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9 March 2011

9 March 2011. Algebra 2. Algebraic Operations 3/9. Terms are considered “like” if they have the same variable AND the same powers on the variable. Like Terms. Mathematics.XEI.303: (16-19) Combine like terms. Algebraic Operations 3/9.

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9 March 2011

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  1. 9 March 2011 Algebra 2

  2. Algebraic Operations 3/9 Terms are considered “like” if they have the same variable AND the same powers on the variable. • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  3. Algebraic Operations 3/9 Terms are considered “like” if they have the same variable AND the same powers on the variable. Example: x2, 2x, 5x3, 8x2 Only x2, 8x2 are like terms • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  4. Which of the following are like terms? • 2x and2x2 • 3x and 3 • 4x2 and 4x3 • 5x3 and 8x3 • x and xy 60 0 of 30

  5. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  6. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. Example: 2xy + xy + 5xy = ? • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  7. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. Example: 2xy + xy + 5xy = ? 2 + 1 + 5 = 8 • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  8. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. Example: 2xy + xy + 5xy = ? 2 + 1 + 5 = 8, so 2xy + xy + 5xy = 8xy • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  9. 2a3 + a2 + a + 3a – 4a3 = ? • a9 • 2a7 - 4a3 • 2a3 + a2 + 4a • -2a3 + a2 + 4a 60 0 of 30

  10. 2a3 + a2 + a + 3a – 4a3 = ? 2a3 + a2+ a+ 3a – 4a3= ? Combine like terms -2a3+ a2+ 4a

  11. Like Terms: • Choose any 10 questions from the first 15 • Write the question #, show your work, and write the letter answer choice on your sheet • You have 10 minutes.

  12. 0 0 6 0 0 0 1 8 7 5 4 4 3 2 1 5 4 9 9 6 9 0 8 7 6 5 4 3 2 1 0 3 9 8 7 5 2 0 1 0 9 8 7 6 5 4 3 2 1 0 2 1 9 8 7 3 6 4 5 3 2 1 0 9 8 7 5 4 3 2 1 0 0 6 Time Left Hours Minutes Seconds

  13. Algebraic Operations 3/9 You can multiply or divide the same variable, even if the powers are different. • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  14. Algebraic Operations 3/9 You can multiply or divide the same variable, even if the powers are different. Multiplication: Add exponents Division: Subtract exponents Example: (x2)(x3)(x5)(x7) = ? • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  15. Algebraic Operations 3/9 Example: (x2)(x3)(x5)(x7) = ? • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  16. Algebraic Operations 3/9 Example: (x2)(x3)(x5)(x7) = ? Add all the exponents on ‘x’ 2 + 3 + 5 + 7 = 17 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  17. Algebraic Operations 3/9 Example: (x2)(x3)(x5)(x7) = ? Add all the exponents on ‘x’ 2 + 3 + 5 + 7 = 17 (x2)(x3)(x5)(x7) = x17 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  18. Algebraic Operations 3/9 Example 2: • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  19. Algebraic Operations 3/9 Example 2: Larger x is on top, subtract the bottom power from the top power: • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  20. Algebraic Operations 3/9 Example 2: Larger x is on top, subtract the bottom power from the top power: Larger y is on bottom, subtract the top power from the bottom power: • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  21. (xy2)(x3y2) = ? • x3y4 • x2y • x4y4 • xy7 • xy8 60 0 of 30

  22. (xy2)(x3y2) = ? • (xy2)(x3y2) = ? x4

  23. (xy2)(x3y2) = ? • (xy2)(x3y2) = ? x4y4

  24. Algebraic Operations 3/9 If you are raising a variable with an exponent, multiply the powers. Example: (a3)4 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  25. Algebraic Operations 3/9 If you are raising a variable with an exponent, multiply the powers. Example: (a3)4 3*4 = 12 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  26. Algebraic Operations 3/9 If you are raising a variable with an exponent, multiply the powers. Example: (a3)4 3*4 = 12 (a3)4 = a12 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  27. Exponent Rules: • Complete ten questions out of # 16-30 • Write the question #, show your work, and write the letter answer choice on your sheet • You have 10 minutes.

  28. 0 1 9 0 0 0 5 3 8 6 5 4 3 2 1 7 0 9 5 1 8 7 6 5 4 3 2 3 0 4 9 8 7 6 5 4 4 2 3 9 8 7 6 5 4 2 7 1 0 2 1 9 8 6 1 5 0 0 3 2 1 0 4 8 9 6 5 4 3 2 1 0 7 Time Left: Hours Minutes Seconds

  29. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  30. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: Add the numerators together. • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  31. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: Add the numerators together. 4 + 6 = 10 • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  32. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: Add the numerators together. 4 + 6 = 10 • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  33. . • 7x/6 • 7x/3 • 10x/9 • 10x/6 • 10x/3 60 0 of 30

  34. Algebraic Operations 3/9 If you are adding two fractions with a different denominator: • Adding Fractions Mathematics.NCP.501: (24-27) Find and use the least common multiple

  35. Algebraic Operations 3/9 If you are adding two fractions with a different denominator: Multiply the denominators: • Adding Fractions Mathematics.NCP.501: (24-27) Find and use the least common multiple

  36. Algebraic Operations 3/9 If you are adding two fractions with a different denominator: Cross Multiply • Adding Fractions Mathematics.NCP.501: (24-27) Find and use the least common multiple

  37. Adding Fractions: • Complete # 31-40 • Write the question #, show your work, and write the letter answer choice on your sheet • You have 10 minutes.

  38. 0 0 6 0 0 0 1 8 7 5 4 4 3 2 1 5 4 9 9 6 9 0 8 7 6 5 4 3 2 1 0 3 9 8 7 5 2 0 1 0 9 8 7 6 5 4 3 2 1 0 2 1 9 8 7 3 6 4 5 3 2 1 0 9 8 7 5 4 3 2 1 0 0 6 Time Left Hours Minutes Seconds

  39. Simplifying Expressions 3/8 Simplify 3(2q + r) Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions

  40. Simplifying Expressions 3/8 Simplify 3(2q + r) 6q + 3r + 20q – 35r Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions

  41. Simplifying Expressions 3/8 Simplify 3(2q + r) 6q + 3r + 20q – 35r Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions

  42. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Make a 2x2 square box Box Method XEI.405:Multiply 2 Binomials

  43. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Write the first binomial across the top x +4 Box Method XEI.405:Multiply 2 Binomials

  44. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Write the second binomial going down x +4 x -3 Box Method XEI.405:Multiply 2 Binomials

  45. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply x*x x +4 x x2 -3 Box Method XEI.405:Multiply 2 Binomials

  46. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply x*4 x +4 x x2 +4x -3 Box Method XEI.405:Multiply 2 Binomials

  47. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply -3*x x +4 x x2 +4x -3 -3x Box Method XEI.405:Multiply 2 Binomials

  48. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply -3*4 x +4 x x2 +4x -3 -3x -12 Box Method XEI.405:Multiply 2 Binomials

  49. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) List each term inside the box x +4 x x2 +4x -3 -3x -12 x2 + 4x – 3x - 12 Box Method XEI.405:Multiply 2 Binomials

  50. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Simplify x +4 x x2 +4x -3 -3x -12 x2 + 4x – 3x – 12 = x2 + x - 12 Box Method XEI.405:Multiply 2 Binomials

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