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LEAVING CERT ALGEBRA

This summary covers key sections in Leaving Cert Algebra, including simplifying rules, factorization, functions, equations, and inequalities. Learn methods for simplifying, multiplying surds, and solving simultaneous equations with two unknowns. Understand indices, quadratics, and expressions in terms of variables. Examples provided for easy comprehension.

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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. Method 3 Method 1 Method 2 SECTION 1 SIMPLIFYING

  6. Calculator

  7. Calculator

  8. 1st 2nd Method 1 Method 2 Square the 1st. Square the 2nd . Twice the 1st by the 2nd Square the 1st. Square the 2nd . Twice the 1st by the 2nd

  9. 1st 2nd Square the 1st. Square the 2nd . Twice the 1st by the 2nd Square the 1st. Square the 2nd . Twice the 1st by the 2nd

  10. 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 .

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

  12. Method 1 Method 2

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

  14. - + £ 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

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

  16. SECTION 6 INDICES

  17. Leaving cert question What does this mean ? Are there any other ways of saying it or understanding it ? ’04, LCO, Paper 1

  18. ’04, LCO, Paper 1

  19. Work done so far ? Part (i) Part (ii) Multiply across by 2 ’04, LCO, Paper 1

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