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Final Exam

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Final Exam Introduction

Welcome to the Final Exam for MAT 120: College Algebra.

Now that you have successfully completed the assessments and assignments for this course, you are ready to take the online final examination. The final exam is an essential component of the course and should be completed after all other assignments have been graded and returned to you. However, the final exam must be completed no later than the course end date. This section prepares you to complete the final successfully.

This exam cannot be paused and returned to later. Please ensure that you have allotted uninterrupted time to complete your final exam.

Proctored Exam

The MAT 120 final exam is a proctored exam.

In order to take a proctored Final Exam, students must obtain approval from AAU (see the Allied American University Catalog) for their choice of proctor prior to taking the exam. The Proctor Request Form takes 48-72 hours to process; therefore, it is important for students to budget their time accordingly so that they have enough time to schedule the exam after the form has been processed, but before the course end date.

See the ARC for more details regarding AAU's proctoring policies. Read the Proctored Final Exam Instructions, Who Qualifies as a Proctor?, Proctor U, and Important Notes sections carefully.

For further questions, please contact your Program Success Advocate.

The student will have three (3) hours to complete the exam.

What will the final exam look like?

The final is composed of multiple-choice and true-false questions.

Final Exam Instructions

Please follow these instructions to complete the Final Exam and submit it successfully:

1. To begin the Final Exam, click on the Start button.

2. Questions are multiple-choice and true-false.

3. Choose the answer that best corresponds to the question.

4. Review your answers thoroughly before submission. You can change your answers at any time during this assessment.

5. When you are ready to submit, click the Finish button.

If you have any problems with the Final Exam, please e-mail your professor. This assessment cannot be paused and returned to later. Please ensure that you have allotted uninterrupted time to complete this assessment.

Note: You are only allowed one (1) attempt for this assessment.

Please DO NOT begin until you have read the information above.

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Question

Simplify and express your answer using positive exponents only.

Solve the equation.

a. 1

b. 22,501

c. 1 and 22,501

d. No real solutions

Determine if g is the inverse of f:

a. Yes

b. No

A chemist has two solutions: one containing 40% alcohol and another containing 70% alcohol. How much of each should be used to obtain 80 liters of a 49% solution?

a. 60 liters of 40% solution and 20 liters of 70% solution

b. 50 liters of 40% solution and 30 liters of 70% solution

c. 56 liters of 40% solution and 24 liters of 70% solution

A mail-order garden equipment business shipped 120 packages one day. Customers were charged $3.50 for each standard-delivery package and $7.50 for each express-delivery package. Total shipping charges for the day were $596. How many of each kind of packages were shipped?

a. 76 standard packages; 44 express packages

b. 44 standard packages; 76 express packages

c. 66 standard packages; 54 express packages

d. 54 standard packages; 66 express packages

Determine whether the function is one-to-one. f(x) = 7x2 + 8

a. One-to-one

b. Not one-to-one

Solve the system of equations by the elimination method.

2x + 5y = –12 7x – 5y = 3

a. (–1, –3)

b. (–1, –2)

c. (0, –2)

d. (0, –3)

Reflect A, B, C, and D through the x-axis and give the coordinates of the reflected points, A', B', C', and D'.

a. A' = (0, –1), B' = (–6, –3), C' = (–1, 3), D' = (5, 2)

b. A' = (0, 1), B' = (6, 3), C' = (1, –3), D' = (–5, –2)

c. A' = (–1, 0), B' = (–3, –6), C' = (3, –1), D' = (2, 5)

d. A' = (1, 0), B' = (–3, 6), C' = (3, 1), D' = (2, –5)

Perform the indicated operations and simplify. 5x – 4x[8 – 3(x – 2)]

a. 6x2 – 3x

b. 12x2 – 51x

c. 12x2 + 5x + 6

d. 12x2 + 5x – 6

10.

Solve by factoring. 3x2 = –18x

a. 0, –6

b. 0, 6

c. 6, –6

d. 2, 6

11.

Indicate whether the graph is the graph of a function.

a. Function

b. Not a function

12.

Solve. 9x2 = –5x

a. -

b. -

c. -

d. -

13.

Evaluate x to four significant digits. ln x = –1.445

a. 0.2357

b. 0.2711

c. 0.3589

d. 0.4513

14.

How much pure antifreeze must be added to 12 gallons of 20% antifreeze to make a 40% antifreeze solution?

a. 2 gallons

b. 4 gallons

c. 6 gallons

d. 8 gallons

15.

Find (f + g)(–3).

a. 0

b. 1

c. 2

d. 3

16.

The radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 20-g mass of americium-241. How much will be left after 377 years? Compute the answer to three significant digits.

a. 10.9 g

b. 12.0 g

c. 13.2 g

d. 13.8 g

17.

Write an equation of the line that contains the indicated point and meets the indicated condition(s). Write the final answer in the standard form Ax + By = C, A > 0: parallel to 3x + 4y = 8.

a. 3x + 4y = 29

b. 3x + 5y = 20

c. 3x + 5y = 29

18.

Factor out, relative to the integers, all factors common to all terms. 18x4 + 21x3 + 21x2

a. 3x2(6x2 + 21x + 21)

b. 3x2(6x2 + 7x + 7)

c. 18x2(x2 + 7x + 7)

d. 18x(x3 + 21x2 + 21x)

19.

