Math 3 Cumulative Review Unit 1

Unit 1 Graph each of the following. 1a. 2 - 5 10

Name: ___________________________ Math 3 Cumulative Review

-3 + 2 2. { < 3 - 1

4

1b. Are points on the line 2 - 5 10 solutions for the inequality? Using a sentence or two, explain why or why not.

3. {- +

-

Find two solutions that work for all three inequalities.

4. Explain why a system of equations only has one solution while a system of inequalities has infinitely many solutions.

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5. Superbats Inc. Manufactures two different types of wood baseball bats, the Homer-Hitter and the Big Timber. The Homer-Hitter takes 5 hours to trim and turn on the lathe and 4 hours to finish. Each of the Homer-Hitter sold makes a profit of $19. The Big Timber takes 10 hours to trim and turn on the lathe and 6 hours to finish, and its profit is $34. The total time available for trimming and lathing is 140 hours. The total time for finishing is 90 hours. How many of each type should be produced in order to maximize their profit? What is the maximum profit?

Define your variables:

X=

Y=

Objective Function:

Constraints:

Graph the system:

Show ALL work to find maximum profit:

Final answer written in a full sentence: 2

Unit 2

Given the following sequences, determine whether it's arithmetic, geometric or neither. Then find the

next 3 terms.

6. -25, -34, -43, -52, ...

7. -2, 8, -32, 128, ...

8. -58, -39, -20, -1, ...

9.

5 , 9 , 13 , 17 , 21 , ...

34 5 6 7

Use the given equation to find the first 3 terms of the sequence.

10. = -3 + 8

11. = -1 4 1 = 3

Given the first 4 terms of the sequence, find the explicit formula and the recursive formula.

12. 22, 14, 6, -2, ...

13.

2 3

,

1,

3 2

,

9 4

,

287,

...

Write the explicit formula for the equation.

14. = -1 5 1 = -2

15. = -1 - 1.5 1 = 7

Write the recursive formula for the equation. 16. = -3 + 1.7

17. = -3(4)-1

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Use formulas for sequences and series to solve each of the following. Show ALL work for full credit. Write your final answer in a sentence. 18. Hector gets better and better at a video game every time he plays. He scores 20 points in the first game, 25 in the second, 30 in the third, and so on. How many points will he score in his 27th game? How many points total did he score?

Write your sentences here:

19. Samantha decides that she is going to save $500 of her paycheck each month. As hard as she tries, each month she only saves 80% of the previous month. What does she save on the 11th month? How much did she save total in those 11 months? How much would she save if she continued the pattern forever?

Write your sentence here:

Unit 3

Write the equation of a line parallel to each of the following. Show ALL work for full credit.

20. 7 + 3 = 33

21.

4

22. Parallel to = 3 + 1 through (-7, 4)

Write the equation of a line perpendicular to each of the following. Show ALL work for full credit.

23. = -2 + 13

24.

Find the missing angles given that a b, m1= ?, and m2= ?.

25. m3= _______ 28. m6= _______ 31. m9= _______

26. m4= _______ 29. m7= _______ 32. m10= _______

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27. m5= _______ 30. m8= _______

Use what you know about two parallel lines and a transversal to solve for x. Show ALL work for full credit.

33.

34.

(5 + 46)?

(11 - 80)?

(15 + 85)? (-8 + 67)?

Use what you know about parallelograms to find the missing information.

35. = _______ 38. = _______ 41. m = _______ 44. m = _______

36. = _______ 39. = _______ 42. m = _______ 45. m = _______

37. = _______ 40. = _______ 43. m = _______ 46. m = _____

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Unit 4 Evaluate each of the following. 47. () = -142 + - 6 for (-8)

48.

()

=

3-10 +6

for

(4)

Factor the following. 49. 32 + 21 + 24

50. 42 - 49

Factor to solve the following. Show all work for full credit.

51. 42 + 14 = -10

52. 82 + 56 = 0

Use the quadratic formula to solve for x. Write the exact solution and the approximate solution. Round answers to the nearest thousandth (3 decimal places). Don't forget to check your answer! Show all work for full credit.

53. 72 = 22 + 7

54. 32 - 42 = 11

55. Draw a picture of a quadratic that has 2 imaginary, complex roots 7

Complete the square on the following equations to put them into vertex form. Show all work for full credit.

56. = 2 - 8 + 21

57. = 42 - 16 + 11

58.

Write

the

transformations

for

=

-

(

-

)

+

Unit 5

Find all real and complex roots of the polynomial function.

59. () = 4 + 3 - 332 + 9 - 378

60. () = 23 + 62 + 5 + 15

Write the equation of the polynomial function that satisfies the following conditions. Write your equation in standard form.

61.

62. Quadratic with a root of 2 - 5

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