1. C4 Hexagon Topics What is Esmee up to?

2. Our C4 Hexagon Esmee is just about to complete her last A Level maths topics. Here they are: Esmee is just about to complete her last A Level maths topics. Here they are: Partial fractions Coordinate Geometry Binomial Expansion Differentiation Integration Vectors

3. The C4 Mind map Click here Click here

4. A nice recap of our primary years Esmee’s younger brother Ernest is in P5. He is a maths genius and can easily add the following fractions: Esmee’s younger brother Ernest is in P5. He is a maths genius and can easily add the following fractions: His teacher has given him a challenge to add algebraic fractions together: His teacher has given him a challenge to add algebraic fractions together:

5. Ernest’s challenge questions

6. How would we work backwards?

7. Partial fractions Linear factors Linear factors The cover up method The cover up method

8. The cover up method How do we find the values of a and b?

9. Another example proving our theory:

10. Last one: Express the following fraction as the sum/difference of three fractions. In other words express as partial fractions.

11. “I like pictures!” says Ernest Ernest is a visual learner and learns best when given a pictorial representation of mathematical concepts. Ernest is a visual learner and learns best when given a pictorial representation of mathematical concepts. Click on this applet to see the graphs of partial fractions: Click on this applet to see the graphs of partial fractions:

12. Your investigation Partial fractions Quadratic factors- is this really in our syllabus? Quadratic factors- is this really in our syllabus? Shall we do it? Shall we do it? Use mathsnet.net to investigate how to write an algebraic fraction with a quadratic factor in the denominator into partial fractions. Use mathsnet.net to investigate how to write an algebraic fraction with a quadratic factor in the denominator into partial fractions.

13. The steps

14. More steps

15. Quadratic factors in the denominator What is the rule? What are the steps? What is the rule? What are the steps? So if there is a quadratic factor in the denominator then the numerator of the partial fraction will be Ax+B. But remember factorize first if possible! So if there is a quadratic factor in the denominator then the numerator of the partial fraction will be Ax+B. But remember factorize first if possible! Example 1: Example 1:

16. Repeated Linear Factors Look at the graphical representation of repeated linear factors: Look at the graphical representation of repeated linear factors:

17. Partial fractions Repeated Linear Factors Repeated Linear Factors

18. So how do you work backwards?

19. Arthur

20. A quick quiz Five questions: Five questions: A true or false quiz A true or false quiz

21. What is an improper fraction? Give Ernest some examples of some improper fractions? Give Ernest some examples of some improper fractions? What about some examples of some algebraic improper fractions? What about some examples of some algebraic improper fractions?

22. Partial fractions Improper algebraic fractions Improper algebraic fractions Use the FAMILY division method Use the FAMILY division method Dad Dad Mum Mum Sister Sister Brother Brother

23. An example Split the following into partial fractions: Split the following into partial fractions:

24. Kelvin

25. Flow chart Make a flow chart of the steps you would take to split an algebraic fraction into partial fractions. Make a flow chart of the steps you would take to split an algebraic fraction into partial fractions.

26. The flow chart Is it an improper fraction? Are there only linear factors in the denominator? Is there a quadratic factor in the Denominator? Are there repeated linear factors in the Denominator?

27. Why do we want to find partial fractions? When we split a fraction to partial fractions it helps us to find the integral of the function using a standard result? What is this standard result? When we split a fraction to partial fractions it helps us to find the integral of the function using a standard result? What is this standard result? Why do we want to find the integral of a function? Why do we want to find the integral of a function?