Friday Test
Identify the choice that best completes the statement or answers the question.
____ 1. Which is the graph of ?
____ 2. graph the complex number .
.Short Answer
3. A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a function of distance d.
4. What is the vertex of the graph of the function ?
Solve the equation.
5.
6.
7.
8.
9.
Solve the equation or formula for the indicated variable.
10. , for U
Solve the equation. Check for extraneous solutions.
11.
12. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 2 or greater than 7 in a single spin?
13. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).
Solve the system by the method of substitution.
14.
15. A group of 52 people attended a ball game. There were three times as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.
Use the elimination method to solve the system.
16.
Solve the system of inequalities by graphing.
17.
18. State the dimensions of the matrix. Identify the indicated element.
Evaluate the determinant of the matrix.
19.
20. Use the vertex form to write the equation of the parabola.
21. Identify the vertex and the y-intercept of the graph of the function .
22. Write in vertex form.
Factor the expression.
23.
24.
25.
26. Solve by factoring.
= 0
Solve the equation by finding square roots.
27.
28. Simplify using the imaginary number i.
Write the number in the form a + bi.
29.
30. Find .
Simplify the expression.
31.
Solve the quadratic equation by completing the square.
32.
33.
Use the Quadratic Formula to solve the equation.
34.
35. Write 4x3 + 8x2 – 96x in factored form.
36. Find the zeros of . Then graph the equation.
Divide using synthetic division.
37.
38. The dimensions in inches of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x – 1. The volume is about 7.6 ft3. Find the dimensions of the box in inches. Round to the nearest inch.
39. Solve . Find all complex roots.
40. Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.
41. For the equation , find the number of complex roots and the possible number of real roots.
42. In how many different orders can you line up 8 cards on a shelf?
43. There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?
44. The Booster Club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk, coffee, tea, or cola. How many possible meal combinations are there?
Use Pascal’s Triangle to expand the binomial.
45.
46. Determine the probability of getting four heads when tossing a coin four times.
47. Determine the probability that you will get 3 green lights in a series of 5 lights. Assume red and green are equally likely occurrences.
48. Simplify . Assume that all variables are positive.
49. Let and . Find .
50. An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the quail population.
51. Write an exponential function for a graph that includes (1, 15) and (0, 6).
52. Graph .
53. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years?
Graph the logarithmic equation.
54.
55. Use the Change of Base Formula to evaluate . Then convert to a logarithm in base 3. Round to the nearest thousandth.
56. Solve .
57. Solve . Round to the nearest ten-thousandth.
58. Solve . Round to the nearest thousandth.
59. Find the horizontal asymptote of the graph of .
Multiply or divide. State any restrictions on the variables.
60.
Add or subtract. Simplify if possible.
61.
Suppose Q and R are independent events. Find P(Q and R).
62. P(Q) = 0.41, P(R) = 0.44
63. Two urns contain white balls and yellow balls. The first urn contains 9 white balls and 9 yellow balls and the second urn contains 8 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
Suppose S and T are mutually exclusive events. Find P(S or T).
64. P(S) = 20%, P(T) = 22%
65. If all possible results are equally likely, what is the probability that a spin of the spinner will land on an upper case letter or a consonant?
66. Write an equation of a parabola with a vertex at the origin and a focus at (–2, 0).
67. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.
68. Identify the vertex, focus and the directrix of the graph of .
Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics.
69. vertices at (–5, 0) and (0, 4)
70. Write an equation of an ellipse with center (3, –3), vertical major axis of length 12, and minor axis of length 6.
Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci.
71.
72. The sequence 15, 21, 27, 33, 39, ..., 75 has 11 terms. Evaluate the related series.
73. Use summation notation to write the series 49 + 54 + 59 + ... for 14 terms.
74. Use summation notation to write the series 2 + 4 + 6 + 8 + ... for 10 terms.
75. Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred afternoon classes given he or she is a junior. Round to the nearest thousandth.
When Do You Prefer to Take Classes?
Freshman / Sophomore / Junior / SeniorMorning / 19 / 2 / 6 / 16
Afternoon / 17 / 3 / 13 / 15
Evening / 8 / 14 / 9 / 7
Find the mean and standard deviation of the of data. Round to the nearest tenth.
76. 20, 16, 18, 14, 9, 20, 16