Final Exam Review (Multiple Choice) SHOW ALL WORK FOR CREDIT (Exponents and Radicals) 1. Simplify the following: a.
3
d.
b.
c. (
e.
f.
g.) Rewrite so there are no negative exponents
2.
3.
4.
Put the following number sets from least to greatest -2 2 5, , , , 16
Simplify each expression: a. ( )(4 )
b. 2
+3
Calculate the perimeter of the pentagon
+5
c.
(a
(
(Exponential Functions) 5. Identify whether each table contains pairs of values that could be modeled by an exponential function, linear function, quadratic function, or none. a.
X
Y
0
1
1
b.
X
Y
c.
X
Y
d.
X
Y
-1
-2
0
-2
-2
0
-1
1
-1
1
2
-5
1
0
0
0
2
3
-8
2
1
-3
1
4
6-9: Use the exponential growth and decay formulas to answer the following questions. Exponential growth:
Exponential decay:
6. In 2000 the population of deer in a local forest was approximately 1,100. If the population decreases at a rate of 4%, write an expression which represents the population five years later?
7. Joe borrows $500 at 8% interest. Write an equation to represent the amount of money f(t) that Joe will owe after t years.
8. Mary invests $2000 at .6% interest compounded annually. Write an equation to represent the amount of money f(t) that Mary will have in the account after t years.
, where A = the number 9. A certain radioactive element decays over time according to the equation of grams present initially and t = time in years. If 9000 grams were present initially, how many grams will remain after 400 years?
10. Which equation models the data in the accompanying table? Time in hours, x Population, y
a.
0 5
1 10
2 20
3 40
b.
4 80
c.
Graph 11.
12.
13.
14.
5 160
6 320
d.
(Polynomials) 3 15. Simplify 2 x
2 17. Subtract (5 x
7 4 x2 6 x 7 x2 3
x 7) ( 9 x 2 4 x 2)
19. Multiply (5r 3)(r
2)
21. Factor completely
2 16. Add (2 y
18. Multiply
4 y 3) (6 y 1)
6 x 2 (3 x 2 4 x 8)
20. Factor out the GCF:
22. Factor by grouping: 2x3 – 4x2 + 4x – 8
(Quadratics) 23. Complete the Square to find the roots:
24. Use Square Roots to find the x-intercepts:
25. Use the Quadratic formula to find the solutions:
26. Given the quadratic equation,
27. Given the quadratic equation,
28. Given the quadratic equation parent graph
, identify the zeros.
, write the equation in standard form.
, identify the translations when compared to the
29. Find the roots of the following quadratic equation,
30. Given the quadratic equation,
.
, identify the Axis of Symmetry and Vertex.
31. Solve the quadratic using any method to find the vertex and solutions.
32. Give the vertex of this quadratic equation.
33. Given the graph, write the function in vertex form of the following translation compared to the parent function , given that there is no shrink or stretch. a. b.
34. Graph the quadratic equation
?
35. Write a Quadratic Equation in vertex form that would show a transformation from the parent graph by being shrunk by
1 ,shifted 7 to the right, and down 10. 5
36. Write a Quadratic Equation in vertex form that would show a transformation from the parent graph by being stretched by 4, shifted 2 to the left, and up 3.
37. Describe the translation of a parabola with the following quadratic equation:
38. Describe the transformation from the parent graph of the following Quadratic Equation: y
39. Sketch a parabola that shows a vertex of (2, -1) Roots: 1 and 3
41. Graph
40. Sketch the parabola y
x2
2( x 4) 2 5
6x 8
Exponents and Radicals Answers: 1.
a)
2. 3. 4.
-2 , a) 12 84
b) ,
c)-
d)
, 5, 2 b) 18
, 16, c)
Exponential Functions Answers: 5. a. linear b. linear c. quadratic 6. 7. 8.
e)
f)
g)
d. exponential
/ Decay / Growth / Growth
9. 1000 g. 10. d 11.
12.
13.
14.
Polynomials Answers: 3 15. 2 x
3x 2 6 x 4 2y 2
2 16. 2 y
17. 14 x
2
5x 9 3 2 18. 18 x 24 x 48 x 2 19. 5r 7 r 6 4
20. 21. 22. Quadratics Answers: 23. 24. 25. 26. x= -2 and 6 27. 28. left 4 down 9 29. x= 4 and -8 30. A.O.S: x= 7 vertex: (7, 8) 31. Vertex: (-3, 25) Solutions: x=-8 and 2 32. (3, -17) 33. a.)
b.)
34.
35. y 36.
1 ( x 7) 2 10 5
37. stretched/skinny by 2 right 3 up 5 38. stretch/skinny by 2 left 4 up 5. 39.
40.
41.
Statistics Answers: 42. Minimum, Q1, median, Q3, maximum 43. a. True. It explains how spread out or condensed a given distribution is/a given set of data is. It is typically used with the mean in histograms. b. False. It is a measure of center that is resistant to outliers. It is typically used with box plots. c. False. It is a measure of spread typically used with boxplots that is calculated by Q3 – Q1. d. False. The range can be any non-negative value. It is calculated by maximum – minimum. 44. The original data is retained (unlike a histogram or a box plot, where the original data is lost/cannot be identified). 45. a. True. A box plot is divided into quartiles, which means quarters, 4th’s. b. True. A dot plot do retain original data though. c. False. The columns must be the same width (so each class is 3 wide, or each class is 5 wide, etc.) or it will indeed be misleading.
d. True. The median is not influenced by outliers (this quality is called resistant). So if you have a distribution with an outlier (s), it is wise to display your distribution graphically using a box plot. 46. Answers may vary. 47. Answers may vary. Example of right skewed: 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8. Example of symmetric: 1, 2, 2, 2, 3, 3, 3, 4. 48. Q1-Q3= 50%
Q1 to Max =75%
49. Answers may vary 50. a. 37 b. 37/100 c. 11/60 d. 19/100 e. 37/100 + 60/100 – 25/100 = 72/100=18/25 (reduce) 51. a. Species B b. Both are about the same. c. Species B. 52. a. Dot plot, box and whiskers and histogram b. 2 way table 53.
54. a. census b. sample c. sample d. census 55. Categorical data. Eye color, hair color, the type of car you drive. Numerical data. Your most recent test score, your height, the number of pets you have. 56. a. b. c. d.
categorical numerical categorical numerical
57. Lower boundary: 7 Upper boundary: 15 Yes, 16 is an outlier
