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

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

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

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

SECTION 1 SIMPLIFYING

NOTES

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x ( x + y ) + y ( x + y )

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:

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

SECTION 2 FACTORS

Method 1 Brackets Method 2 Big X Method 3 Guide Number

Method 1 Brackets Method 2 Big X Method 3 Guide Number

Method 1 Using Factors Method 2 Using Quadratic Formula

Method 1 Using Factors Method 2 Using Quadratic Formula

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

Method 2 Method 1

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

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

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

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

Method: Get a common denominator

Method: Use previous answer and cancel

Method: Use previous answer and solve

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

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

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

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

2006 Paper 1: Question 2

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

2006 Paper 1: Question 3