# Project #30305 - Algebra 2

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STUDENT MANUAL ALGEBRA II / LESSON 10

Lesson 10

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Please complete the following cumulative assessment. Ask you instructor if you have any

questions during the test. Be sure to show all of your work.

Evaluate and simplify the following expressions. Show all your work.

1. 2(x + 6) – 4 + x

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2. (x +4) • 9

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3. y + 7 + 8 – 7(x -8)

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4. (4 – 5) + x(6 – 8)

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STUDENT MANUAL ALGEBRA II / LESSON 10

5. y(4 – 8) – 3y

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Solve the following expressions when x = 2, y = 3. Show all your work.

6. y(4 – 8) – 3y

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7. x + 8y – 16x(1- 3)

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Write the symbolic form of the written expressions given below. First write them in

written expression, and then with the appropriate order of operations, evaluate the

expression and simplify or solve. Show your work.

8. Three less than the product of thirteen squared and four.

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STUDENT MANUAL ALGEBRA II / LESSON 10

9. The product of eight minus six and x.

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10. The square root of thirty-six plus the sum of eight and four squared.

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11. Nineteen less than the product of seven and four minus the quotient of sixteen and

four.

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Now, on your own, multiply and divide and simplify the following exponential

12. 62 • 67 • 66 =

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13. xy6 ÷ y5 =

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STUDENT MANUAL ALGEBRA II / LESSON 10

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14. 8x8 ÷ x5 =

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15. 3y6 ÷ y5 =

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16. z10xy ÷ z5 =

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17. (n5 • n7 ) + (x8 ÷ x5) =

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18. (53 • 52 ) - (88 ÷ 86) =

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STUDENT MANUAL ALGEBRA II / LESSON 10

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Turn the following expressions in radical form into exponential expressions in

fractional form. You do not need to evaluate any of the expressions, just put them in

simplest form.

19. √144180 =

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20. w√xy + z =

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21. √354 =

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Turn the following expressions in radical form into exponential expressions in

rational form and then multiply and simplify the rational exponential expressions.

You do not need to evaluate any of the expressions, just put them in simplest form.

22. 3x√6 • 3x√69 =

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STUDENT MANUAL ALGEBRA II / LESSON 10

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23. √94y • √93x =

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Turn the following expressions in radical form into exponential expressions in

rational form and then multiply and simplify the rational exponential expressions

and then divide. You do not need to evaluate any of the expressions, just put them

in simplest form. Show all your work.

24. √57 • √56 ÷ 5√53 =

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25. √m p • √m4 ÷ √mn =

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First raise the powers of all variables and numbers indicated, and then turn the

following expressions in radical form into exponential expressions in rational form.

You do not need to evaluate or solve any of the expressions, just put them in

simplest exponential form. Show all your work.

26. 5√(x 3 )8 • x4 =

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STUDENT MANUAL ALGEBRA II / LESSON 10

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27. 5√5y • (54)3 =

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28. 9√ zy • (z4)2x =

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29. √(34)8 • 34=

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30. 3√ 94 • (92)3 =

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STUDENT MANUAL ALGEBRA II / LESSON 10b

Please complete the following cumulative assessment. Ask you instructor if you have any

questions during the test. Be sure to show all of your work.

Determine the degree of each polynomial listed.

31. 4x4 y3 + v y + 7

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32. 8n5 – 4n2 – x

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33. 134x10 y3 + x2 v y + 7

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STUDENT MANUAL ALGEBRA II / LESSON 10b

Determine the leading term, leading coefficient, and constant term of the polynomial

below.

34. 3645v15 v12 w10x8y6 z4 + 7

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Determine if the binomial is a perfect square binomial. If so, show the original

monomial squared.

35. x2+ 16

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36. x4 + 12x2+ 36

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Add the following polynomials by combining like terms, and place them into

simplest form.

37. (3xy2+ 6yx5 + 11yz9 + y + 87) + (13yx5 + 13xy2 + y + 10 + yx5)

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STUDENT MANUAL ALGEBRA II / LESSON 10b

38. (n2 + 4 + 4o3 + n) + (4 + n + 4m2n2 + 8n2) + (18 + 9m2n2 + 4o3 + 9n2)

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39. (12 +6s4t2 +s) + (10 + s + 6s4t2 + 8s2) + (21+ 6s4t2 + 7s4t2)

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Subtract the following polynomials. Be sure to place the polynomials in their

40. (m2 + 14 - 4o3 + m) - (14 + m + 14m2n2 + 8m2) - (14 + 14m2n2 - 4o3 + 4m2)

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STUDENT MANUAL ALGEBRA II / LESSON 10b

41. (21+ 14s4t2 - 7s4t2) - (t2 +5s4t2 +s) - (10 t2 - 6s4t2 + 7s2)

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42. (x - z9+ 2xy2) - (8z9 + 43xy2 - 16y + 10z9+ 3xy2) - (3yx5) - (13xy2 - 19y + 3z9)

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First square the binomial below, place it into perfect square trinomial form, and then

subtract the trinomials. Show all your work.

43. (7b2 - 7) 2 - (2b2 - 11) 2

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STUDENT MANUAL ALGEBRA II / LESSON 10b

Multiply the following polynomials. Be sure to place the polynomials in their

44. (4mo2 - 8n2) (16mo2 + 12mno2 – 5m)

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45. (- 3xy7 + y) (3 + 2z3 – 17)

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46. (3ab5 - 12ab3) (7a - 4ab2 – 18)

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STUDENT MANUAL ALGEBRA II / LESSON 10b

47. (3a + 15ab3) (5ab7 - 3ab2- 5)

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48. (5r + 6s4t2 - 4st2)(2st5 + 8s4t2 - 4st2)

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49. (5m2n2 + 5o3 + m)(5m2n2 + 5m2 + 5m)

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STUDENT MANUAL ALGEBRA II / LESSON 10b

Find the greatest common factor in the following polynomials. Show all your work.

50. 4mn7o2 + 8n2o+ 16mn3o2 + 12mn3o2 – 20mn2 o

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51. - 3xy7z + xyz3 + 2xyz3 + z

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52. 2ab5 - 12ab3 + 4ab2 + 18 b2

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53. 3ab5 + 15ab3 + 5ab2 - 3ab2- 5b

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STUDENT MANUAL ALGEBRA II / LESSON 10b

Divide the following polynomials by the monomials listed. Show all your work.

54. 20yx7 + 10xyz6 + xy4 + 30xy2 ÷ 2xy

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55. 4mn7o2 - 16mn3o2 + 12mn3o + 8mn2o ÷ 4mn2 o

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56. - 3xy7z + xyz3 + 2xyz ÷ yz

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STUDENT MANUAL ALGEBRA II / LESSON 10b

57. 84ab5 - 12ab3 + 4ab2 + 18b2 ÷2b2

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Use the long division method to divide the following polynomials. Show all your

multiplication of the two polynomials, and then rewrite the original division problem

as a multiplication problem with the solution.

58. (4a2 + 22a - 12) ÷ (a + 6)

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29. (x3 + 4x3 + x -6) ÷ (x + 2)

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STUDENT MANUAL ALGEBRA II / LESSON 10b

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30. (6b3 – 24b -6b2 + 24) ÷ (b2 - 4)

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 Subject Mathematics Due By (Pacific Time) 05/10/2014 12:00 am
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