Graphs of sin x and cos x - harder transformations

Graphing something like y = sin (2x + 30)

Practice questions:

http://www.examsolutions.net/maths-revision/core-maths/trigonometry/transformation%20graphs/exam-questions/Edexcel/C2/questions.php

Graphs of sin x and cos x - easier transformations

How to sketch the graphs of 
 y = sin x
y = sin 3x
y = 1 + sin 3x
etc. 

Practice questions:

http://www.myimaths.com/tasks/library/alevel/lib/loadTask.asp?title=alevel/core2/trigIntro/Trigintro5TransformOH&taskID=2049

Examsolutions practice questions: area of curves

http://www.examsolutions.net/maths-revision/core-maths/integration/applications/area/exam-questions/Edexcel/C2/questions.php

Area between two curves

To find the area between two curves:

   subtract the two equations, 

   then integrate. 

   khalaas. 

Practice Questions:

http://www.myimaths.com/tasks/library/alevel/lib/loadTask.asp?title=alevel/core2/Integration/integration5LinesOH&taskID=2058

 

Integrating to find area under a graph

How to use integration to find the area under a curve. 

Special notes:  

- Sometimes integration gives a negative answer, so ignore the negative.  

- Areas below the x-axis should be done separately to areas above the x-axis

- For more complex questions, use a two-step technique to take away the area under the curve from the whole shape.

Practice Questions:

http://www.myimaths.com/tasks/library/alevel/lib/loadTask.asp?title=alevel/core2/Integration/integration4AreaNegOH&taskID=2057

Integrating Harder Expressions

If an equation has brackets, you need to expand the brackets first before you integrate.  

Question:  Integrate  (1 + e^½x)(1 – e^½x)

Area under a graph using integration

To find the area under a graph we integrate the equation. 

Example Question:  Find the area under the curve between 1 and 4. 

(video to follow)

Practice Questions:

http://www.myimaths.com/tasks/library/alevel/lib/loadTask.asp?title=alevel/core2/Integration/integration3AreaOH&taskID=2056

Solving modulus equations / Harder graphs of the modulus function

How to solve an equation that has modulus in it. 

Question:  Solve  │2x + 7│= 9

How to draw graphs of modulus functions eg. y = │2x + 3│  - 1

Modulus Function

│-5│ is equal to 5 because we ignore the minus sign. 

How to sketch the graph of   y =│3x - 2│

Practice questions:  

http://www.myimaths.com/tasks/library/alevel/lib/loadLesson.asp?title=alevel/core3/Functions/functions4Modulus&taskID=2141

http://www.myimaths.com/tasks/library/alevel/lib/loadTask.asp?title=alevel/core3/Functions/functions4ModulusOH&taskID=2141