Tues Mar 26th -Solving Trig Equations

LEARNING OBJECTIVE: Discover how to solve complex trig equations, using knowledge og trig graphs
SUCCESS CRITERIA: You will be able to solve trig equations

LESSON: Work thorugh this lesson, then have a go at Ex 10B, then this lesson and have a go at Ex 10C

PLENARIES: Checking answers to onscreen questions, support of individuals / groups

Thurs - Mar 21st trig Identities

LEARNING OBJECTIVE: To Understand and be able to use trig identities to simplify and solve trig equations

SUCCESS CRITERIA: You will learn to use the identity sin²x + cos² x =1 and tan = sin/cos to help simplify and solve trig equations

LESSON: Work through The Mymaths Lesson Special Triangles and Identities, then have a go at the questions in Ex 10A

Tues 19th Mar - Using Trig graphs to find values and trig identities

LEARNING OBJECTIVE: Understand how to use the symmetry of trig graphs to find identities

SUCCESS CRITERIA: You will be able to solve trig equations and list trig identities

LESSON:  First Show how to use triangles to find exact answers for angles 30, 60, and 45 degrees

Students a to work through Ex 8B, 8C, 8D, 8E and 8F

PLENARIES: Supporting Students at their desks, Checking answers from back of text book

Weds 13thn using Partial fractions and Substitution March - Integration

LEARNING OBJECTIVE: Discover more techniques to aid integrating complex functions

SUCCESS CRITERIA: You will be able to integrate complex algebraic fractions using POartial Fractions and Substitution methods

LESSON:
Integration Using Partial Fractions -  Complete Ex 6d
Integrating using substitution
Harder Substitution - Complete 6F

Look at section 6.5 in text book and have a go at Ex 6E

Tues 12th Mar - How to use Trig graphs to work out sin,cos and Tan values greater than 90 and less than 0 and Transforming Trig Graphs

LEARNING OBJECTIVE: Discover how to use trig graphs to work out values of sin/cos/tan greater than 90 and less than 0. Also look at the results of transforming trig graphs.

SUCCESS CRITERIA: You will be able to find the sin/cos/tan of any angle, and use the graphs to find trig identities. You will also be able to sketch a trig graph after it has been transformed.

LESSON: USe theses Lesson to show how to use trig graphs to aid finding trig values.

Sin and Cosine Graphs
Tan Graphs
Transforming Trig Graphs

PLENARY: Checking answers, Encouraging participation with the IWB, support at students desks

Weds Mar 6th P3 & 4 - Integration of Trig Functions

LEARNING OBJECTIVE: Discover how to Integrate Sine, Cosine and other trig Functions and how to integrate some expressions using inspection (guesswork) techniques
Quick review of LAst weeks Work using These Lessons:
1. Integration of Sine and Cosine

2. Integration by Inspection
3. Integration of Exp(x) and 1/x


LESSON: Continue to develop Integration skills using these lessons

4. Integration of Trig Functions

Using this knowledge and the list of standard integrals on page 88 of text book (some of which are in Formula Booklet), have a go at Ex 6A page 89 and 6B on Page 92 and 6C on Page 94
 Give some time to work thorugh these exercises. If time look at Using Partial Fractions to help with Integration using this lesson 
5. Using Partial Fractions to help Integrate more Complex Functions

Fri1st/Tues 5th - The TRapezium Rule

LEARNING OBJECTIVE: TO Understand how to work out the area underneat a curve approximately using the trapezium rule

SUCCESS CRITERIA: You will be able to approximate the area under a curve using the trapezium rule

LESSON: Work thorugh this Mymthas Lesson

HOMEWORK: AFter worked though this lesson you should be able to solve all the questions in Ex 11E (Homework for Friday 8th March)

Tues 26th Feb -Review of C2 Differentiation Problems and Finding Area between two Curves

LEARNING OBJECTIVE: You will discover how to use integration to find the area between two curves

SUCCESS CRITERIA: You will be able to use integration techniques to find the area between two curves.

STARTER: YHomework record on IWB - Discussion, then use q5 from Ex 9b and q4 from Ex 9c to revise techniques and point out areas of weaknesses in student answers to homeworks.

Solutions must be presented in a way that is easy to follow, examiners WILL NOT look to find solutions in jumbled up responses.

