1. LEAVING CERT ALGEBRA SUMMARY OF THE SECTIONS IN L.C. ALGEBRA NOTES
1. SIMPLIFY
Squaring Rule
Division in Algebra
Surds

2. NOTES
Common (grouping)
Quadratic
2. FACTORS
Difference of two squares
Sum and difference of two cubes

3. NOTES
Linear
Quadratic
Cubic
3. FUNCTIONS AND EQUATIONS
2 unknowns
Simultaneous
Non-linear
Express in terms of

4. NOTES Linear 5. INEQUALITIES Quadratic from Graphs 6. INDICES Single
Double
Linear
5. INEQUALITIES
Quadratic from Graphs
6. INDICES

5. SECTION 1 SIMPLIFYING

6. NOTES

8. Calculator

9. Calculator

10. x ( x + y ) + y ( x + y )

11. When simplifying surds we use the following :1.
Example:
Example: 2.
Example: 3.
Only like surds can be added or subtracted. 4.
Example:
Example:
5. Multiplying surds
Example: .
Example:

12. Example:
Irrational Denominator
6. Irrational Denominator
Rational Denominator
Example:
Irrational Denominator
Rational Denominator

14. SECTION 2 FACTORS

15. Method 1 Brackets
Method 2 Big X
Method 3 Guide Number

16. Method 1 Brackets
Method 2 Big X
Method 3 Guide Number

18. Method 1 Using Factors
Method 2 Using Quadratic Formula

19. Method 1 Using Factors
Method 2 Using Quadratic Formula

20. Method 1 Using Factors
Method 3 Using Quadratic Formula
Method 2 Using 

21. Method 2
Method 1

23. This rearranging is often called
“changing the subject of the formula” or “express in terms of ”.

25. SECTION 5 INEQUALITIES -1 x -3 3x sign. a also is symbol inequality
The
signs 3 6 9 - +
Change 1
- 2
- 1
- 3
- 4 2 3 4 5

26. bits.
two
into up
Split 1
- 2
- 1
- 3
- 4 2 3 4 5

27. 2. (a) Find the value of 3(2p – q) when p = -4 and q = 5
3(2(-4) – 5)
3( -8 -5)
3(-13)
Value is -39
’04, LCO, Paper 1

28. Method: Get a common denominator

29. Method: Use previous answer and cancel

30. Method: Use previous answer and solve

31. Method: Isolate x
Step 1: Take b from both sides
Step 2: Divide both sides by a

32. Method: Solve the inequality and then select all appropriate integers for the set
Remember the set of integers Z contains all positive and negative whole numbers and zero.
A = 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 8 -6 -7 -8

33. Multiply both sides by 2
Take 1 from both sides
Divide both sides by 3
Multiply both sides by -1
Remember this will change the direction of the inequality
List the solution set
Or show the solution set on the number line 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 8 -6 -7 -8

34. 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 8 -6 -7 -8

35. 2006 Paper 1: Question 2

36. Solve simultaneously between Equation 1 and Equation 2 to find the values of a and b

37. 2006 Paper 1: Question 3