This is the summer math packet if you are entering Algebra 3 Trig next year. I

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1 Summer Math Packets Rising Algebra 3 Trig Students Dear WCCS Students, This is the summer math packet if you are entering Algebra 3 Trig next year. I recommend you put this aside until August first and then start doing the review problems. This will refresh your memory right before you come back to school. This packet will be collected the first day back and graded and there will be a test over the material the first week of school. If you have questions about how to work the problems, google videos that you may find or ask a friend for help. If you are still confused me, and we can get together before school starts to figure out the problems. They should all be review but I know you learned some of the concepts a long time ago. This packet will be collected from each student the first day back and adequate work must be shown for problems as appropriate. Five points will be deducted for each day the assignment is not turned in to the math teacher. Have a wonderful summer! Denise Kendrick dkendrick@wccs.org Page 1

2 1. Classify the number 48 as rational or irrational. 2. Classify the number 29 as rational or irrational. 3. Classify the number as rational or irrational Classify the number 15 4 as rational or irrational. Page 2

3 5. Classify the real number as rational or irrational Approximate the number to three decimal places by rounding. 7. Simplify by using the order of operations Simplify by using the order of operations Simplify by using the order of operations. 8 (8 + 8) + 5 (5 4 2) 10. Simplify the following using the order of operations. 2x ( 7y) + 4z 11. Simplify. 92 ( 3)(2) 12. Expand. 10(6r 3s) 13. Add the fractions and simplify Subtract the fractions and simplify Multiply the fractions and reduce to lowest terms Divide the fractions and reduce to lowest terms. Page 3

4 Approximate the number to three decimal places by rounding 18. Simplify by using the order of operations. 2 ( 4 + 3) + 3 ( 4 2 2) 19. Subtract the fractions and simplify. 5s 9s Evaluate the algebraic expression for the specified values. x µ s for x = 380, µ = 140, s = Simplify r 4 r 7 using properties of exponents. Express in terms of positive exponents. Page 4

5 22. Simplify (4s 4 ) 2 using properties of exponents. Express in terms of positive exponents. 23. Simplify 8z 4 z Simplify (2e 3 f 8 ) 2 using properties of exponents. Express in terms of positive exponents. 25. Simplify (6hk ) 4 ( 3hk ) Express 22,800,000 in scientific notation. 27. Express in scientific notation 28. Write as a decimal. 29. Write as a decimal. 30. Simplify 4q 8 q 6 using properties of exponents. Express in terms of positive exponents. 32. Name the coefficient(s), variable(s), and degree of the monomial 5x Name the coefficient(s), variable(s), and degree of the monomial 4x 3 z Determine whether 6 is a polynomial or not. If it is, state the degree. Page 5

6 35. Determine whether 3x is a polynomial. If it is, state its degree. 36. Determine whether 4x 7 y 2 15 is a polynomial. If it is, state the degree. 37. Subtract the polynomials and express your answer as a single polynomial in standard form, 8z 9 2(z 9 10y + 4) 38. Add the polynomials and express your answer as a single polynomial in standard form. ( 5r 3 4sz 4 + 5y + 2) + ( 7r 3 8sz 4 7y + 3) 39. Subtract the polynomials and express your answer as a single polynomial in standard form. (6q 4 9ab x 5) ( 9q 4 + 6ab 10 9x + 3) 40. Multiply the monomial by the trinomial and express your answer as a single polynomial in standard form. 8m 6 (5m 8 10n 7 5) 41. Multiply the binomial by the trinomial and express your answer as a single polynomial in standard form. (6m 9)(4m 2 8m + 8) 42. Multiply the binomials using the FOIL method and express your answer as a single poylnomial in standard form. (x + 1)(x + 9) 43. Mulitply the binomials using the FOIL method and express your answer as a single polynomial in standard form. (z + 1)(z 3) 44. Multiply the binomials using the FOIL method and express your answer as a single polynomial in standard form. (r 8)(r 9) Page 6

7 45. Multiply the binomials using the FOIL method and express your answer as a single polynomial in standard form. (2s + 4)(3s 6) 46. Name the coefficient(s), variable(s), and degree of the monomial 5r 9 s Add the polynomials and express your answer as a single polynomial in standard form. (2x 9 + 2yx 9 + 3wx 2 3x) + (4x 9 12yx 9 + 5wx x) 48. Multiply the binomials using the FOIL method and espress your answer as a single polynomial in standard form. (7z + 3)(z + 8) 49. Factor the common terms out of the polynomial 35z Factor the common term out of the polynomial e 12 8e. 51. Factor the common term out of the polynomial 5x 9 15x. 52. Factor the common term out of the polynomial 2t 9 + 8t 8 10t Factor the polynomial completely x 2 + 2x Factor the binomial completely k 2 81 Page 7

8 55. Factor the trinomial completely. x 2 + 4xy 21y Factor 4b 6 16b 5 180b 4 into a product of three polynomials. 57. Factor r 3 25r into a product of three polynomials. 58. Factor the common term out of the polynomial 57t 3 57t t 59. Factor the binomial n 2 1 completely. 60. Factor d 3 64d into a product of three polynomials. 61 Graph the following equations. State the domain and range and label the type of function a. Y=3x-2 b. Y=-x+8 c. Y= xx 3 d. Y= xx e. Y= xx f. Y=logx-1 g. Y=x²-5x+5 h. Y=x³-7x+5 Page 8

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