Honors Algebra II Review of the Past

1. Honors Algebra II Review of the Past

2. add 20 to both sides 1.

3. 2. Subtract 15 from both sides

4. 3. subtract 12 from both sides multiply both sides by - 1 or just switch the signs on both sides How can I use my calculator to check equation?

5. 4. divide both side by 12

6. 5. multiply both sides by the reciprocal of Check using your calculator.

7. 6. multiply both sides by 6 Always ask yourself, “What’s Happening to the variable”, then undo the operation. In this problem c is being divided by 6, therefore multiply by 6. Don’t forget the “Golden Rule of Algebra”, what you do to one side of the equation you must do to the other side.

8. 7. add 7 to both sides divide both sides by 2

9. 8. CLT divide both sides by - 3

10. 9. distributive property CLT

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13. 12. CLT

14. 13. When you multiply with the same base, add exponents.

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18. 17. When you raise a power to a power, you multiply exponents.

19. 18. Don’t forget that the 6 is being raise to the third power and so is the x. Common mistake here is to multiply the 6 and 3 and say 18 instead of raising the 6 to the third power.

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26. 25. Use FOIL

27. 26. Multiply each term of one polynomial by each term of the other polynomial, and CLT.

28. 27. Always ask yourself, “what’s happening to the variable that I must solve?”, then undo.

29. 28. To get rid of fractions, multiply by a common denominator.

30. 29. Get all the variables that you are solving for on the same side of the = sign. Notice that to move a term to a different side of the = sign I slide it over and switch the sign.

31. 30. Restate the problem. To simplify square roots, look for perfect squares.

32. 31. Give a little CLT.

33. 32. To simplify square roots, look for perfect squares. CLT.

34. 33. Do you remember your laws of exponents? Subtract the iddy biddy from the biggy wiggy and put where the biggy wiggy is. Make up your own rules.

35. 34. Factor the numerator, factor the denominator, cancel common factors. What can’t x be?

36. 35. First rule of factoring is to factor out the greatest common factor. Second rule is to see if you can factor a quadratic into two binomials.

37. 36. Did you remember this factor pattern from Algebra I? It is the difference of two squares. They factor into two binomials. Just take the square root of both. You cannot factor the SUM of two squares over the set of real numbers.

38. 37. Restate the problem. FOIL. There is a way to do this in one step, if it is a binomial being squared. Square the 1st term, 2nd multiply the two terms together and double them (this is your middle term), 3rd square the last term.

39. 38. 1st rule look for a GCF. Since this is a quadratic equation and a trinomial, see if it will factor into 2 binomials. (Guess and Check is used frequently)

40. 39. Remember that we are factoring quadratic expressions, NOT solving quadratic equations.

41. 40. You can check your answers by FOIL.

42. 41. After you factored out the GCF, you had the difference of two squares, which factors into two binomials.

43. 42. Did you hit a pothole? There are two factors that a both the difference of two squares. This is not a quadratic equation, but it can be put in quadratic form.

44. 43. We are now solving a quadratic equation. To solve a quadratic equation, 1st set the equation = 0, 2nd factor completely, 3rd set each factor = to 0 and solve for the variable. Do you remember the quadratic formula? It’s on the wall.

45. 44. Is this getting easy?

46. 45. Factor the numerator, factor the denominator, cancel common factors. What can’t n be? Why?

47. 46. Same rules as the last problem. What can’t a be? Why?

48. 47. Multiplying fractions are easy. Do you remember your laws of exponents? Subtract the iddy biddy from the biggy wiggy and put where the biggy wiggy is. Make up your own rules.

49. 48. 2 You may leave your answer in factored form. What can’t x be?

50. There is no # 49!