College Algebra Questions

I have 5 exams with 20 questions each. Please see attached.

StudentID: 21772952

Exam: 050352RR – A REVIEW OF BASIC ALGEBRA;GRAPHS,EQUATIONS OF
LINES,FUNCTION

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Questions 1 to 25: Select the best answer to each question. Note that a question and its answers may be split across a page
break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. Solve the following equation for z:
3(z + 2) − 2 − z = –(5 + z)

z = 8

B. z = 3

z = –3

D. z = –8

2. Graph the function g(x) = (x − 1)3.

3. Given f(x) = 2x − 8, find f(3).
A. –3

B. –2

C. 2

D. 3

A.
B.
C.
D.

5. Find the equation of the line perpendicular to the line x = 4 and passing through the point (4, 2).
A. y = 2

B. y = –4

C. y = –2

D. y = 4

6. The cost of two baseball bats is $360. If the aluminum one costs $40 more than the wood one, find the
cost of the aluminum bat.
A. $80

B. $160

C. $200

D. $240

A.
B.
C.
D.

8. Simplify the expression .

A.
B.
C.

9. The slope-intercept form of the equation of a line is

A.
B.
C.
D.

10. Simplify the expression (–3)2.
A. –6

B. –9

C. 6

D. 9

11. Find the slope of the line determined by the equation 6x − 3y = 18.
A. m = –2

B. m = 2

C. m = 6

D. m = –6

12. Tell whether the following equation determines y to be a function of x:

y2 = x + 3
A. Yes

B. Sometimes

C. No

D. Only when x = –1

13. Simplify the expression –32.
A. 6

B. –9

C. 9

D. –6

14. Simplify the expression .

B.
C.
D.

15. Draw the graph of the following linear function and give the domain and range:
h(x) = –2x + 3.

A.
B.
C.

16. A 152-foot piece of rope is to be cut into four pieces. Each successive piece is to be 2 feet longer than
the previous one. Find the length of the shortest piece.
A. 35 feet

B. 40 feet

C. 38 feet

D. 37 feet

17.

A.
B.
C.
D.

18. Complete the following table for the equation y = x + 3:

B.
C.
D.

19. The function f(x) = x3 is called the _______ function.
A. quadratic

B. absolute value

C. squaring

D. cubing

20. Find the slope of the line that passes through the points (–3, –6) and (1, 6).

A.
B.
C.
D.

21. Shifting the graph of an equation up or down is called a/an _______ translation.
A. reflective

B. horizontal

C. Vertical

D. inverse

22.

End of exam

B.
C.
D.

23. Solve the following equation for x:
5(x − 4) = 10
A.

B.
C.
D.

24. Write the numeral 0.034 in scientific notation.

A. 0.34 × 10–1

B. 34 × 10–3

C. 3.4 × 102

D. 3.4 × 10–2

25. Solve the following equation for q:

A. q = –5

B. q = –2

C. q = 5

D. q = 2

StudentID: 21772952

Exam: 050353RR – SYSTEMS OF EQUATIONS; INEQUALITIES

When you have completed your exam and reviewed your answers, click Submit Exam

Answers will not be recorded until you
hit Submit Exam. If you need to exit before completing the exam, click Cancel Exam.

1. Graph the solution set of
x + 2y ≤ 3
x + 2y ≤ 4

2. Choose the correct ways to fill in the blanks in the following sentence.
To solve a system of equations using the matrix method, use __________ to transform the augmented
matrix into one with __________, then proceed to back-substitute.
A. the coefficient matrix, an inverse

B. the coefficient matrix, Gaussian elimination

C. multiplication and addition, zeros in its final column

D. elementary row operations, zeros below the diagonal

3. Are the two equations –6 + y = 2x and 2y − 4x = 12 dependent?
A. No, because the equations are not written the same.

B. No, because they are not parallel.

C. Yes, because they have the same graph.

D. Yes, because both are the equations of straight lines.

4. Solve the system of equations 2x − y + z = –7, x − 3y + 4z = –19, and –x + 4y − 3z = 18.
A. There is one solution, (–1, 2, –3).

