Math 3 Cumulative Review Name Units 1 - 3

[Pages:5]Math 3 Cumulative Review Units 1 - 3

1. Find the indicated term in the arithmetic sequence:

a21 for 10,7, 4,...

Name________________________

2. Find the missing terms in the arithmetic sequence. _____2,_____,_____,_____,_____,_____,20

3. Find the sum of the arithmetic series:

6

2k 3

k 3

4. Find the sum of the arithmetic series: 10 4 (2) ... (50)

5. Find the sum of the geometric series described:

a1 3, n 13, r 2

6. Find the sum of the series described:

9

(2)n1

n1

7. Two of the zeros of the function

h(x) 6x3 11x2 3x 2

are

1 2

and

2 .

What type of zeros is the third? Why?

8. Find all solutions. f (x) x4 x3 12x2 6x 36

9. Use the graph of the function to determine how many real and/or complex solutions the polynomial has. f (x) x4 15x3 70x2 70x 156

10. Napoleon crossed the Alps in 1797. You can find the years of Napoleon's birth and death by solving the following system. How old was Napoleon when he crossed the Alps? 3x - 2y = 1665 -4x + 3y = -1613

11. Graph: y < x + 3 y < -1/2 x - 1

12. Simplify. (5 6i) 8(4 2i) 2i(3 8i)

13. The length of a rectangle is 2 feet more than its width. Find the dimensions of the rectangle if its area is 63 feet.

14. Use the factor theorem to prove whether -2 is a zero of the function.

f (x) x3 3x 2

15. Divide: 4x 3 + 5x 2 - 3x - 1 4x + 1

16. Factor: z 3 + 125

17. . Simplify. x3 y2 (xy4 x3 y x2 y2 )

18. . Simplify. (x 6)(2x2 5x 4)

19. Solve: 10m - 9n = 15 5m - 4n = 10 Divide using long

division. (12 y2 36 y 15) (6 y 3)

20. Graph the following system of inequalities. Name the vertices of the feasibility region. x < 5 y < 4 x + y > 2

21. Divide using synthetic division. (x5 7x3 x 1) (x 3)

22. Solve by completing the square: -3x2 + 3x + 4 = 0

23. PROVE using a two column proof: If : 4(5n 7) 3n 3(4n 9) Prove: n 9

24. Sketch a parabola that opens down and represents a quadratic function with two real zeros, both of which are negative numbers.

25. Determine the number of real solutions of the equation: 3x2 - 6x + 1 = 0

26. Solve using the quadratic formula: 4x2 - 6x = - 2

27. If U is between T and B, find the value of x

and the lengths of the segments.

28. Write a quadratic equation with the roots 2 and -7. Write in the form ax 2 + bx + c = 0:

29. Solve for X.

30. Graph: y < -1 x < 2 y < x + 2

31.

5 6 8 7

2 3 1 4

13 14 16 15

9 10 12 11

Refer to the above figure and identify the special angle pair name. 1) 3 and 13 2) 8 and 10

3) 11 and 15 4) 8 and 6 5) 1 and 6 6) 6 and 10 7) 14 and 15

11. 33.

Determine

.

34. Write a polynomial equation with the following roots.

-2/5 and 2/7

35. Simplify: (-7 - i) (3 + 2i)

36. Solve: 2x 2 - 3x + 1 = 0

37.

12.

Determine the measure of the

angles below.

38. Find the dimensions of a triangle whose sides are 4x + 1, 8 - x, and 5x - 2 and whose perimeter is 23.

a. b. c.

39. Solve: x2 -10 x + 24 = 0

40. Location Mapping needs new software. Software A costs $13000 plus $500 per additional site license. Software B costs $2500 plus $1200 per additional site license. Write two equations to represent the cost of each software and find the break even point.

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