Algebra II Semester 2 ReviewClick on the red squares to find the work and answers for the given question

32

2

41

3

3 - x4

51

3 - x

5

Simplify

1. 2. 3.

4. Divide:

5. Subtract:

Solve the Following:

6. 7.

12 8t - t

30 - t t2

2

9 - x5x - x

3 - x25x

2

22

4 - x9

- 4 - x1 2x

9 x81

9 x

x2

4

3 z 3z

1 z

z

8. (A) varies directly as (c). If A = 24 when c = 8 find an equation that relates A and (c)

9. The distance (d) an object falls to earth (disregarding air resistance) varies directly as the square of the time (t) that its been falling. If it falls 256 ft. in 4 seconds. a) What is the constant of variation (k) b) Find the distance something falls in 10 sec.

10. The variable w varies directly as x and inversely as y. Find an equation that relates the variables if w is 33 when x is 15 and y is 10.

11. L varies jointly as b and the square of w. If L is 225 when b = 2 and w = 5, Find L when b = 27 and w = 4

12. A rectangular solid has a length of 2x + 3 a width of x – 2 and a height of x. Find its volume in terms of x.

13. Add:

14. Find the distance between point A(4 , 3) and Point B(-2 , 1), then find the midpoint of AB.

15. A map for a game you are playing has your start at point (6 , 4) and the goal of the game is at point (10 , -6). Half way in between is a safe spot. a) Find the coordinates of the safe spot b) How far is the starting point from the goal? (1 unit = 4.25 km)

16. Graph f(x) = 2(1/2)x

10x4 - 14x

5x

2 3x

17. Graph f(x) = 2 + ex

18. Graph y = log½ x

19. Find the value of $5500 deposited for 15 years at 6% annual interest a) compounded yearly. b) compounded monthly c) compounded continually

20. Evaluate log4 64

21. Simplify:

22. Express as a single logarithm: 5 logx3 + 2 logxa – 9 logxb

23. Expand using properties of logarithms:

12

17

2e22e

5

33

6 y1)(xx

log

24. The Population of small town called Bob in the is modeled by the equation 1500(1.02)x. The variable x represents the number of years since 1990. What is the projected annual growth, and what should the population of Bob be in 2013?

25. Solve for x to the nearest hundredth: 6.2x = 51

26. Evaluate:

27. Find the mean, median, and mode of the following set of numbers 44 , 29 , 33 , 52 , 35 , 37 , 29 , 44 , 48 , 29

28. Test scores are shown on the box-and-whisker plot below. What Percent of the class scored at or above 76?

29. Find an equation for the inverse of the relation y = - 3x + 2

32

27

13 55 76 85 98

30. Given the following histogram of test scores. How many students scored between 60 and 80?

31. Solve the equation. Check for extraneous solutions.

32. Solve the equation. Check for extraneous solutions.

33. Graph: f(x) = x3

34. Graph: f(x) =

35. The fetch f (in nautical miles) of the wind at sea is the distance over which the wind is blowing. The minimum fetch required to create a fully developed storm can be modeled by s = where s is the speed (in knots) of the wind. Find the minimum fetch required to create a fully developed storm if the wind speed is 25 knots.

x 72 x

4- 8x3

3 2 - x3

11.1 10 f 3.13

36. The volume of a right circular cone is given by the equation V = ⅓ r2h . Where r is the radius and h the height. If the height of the cone is 10in and its volume is 200 in3. What is its radius?

37.Simplify:

38. Simplify:

39. Write the following using radical notation. Assume that all variables represent positive and real numbers.

40. Evaluate the expression using a calculator. Round to three decimal places when appropriate.

41. Graph:

5vtf 32

3

11

5

vw

5

3

y 2

4 162

4 x f(x)

42. Graph f(x) = x3 – 2x

43. Divide by using long division: (2x3 + 6x – 2) ÷ (2x + 2)

44. Divide by using synthetic division: (x3 + 2x2 – 6x – 9) ÷ (x + 3)

45. Subtract: (3x2 – 2x + 3) – (-4x2 – 2x + 7)

46. Add: (3x3 – 7x2 + 1) + (-5x3 – 3x + 9)

47. Multiply: (2x + 3)(4x2 – 4x -1)

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6.2x

6.2

6.2

2.15

Annual growth 2%

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22 x 72 x

x 72 x

x + 72 = x2

0 = x2 – x – 72(x – 9)(x + 8) = 72 x = 9, -8

-8 does not check

Square each sideThen solve

8- 8

8- 64

8- 72 8

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-2x3 - 7x2 - 3x +10