B. There is one solution, (1, 2, 3).

C. There is one solution, (–1, –2, –3).

D. There is one solution, (1, –2, 3).

5. Graph the inequality y ≥ –3.

6. Solve the equation |6x + 3| = 15
A. x = –3 or x = 2

B. x = 4

C. x = 2

D. x = –3

7. When solving the system of equations 6x + 2y = –1 and –x + 10y = 5 by Cramer’s Rule, what are the
values of D, D

x
, and D

y
?

A. D = 58, D
x
= –20, D

y
= –29

B. D = 62, Dx = 20, Dy = 28

C. D = 58, D
x
= 20, D

y
= –28

D. D = 62, Dx = –20, Dy = 29

8. Graph the following solution set:
y ≤ x − 1
y ≥ 2x

A.
B.
C.
D.

9. Graph the following solution set:
x + y ≤ 4
x ≥ 0
y ≥ 0

B.
C.
D.

10. Graph the following solution set:

x ≤ y2
y ≥ x

A.
B.

C.
D.

11. Solve the inequality . Give the result in set notation and graph it.

A.
B.
C.
D.

12. Solve the system of equations 2x − 2y − 2z = 3, x + 4y − z = 2, and –2x − 8y + 2z = –4.
A. There are infinitely many solutions, of the form (x, 0.1, x −1.6).
B. There is one solution, (0.1, 0.1, –1.5).

C. There are infinitely many solutions, of the form (0.1, 0.1, –1.5).

D. There is no solution.

13. Find the equation of the boundary line in the graph below. Then give the inequality represented by the
shaded area.

A.
B.
C.
D.

14. Graph the inequality y < 3x + 1.

A.
B.

C.
D.

15. Use matrices to help find a general solution for this system of equations.

2x − y + 3z = 5
–x + 4y + 4z = –1

A.
B.
C.
D.

16. Consider two ships, one on a course described by the equation 0.6x + 0.3y = 2.1 and the other on a
course described by the equation –0.3x + 0.1y = –1.8. Which of the following sentences best describes the
possibility of a collision?
A. There is no possibility for a collision.

B. There is a possibility of a collision at the point (5, –3) but a collision is not a certainty.

C. There is a possibility of a collision at the point (0, 7) but a collision is not a certainty.

D. There will certainty be a collision at the point (6, 0).

17. The first two rows of the following matrix are already in triangular form.

Finish the job by performing Gaussian elimination on row 3.

What are the contents of row 3 after you have done so?

A. 0 0 3 29

B. 0 0 1 9

C. 0 0 3 –11

D. 0 0 –5 –11

18. If the edge isn’t included in the graph of an inequality, you should draw it as a/an _______ line.
A. solid

B. dashed

C. open

D. closed

19. Solve the inequality . Give the result in set notation and graph it.

A.
B.
C.
D.

20. Convert to a fraction.

A.
B.
C.
D.

21. Solve the system of equations y = 0.6x + 0.2 and 3x − 5y = 4.
A. There are infinitely many solutions.

B. There is one solution, and it is .

C. There is one solution, and it is (0, 0.2).

D. There is no solution.

22. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x − y − z = 5.
A. There are infinitely many solutions.

B. There is one solution, x = 4, y = 2, and z = 3.

C. There is no solution.

D. There is not enough information to solve the problem.

23. Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it.

A.
B.
C.
D.

24. Which of the following ordered pairs is a solution to the system of equations y = x − 6 and 2y = –x +
14?

A.
B.
C.
D.

25. Solve the inequality |5x + 10| ≥ 15. Write the solution in interval notation and graph it.

End of exam

B.
C.
D.

StudentID: 21772952

Exam: 050354RR – POLYNOMIALS AND POLYNOMIAL FUNCTIONS

Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page
break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. Completely factor the expression y2 + 12y + 35.