Solve. Write the solution in interval notation. |x + 7| < 8

a. (–∞, –15) (1, ∞)

b. (–∞, –15] [1, ∞)

c. (–15, 1)

d. [–15, 1]

20.

Graph h(x) = f(x – 2).

21.

Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. x2 + 6xy + y2 = 1

a. Symmetric with respect to the x-axis

b. Symmetric with respect to the y-axis

c. Symmetric with respect to the origin

d. Symmetric with respect to the x-axis, the y-axis, and the origin

22.

Write in exponential form. log 10 0.0001 = –4

a. 0.0001 = 10–4

b. 10 = (0.0001)–4

c. 0.0001 = (–4)10

d. 10 = (–4)0.0001

23.

Factor completely, relative to the integers. x2 + 7x + 8x + 56

a. (x – 7)(x – 8)

b. (x + 7)(x – 8)

c. (x + 1)(x + 56)

d. (x + 7)(x + 8)

24.

Rewrite in equivalent exponential form:

d. 27 = 3x

25.

Find the vertex form of the quadratic function f(x) = –x2 + 4x + 2.

a. f(x) = –(x + 2)2 + 6

b. f(x) = –(x – 2)2 + 6

c. f(x) = –(x – 2)2 – 6

d. f(x) = –(x + 2)2 – 6

26.

The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.

27.

Solve y in terms of:

c. None of the choices apply

28.

Solve to three significant digits: 0.610x2 - 4.28x + 2.93 = 0

a. x = 0.760, 6.20

b. x = 0.769, 6.25

c. x = 7.69, 0.65

d. x = 0, 1

29.

Solve. x2ex + 4xex = 0

a. 0

b. –4

c. 0, 4

d. 0, –4

30.

Evaluate. (–2)–2

a. 1/4

b. 1

c. 2

d. 4

31.

Simplify and express your answer using positive exponents only. (4w10)(7w6)(2w)

a. 13w60

b. 13w17

c. 56w60

d. 56w17

32.

Solve.

a. 3

b. 4

c. 5

d. –4

33.

Solve. 4(x – 2) + 6x = 12

c. 1

d. 2

34.

Solve and write answers in inequality notation. Round decimals to three significant digits:

a. -5.34 < x < 11.9

b. 0.65 < x < 2.52

c. 0 < x < 2.52

d. 1

35.

Evaluate to four decimal places: log 691,450

a. 5.3998

b. 5.8893

c. 5.8398

36.

Which of the following is not a polynomial?

a. 4x3 + 5x – 1

b. 2x –

c. 3xy2 + xy

d. 24

37.

An employee is hired to assemble toys. The learning curve

gives the number of toys the average employee is able to assemble per day after t days on the job. How many toys can the average employee assemble per day after 6 days of training? Round to the nearest integer.

a. 24 toys

b. 25 toys

c. 26 toys

d. 27 toys

38.

Solve. |x – 2| = 7

a. 9, 5

b. 9, –5

c. –9, –5

d. –9, 5

39.

Perform the indicated operations and reduce to lowest terms.

40.

Two trains travel at right angles to each other after leaving the same train station at the same time. One hour later they are 100 miles apart. If one travels 20 miles per hour faster than the other, what is the rate of the faster train?

a. 60 mph

b. 70 mph

c. 80 mph

d. 90 mph

41.

Solve the system of equations by using the elimination method.

x+y=9 2x-3y=-2

a. (4, 5)

b. (9, 1)

c. (9, 0)

d. (5, 4)

42.

Determine if g is the inverse of f. f(x) = 3x – 1 g(x) = x + 1

a. Yes

b. No

43.

A plane carries enough fuel for 20 hours of flight at an airspeed of 150 miles per hour. How far can it fly into a 30 mph headwind and still have enough fuel to return to its starting point? (This distance is called the point of no return)

a. 1,440 miles

b. 340 miles

c. 14,440 miles

44.

Solve by completing the square. x2 + 10x + 19 = 0

a. ±31

d. -

45.

Find the vertex and axis of the parabola, then draw the graph. f(x) = 5(x + 12)2 + 10

Vertex: (12, 10); axis: x = 12

Vertex: (–12, 10); axis: x = –12

46.

Solve the system of equations by the elimination method.

x – y = 4 x + 2y = –14

a. (–2, –6)

b. (–3, –6)

c. (–2, –5)

d. (–3, –5)

47.

Solve the system by the substitution method.

a. x

48.

Find the standard form of the equation for the quadratic function whose graph is shown.

a. f(x) = –x2 + 6x – 5

b. f(x) = –x2 + 3x – 5

c. f(x) = –x2 – 6x – 5

d. f(x) = –x2 – 3x – 5

49.

Solve the system of equations by using the elimination method.

x + y = 4 x – y = 2

a. (1, 3)

b. (–1, 5)

c. (3, 1)

d. (5, –1)

50.

Find the vertex and axis of the parabola, then draw the graph.

Vertex: (–2, –5); axis: x = –2

Vertex: (2, –5); axis: x = 2

Vertex: (2, 5); axis: x = 2

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