to Ex 1D if not completed using the remainder theorem method.

Use this MyMthas Lesson on the Exponential function

Have a go at Ex 3A on page 35

Friday 10th June (Double Lesson) Adding / Subtracting Algebraic Fractions and turning Improper Algebraic Fractions into Mixed algebraic Fractions

LESSON OBJECTIVE: Discover methods to add & Subtract Algebraic Fractions and convert improper algebraic fractions into mixed algebraic fractions into

SUCCESS CRITERIA: You will be able to add/subtract algebraic fractions and use the factor theorem to convert improper algebraic fractions into mixed algebraic fractions

LESSON: Adding and Subtracting Algebraic Fractions lesson, using exercise screens to practise skills. Then have some time to start working thorugh Ex 1C on page 7

Numbers – Improper fractions to Mixed Numbers

Algebraic Fractions are improper when the numerator has a larger degree than the numerator (ie there is a bigger power on the top than the bottom)

Two Methods – Long Division and Use of the remainder theorem

The Remainder Theorem states that for any polynomial F(x) you can find Q(x) such that

F(x) = Q(x) x divisor + remainder

Example 1

Divide x³ + x² – 7 by x – 3 first by long division and then by Factor theorem

Example 2 Turn the following improper algebraic fraction into a mixed algebraic fraction again using both methods:

(X⁴ + x³ + x – 10) / (x² + 2x – 3)

Have a go at Ex 1D you must practice both methods

Weds June 8th – C3 Start – Algebraic Fractions

LEARNING OBJECTIVE: To develop skills in adding, subtracting, multiplying and dividing algebraic fractions

SUCCESS CRITERIA: You will be able to four all four operations with algebraic fractions

STARTER: Can you complete all of Ex 1A on Page 3 and All of Ex 1B on page5&6 in 15 mins

LESSON: Adding and Subtracting Algebraic Fractions lesson, Cancelling Fractions Lesson, Multiplying Algebraic Fractions Lesson

Ex 1c on page 7 (to be completed for Homework by Next week

PLENARY: Checking answers, feedback on confidence so far.

June 7th 2011 – Your Maths Lesson Blog

When you first view this lesson blog, save the URL in your favourites so that you can quickly return.

Mr Sp8