LESSON: Use this lesson to show how to find the area between a line and a curve (No need to do area between two curves NOT in C2). Then look at Example 6 and Example 7 in text book

HOMEWORK: Ex  11D (For March 8th)

NB I will not be in lesson on Thursday, You must attend as a memebr of staff will be on cover and will take the register. Please use the time to work on this exercise (or the work that is due in for FRiday of this week - Exercises PLUS C1 Paper)

Wed 26th Feb C4 Integration

LEARNING OBJECTIVE: Discover how to Integrate Sine, Cosine and other trig Functions and how to integrate some expressions using inspection (guesswrok) techniques

LESSON: USe these lessons to develop integration skills
1. Integration of Sine and Cosine
2. Integration by Inspection
3. Integration of Exp(x) and 1/x
4. Integration of Trig Functions

Using this knowledge and the list of standard integrals on page 88 of text book (some of which are in Formula Booklet), have a go at Ex 6A page 89

Fri 15th Feb - Time to solve problems

Today STudents have a chance to practice all concepts and techniques taught during the week.

Thurs 14th Feb - Area under a curve & Negative Areas!

LEARNING OBJECTIVE: Consolidtae the notition of using INtegration to find the area under a curve and how to deal with negative areas.

SUCCESS CRITERIA: You willi be able to find the area under a curve using integration

LESSON: Consolidate Tuesdays Lesson using screen 7 Onwards from this lesson
Then work through This Lesson to show how to deal with areas under a cuirve when they are all or partial below the x - axis

HALF TERM HOMEWORK REMINDER: - Deadline is Feb 29th
From C1 EX 8C, 8D, 8E plus 8F Question 9
From C2 Ex 11A, 11B, 11C

PLUS Attempt  the C1 paper

Y13 - Weds 13th Feb - Using the binomial expansion for more complicated expressions and Fractions

LEARNING OBJECTIVES: Discover how the binomial expansion can help find approximate expansions for more complicated examples and fractions

SUCCESS CRITERIA: You will be able to utilise the binomial expansion to solve more comples problems

LESSON: USe this lesson to explore more difficult uses of the binomial expansion

PLENARIES: SUpport when having as go at on screen expansions, checking solutions

HOMEWORK: EX  3B,3C, 3D Plus 2 exam questoins (of your choice) from Ex 3D

Y12 - Tues 12th - Finding Particular Solutions

LEARNING OBJECTIVE: Discover how to find the particular solution when we know a point onf the given line.

SUCCESS CRITERIA: You will be able to solve a variety of problems when given a differential equation and a particular point on the line

LESSON: Revision of Integration and quick look at types of questions in Ex 8C and 8D.

Now work thorugh This Lesson

If time look at area under a curve via this lesson

PLENARIES: SUccess of on screen questionsm,support at desks, checking answers....

Fri 8th Feb - Introduction to Integration

LEARNING OBJECTIVE: To Discover how to undo differentiating by Integrating

SUCCESS CRITERIA: You will be able to write down the INdefinite Integral if you are given a differential equation

LESSON: Work thorugh this MYmaths Lesson, then have a go at Ex 8A and 8B in C1 text Book.

PLENARIES: Q&A of Students , contributions to lesson, answers to questions

Thurs 7th Feb - Applications of being able to find turning points using the second derivative

LEARNING OBJECTIVE: To consolidate understanding of how the second derivative can help in establishing what kind of turning point we have and practical examples of these techniques

SUCCESS CRITERIA: You will be able to establish turhing pints, describe whether they are max, min or inflexions and be able to use these techniques to solve real problems.

STARTER: Use Fooplot to explore the relationship betweeen a function its first and second derivative.

Now work thorugh this lesson to consolidate th4e use of the second derivative and its applications

PLENARY: Student feedback, answers to onscreen questions..

HOMEWORK: C2 Ex 9A, page 130/131,ex 9B and ex 9C

Year 13 - Imporoper Fractions to Partioal Fractions and

LEARNING OBJECTIVE: How to deal with an improper polynomial fraction. Using the binomial expansion to deal with fractional and negative powers

SUCCESS CRITERIA: You will be able to express an improper fraction as a quotient and partial fractions and you will be able use the binomial expansion ti deal with fractional and negative powers..

