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LEAVING CERT ALGEBRA

LEAVING CERT ALGEBRA. SUMMARY OF THE SECTIONS IN L.C. ALGEBRA. 1. SIMPLIFY. Squaring Rule. Division in Algebra. Surds. Common (grouping). Quadratic. 2. FACTORS. Difference of two squares. Sum and difference of two cubes. Linear. Quadratic. Cubic. 3. FUNCTIONS AND EQUATIONS.

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LEAVING CERT ALGEBRA

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

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

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

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

  5. SECTION 1 SIMPLIFYING

  6. Calculator

  7. Calculator

  8. x ( x + y ) + y ( x + y )

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

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

  11. SECTION 2 FACTORS

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

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

  14. Method 2 Using Quadratic Formula Method 1 Using Factors

  15. Method 1 Using Factors Method 2 Using Quadratic Formula

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

  17. Method 1 Method 2

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

  19. - + £ 3 x 6 9 - £ - 3 x 9 6 - £ 3 x 3 Change signs The inequality symbol is also a sign. ³ 3x -3 ³ x -1 - 4 0 - 2 - 1 - 3 2 3 4 1 5 SECTION 5 INEQUALITIES

  20. Split up into two bits. - 4 0 - 2 - 1 - 3 2 3 4 1 5

  21. 2. (a) Find the value of 3(2p – q) when p = -4 and q = 5 2. (a) Find the value of 3(2p – q) when p = -4 and q = 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

  22. common denominator = Method: Get a common denominator

  23. Method: Use previous answer and cancel

  24. Method: Use previous answer and solve

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

  26. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 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 =

  27. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 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

  28. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

  29. 2006 Paper 1: Question 2

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

  31. 2006 Paper 1: Question 3

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