Prime

B. (y − 7)(y − 5)
C. (y + 7)(y + 5)

D. (y + 7)(y − 5)

2. Solve the equation 3z3 − 300z = 0.
A. z = 0, z = 10, and z = –10

B. Prime

C. z = –4 and z = 1

D. z = 0

3. Completely factor the expression 4q2 + 27r4.
A. 4q(q + 27r)

B. 31q2r4

C. 27r4(4q2 + 1)

D. Prime

4. Solve the equation x2 + 4x − 45 = 0.
A. x = 15 and x = 30

B. x = 9 and x = –5

C. No solution

D. x = –9 and x = 5

5. Completely factor the expression 16×4 − 81y4.
A. Prime

B. 0

C. (4×2 − 9y2)(4×2 + 9y2)

D. (2x + 3y)(2x − 3y)(4×2 + 9y2)

6. Completely factor the expression 7(x − y) − z(x − y).
A. (x − y)2(7 − z)3

B. Prime

C. (x − y)(7 − z)
D. (x − y)(7 + z)

7. Find the product of (x − 2y)2.
A. x2 + 4y2

B. x2 − 4xy + 4y2

C. x2 + 2xy + 4y2

D. x2 + 4xy + 4y2

8. Solve the equation

9. Find the product of (2a + 3b)(2a − 3b).
A. 4a2 − 9b2

B. 4a2 − 6b2

C. 4a2 + 12ab − 9b2

D. 2a2 − 3b2

10. Completely factor the expression 2a3 − 128.
A. 2(a3 − 64)

B. 2(a − 4)3

C. 2(a − 4)(a2 + 4a + 16)
D. Prime

11. Find the value of the expression 2xy − x2y when x = 2 and y = 3.
A. 24

B. 0

C. 6

D. –24

12. Completely factor the expression a2 + 4b − ab − 4a.

A. Prime

B. (a − b)(a − 4)
C. (a + b)(a − 4)
D. (a + b)(a + 4)

13. Simplify the expression –2(4y2 + 3z3 + 5) + 3(2y2 − 5z3 + 3).
A. –14y2z3 + 6y2 − 1

B. –21z3 − 2y2 − 1

C. 9z3 − 14y2 + 19

D. 21z3 + 2y2 + 1

14. Completely factor the expression 48u4v4 − 18u2v2 − 3u8v5.
A. Nonfactorable

B. 3u2v2(16u2v2 − 6 − u6v3)

C. u2v2(48u2v2 − 18 − 3u6v3)

D. 3(16u4v4 − 6u2v2 − u8v5)

15. Completely factor the expression 16t3 − 50t2 + 36t.
A. 2t(8t + 9)(t + 2)

B. Prime

C. 2t(8t − 9)(t − 2)
D. 2t(8t − 25t + 18)

16. Graph the polynomial function f(x) = x3 − 1.

B.
C.
D.

17. Find the product of –3a3b(2a0b4 − 4a2b3)
A. –6b5 + 14a5b4

B. 12a5b4 − 6a3b5

C. –6b4 + 12a6b3

D. 14a5b4 − 6b5

End of exam

18. Simplify the expression 2ab4 − 3a2b2 − ab4 + a2b2.
A. ab4 − 2a2b2

B. 2a2b8 − 3a4b4

C. 0

D. a2b8 − a2b8 − 2a4b4

19. Completely factor the expression r2 − 2r + 1.
A. r(r − 2) + 1
B. (r − 1)(r − 1)
C. (r + 1)(r − 1)
D. Prime

20. Perform the indicated operations on the expression below.

(5a3 + 3a – 2) – (4a3 + a2 + 5)

A. 3a6 − 7

B. a3 − a2 + 3a − 7

C. 20a3 + 3a2 − 10

D. a3 + a2 + 3

StudentID: 21772952

Exam: 050355RR – RATIONAL EXPRESSIONS

1. Perform the indicated operations and simplify the following expression:

2. Divide the following expression:

A.
B.

3. The intensity I of light varies inversely with the square of the distance d from the source, expressed in

the equation . If the intensity is of a candela 16 feet from the source, what is the constant of

proportionality?
A. 128 candela-square-feet

B. 2 candela-square-feet

C. 32 candela-square-feet

D. 256 candela-square-feet

4. Perform the indicated operations and simplify the following expression:

A.
B.
C.
D.

5. Simplify the following expression:

A.
B.
C.
D.

6. Simplify the following expression:

A.
B.
C.
D.

7. Perform the indicated operations and simplify the following expression:

A.
B.
C.
D.

8. Find the result of the polynomial division (3×2 − 2) ÷ (x + 4).

A.
B.
C.
D.

9. Divide the following expression:

(x2 + 10x + 21) ÷ (x + 7)
A. x + 5

B. x + 3

C. x2 + 3

D. x − 2

10. Simplify the expression

A.
B.
C.
D.

11. Solve the following equation:

A. y = 4

B. y = –4

C. y = –3

D. y = 3

12. Solve the following equation:

A. t = 1

B. { }

C. t = 2

D. t = –1

13. Which sum yields ?

A.
B.
C.
D.

14. Perform the indicated operations and simplify the following expression:

A.
B.
C.
D.

15. The total resistance R of two resistors in parallel is given by where R1 is the resistance of the

first and R2 the resistance of the second. Solve that equation for R1 and simplify.

