The document discusses partial fraction decomposition and the cover-up rule. It explains that the cover-up rule can be used as a shortcut to substitution when decomposing algebraic fractions. It also notes that the faster method of comparing like terms should be used when possible to find the coefficients in a partial fraction decomposition.

1. DHS H2 MATHEMATICS : a revision package NEXT

2. NEXT

3. NEXT

4. NEXT

5. NEXT

7. Note that x 2 is a repeated linear factor (i.e. x repeated twice) NEXT

8. We want to find what values are A, B and C. NEXT

9. NEXT COVER-UP RULE COMPARING SUBSTITUTION

10. NEXT COVER-UP RULE COMPARING SUBSTITUTION

11. NEXT If you are quick, skip this step and go to the next step (i.e. equate the numerators)... COVER-UP RULE COMPARING SUBSTITUTION

12. NEXT COVER-UP RULE COMPARING SUBSTITUTION

13. It is actually faster here to compare like terms in x to find B and C . So always try to use the faster method. NEXT This makes B disappear, leaving only C . COVER-UP RULE COMPARING SUBSTITUTION

14. NEXT To check whether your partial fractions are correct, "combine" back the partial fractions on the RHS to see if you could obtain the algebraic fraction on the LHS. COVER-UP RULE COMPARING SUBSTITUTION

15. NEXT COVER-UP RULE rewind COMPARING SUBSTITUTION

16. NEXT The cover-up rule is actually a shortcut for substituting values of x. Can you see out why? COVER-UP RULE rewind COMPARING SUBSTITUTION

17. Click on correct answer to proceed COVER-UP RULE rewind COMPARING SUBSTITUTION

18. Yes, this is the correct answer! NEXT COVER-UP RULE rewind COMPARING SUBSTITUTION

19.   NEXT not fully factorised fully factorised

20.  degree 3  degree 1  degree 1  degree 1  II NEXT

21. NEXT

22. proper fraction now improper fraction (deg of numerator > deg of denominator) NEXT LONG DIVISION SPLITTING NUMERATOR

23. "introduce" denominator in the numerator improper fraction (deg of numerator = deg of denominator) split the numerator to create proper fraction NEXT LONG DIVISION SPLITTING NUMERATOR

24. Click on correct answer to proceed A, B B, C B, D C, D

25. Bingo! NEXT A, B B, C B, D C, D