LESSON: Dealing with an Improper fraction, Using Binomial Expansino to deal with negative and fractional Indices
Ex 1E and 1F and 3A and 3B

Yr 12 - Increasing and decreasing functions, Finding Turning Points and Inflections

LEARNING OBJECTIVE: To Discover what is meant by and increasing function and a decreasing function and how to use the second derivative to find turning points and inflections.

SUCCESS CRITERIA: You will be able to find functions or sections of functions that are increasing (or decreasing) and also find maximum, minimum and inflections of  functions using second derivative and/or increasing/decreasing functions.

LESSON: Turning Points, Using Second Derivative

HOMEWORK: C2 Ex 9A, page 130/131,ex 9B and ex 9C

Yr 12 - Fri Feb 1st - Finding the rate of change of a functionat a particular point

LEARNING OBJECTIVE: DIscover how to use differentiation to solve problems where one variable changes with respect to another variable.
SUCCESS CRITERIA: You will be able to use differntiation to solve real life problems

FACTS:

• The rate of change of velocity with respect to time is known as acceleration
• The rate of change of displacement with respect to time is known as velocity

LESSON:

example: Given that volume of an expanding sphere is related to its radius by the equation V= 4/3 πr^{3, find the rate of change of the volume with respect to the radius at the instant where the radius = 5cm.}

<sup>Exam Question: Q 13 Page 131

Now work thorugh Ex 7G to be completed by Next Fri - 9th Feb</sup>

Yr 12 - Thur 31st Jan - Using Differentiation to find equatoins of Tangents and Normals to curves at specified points.

LEARNING OBJECTIVE: To discover how to use differentiation to and knowledge of tangents to find the equations of tangents and Normals to curves at specified points

SUCCESS CRITERIA: You will be able to work out the equation of Normals and tangents at specified point(s) on a curve

LESSON: Reminder on how to find the equation of a line on a curve if we know the coords of the point and the gradient at that point, using the formula y-y₁ = m(x - x1)
Use this Lesson to develop skills.

Complete exercise 7H for Homework by 9th Feb - Ex 7E and

7F already set.

YR 13 - Partial Fractions

LEARNING OBJECTIVE: DIscover how to solve partial Fractions
SUCCESS CRITERIA: You will be able to solve a partial Fractions Problem

STARTER: Two difficult adding Fractions additiona subtraction questions on the IWB

LESSON: Screens 7,8 & 9 from This Lesson.
 Then  work thorugh this Lesson.

If we do not get past Screen 5 then Ax 1A,1B and 1C are homework, If we get past screen 5 the add Ex 1D to homework list for Next Weds. (6th Feb)

Tue 29th Jan - More work on index notation and 2nd Differential

LEARNING OBJECTIVE: understand what is meant by the second order derivative

SUCCESS CRITERIA: You will be able to differentiate a function a second time to find the second order derivative

STARTER: Use A* GCSE Looop cards to practise work on index notation

LESSON: Show with some examples what is meant by the second order derivative, explaining the notation used.

Have a go at exercise 7E and 7F

PLEANRIES: Checking work, supporting students

y12 - Week beginning 21st January 2013

LEARNING OBJECTIVE: Discover what differentiation is and be able to prove it from 1st principles

SUCCESS CRITERIA: YOu wil understand what is meant by differentiation and be able to explain how to find it from first principles

LESSON: Work thorugh Thes two Lessons to Develop the ideas of Differentiation

Lesson 1 - First Principles
Lesson 2 - Differentiating Polynominals

Exercise 7B page - page 120

Week Beginning 7th January - Year 12 Lesons - Revision for Stats Paper

LEARNING OBJECTIVE: Work thorugh as Many S1 papers as possible

SUCCESS CRITERIA: You will gain your target grade in the paper or discover what are your main areas for revision.

LESSON: HAnd out S1 papers, mark papers already attempted, use Mixed exercises in chapters for targetted revision

PLENARIES: Marking papers, checking grades, discussion on areas to revise.

Week beginning 7th January - D1 revision

LEARNING OBJECTIVE: Work thorugh as Many D1 papers as possible

SUCCESS CRITERIA: You will gain your target grade in the paper or discover what are your main areas for revision.

LESSON: HAnd out D1 papers, mark papers already attempted, use Miced exercises in chapters for targetted revision

PLENARIES: Marking papers, checking grades, discussion on areas to revise.