A.
B.
C.
D.

16. Perform the indicated operations and simplify the following expression:

A.
B.
C.

End of exam

17. Simplify the following expression:

A.
B.
C.
D.

18. It costs $500 to have a booth at the fair for one day and $2.75 for Aunt Ida to produce one of her
famous shepherd’s pies. What is the function that gives the average cost in dollars per pie for one of Aunt
Ida’s days at the fair?

A.
B.
C.
D.

19. Solve this proportion for the variable:

A. y = 2

B. y = –2

C. y = –4

D. y = 4

20. Express this sentence as a formula: z varies directly with the square of s.

A.
B.
C.
D.

StudentID: 21772952

Exam: 050356RR – RADICALS AND RATIONAL EXPONENTS

1. Simplify (6 − i)(2 + i).
A. 13 − 8i
B. 11 + 4i

C. 13 + 4i

11 + 8i

2. Simplify .

3. Which of these radical expressions simplifies to x?

A.
B.
C.
D.

4. Expand and simplify. Assume y ≥ 0.

A.
B.
C.
D.

5. Two children in nearby houses attempt to use walkie-talkies to communicate. The walkie-talkies reach
one quarter of a mile (1320 feet). From one child’s house to the other, the walk along the city sidewalks is
as follows: Proceed 450 feet from the first house to the nearest corner, turn right 90° and proceed another

1050 feet. Are the children’s houses within the 1320-foot range of one another? Choose the best answer.
A. Yes, because city blocks are much smaller than one quarter of a mile.

B. No, but if the turn were to the left instead, they would be within range.

C. Yes, as the distance formula indicates.

D. No, because the distance is greater than 1320 feet.

6. Solve for x.

A.
B.
C.
D.

7. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?

A. The mean is and the standard deviation is 5.

B. The mean is 4.86 and the standard deviation is 5.63.

C. The mean is and the standard deviation is approximately 5.6252.

D. The mean is and the standard deviation is approximately 5.6252.

8. Which of these expressions simplifies to ?

A.
B.
C.
D.

9. Simplify by rationalizing the denominator.

A.
B.
C.
D.

10. If the hypotenuse of a right triangle is 6m and one side is 4m, what is the length of the other side?

A.
B.
C.
D.

11. Rationalize the denominator of assuming x ≥ 0 and y ≥ 0.

A.
B.
C.
D.

12. Solve for x.

A. The two solutions for are complex numbers.

B. x = 2 or x = 8

C. x = 4 or x = –4

D. x = 2

13. Choose the best description of the radical expression .

A. It can be simplified to –3.

B. It can be simplified, but the result is a complex number.

C. It can be simplified to , but no further.

D. It is in simplified form.

14. Compute the value of .

A.
B.
C.
D.

15. Solve for x.

A. 40

B. 4

C. 50

D. –41

16. Which of these phrases best describes the standard deviation?
A. It is equal to the mean squared.

B. It increases as more measurements are taken.

C. It is a measure of variability.

D. It is a radical expression using n variables.

17. Simplify .

A.
B.
C.
D.

18. Simplify .

A.
B.
C.
D.

19. Simplify .

A.
B.
C.
D.

20. Rationalize the denominator of .

A.
B.
C.
D.

21. To solve for x, begin with which of these steps?

A. Square both sides of the equation.

B. Combine the two like radicals, then square both sides.

C. Eliminate the negative in the second radical expression.

D. Isolate one radical expression.

End of exam

22. Simplify i23.
A. i

B. –1

C. –i

D. 1

23. Expand and simplify. Assume c ≥ 0 and d ≥ 0.

A.
B.
C.
D.

24. Which expression has the same value as 25½?
A.

B.
C.
D.

25. Which of these expressions is in simplified form?

A.
B.
C.
D.

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