Exam: 050290RR – A Review of Basic Algebra; Graphs, Equations of Lines, and F

1. Solve the following equation for q:

A. q = –5

B. q = 5

C. q = –2

D. q = 2

2. Graph the function f(x) = x

A.

B.

C.

2

– 2.

D.

3. Find the slope of the line determined by the equation 2x = y.

A. m = –3

B. m = 2

C. m = 3

D. m = –2

4. Write the numeral 0.034 in scientific notation.

A. 3.4 × 10

B. 3.4 × 10

C. 34 × 10

D. 0.34 × 10

–2

2

–3

–1

5. If the sum of the measures of two angles equals _______, the angles are called supplementary angles.

A. 360°

B. 270°

C. 180°

D. 90°

6. The quotient of two real numbers with the same sign is

A. 0.

B. infinite.

C. equal.

D. positive.

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

A.

B.

C.

D.

8.

A.

B.

C.

D.

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

y

2

= x + 3

A. Only when x = –1

B. Yes

C. No

D. Sometimes

10. Graph the equation

A.

B.

C.

D.

11. On the rectangular coordinate system, plot the point (–1, –2).

A.

B.

C.

D.

12.

A.

B.

C.

D.

13. 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

14. Which one of the following equations represents the y-axis?

A. y = –1

B. y = 0

C. x = 0

D. x = –1

15. Simplify the expression (–3)

A. –6

B. 9

C. 6

D. –9

2

.

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. 40 feet

B. 35 feet

C. 38 feet

D. 37 feet

17.

A.

B.

C.

D.

18.

A.

B.

C.

D.

19. Write the result of the following computation in scientific notation and perform the indicated operations:

A. 2 × 10

B. 2 × 10

C. 21

D. 42

9

–9

20. Simplify the expression .

A.

B.

C.

D.

21. Graph the following set on a number line: {x|x = –1}.

A.

B.

C.

D.

22. Find the slope of the line joining the points A (–3, 2) and B (0, 4).

A.

B.

C.

D.

23. Simplify the expression –3

A. 9

B. –9

C. –6

D. 6

24. Given f(x) = 2x – 8, find f(3).

A. –2

B. –3

C. 3

D. 2

.

25. Simplify the expression .

A.

B.

C.

D.

Exam: 050291RR – Systems of Equations; Inequalities

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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 inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.

A.

B.

C.

D.

2. Solve the inequality 4 < –z – 4 < 11. Give the result in set notation and graph it.

A.

B.

C.

D.

3. Solve the equation |x| = 7.

A. x = 7 or x = –7

B. x = 7

C. Undefined

D. x = –7

4. The matrix below is the augmented matrix of a system of three equations in the variables x and y. Solve

for x and y.

A. Infinitely many solutions

B. One solution,

C. No solution

D. One solution (0, 9)

5. 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 no solution.

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

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

6. Graph the following solution set:

x = y

2

y = x

A.

B.

C.

D.

7. Which of the following phrases correctly describes the graph of the system of equations

and y = 2 – x?

A. The graph is of two parallel lines that do not intersect.

B. The graph is of a line and a parabola, which intersect at two points.

C. The graph is of two lines that intersect at a single point.

D. The graph is of two lines that coincide.

8. Graph the inequality y = –3.

A.

B.

C.

D.

9. Aunt Jane’s Pies had a tent at the county fair. Unfortunately their cash register broke, so they have no

receipts. They know from counting their left over paper plates that they made 413 sales. They know from

the cash box that they made $2,243. If they only sell two kinds of items at the fair tent, a piece of pie for

$4 and pie á là mode for $7, help them figure out how many of each kind they sold.

A. They sold 216 pieces of pie and 197 pies á là mode.

B. The system of equations is inconsistent, and therefore their plate counting or money counting must have an error.

C. They sold 610 pieces of pie and 4683 pies á là mode.

D. They sold 355 pieces of pie and 58 pies á là mode.

10. Graph the inequality 3x = –4y – 4.

A.

B.

C.

D.

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

values of D, D

A. D = 62, D

x

x

, and D

= –20, D

= 29

B. D = 62, D

x

= 20, D

= 28

C. D = 58, D

x

= 20, D

y

y

y

= –28

D. D = 58, D

x

= –20, D

= –29

y

y

?

12. Solve the equation |6x + 3| = 15

A. x = –3

B. x = 2

C. x = –3 or x = 2

D. x = 4

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

A.

B.

C.

D.

15. 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. multiplication and addition, zeros in its final column

B. the coefficient matrix, an inverse

C. the coefficient matrix, Gaussian elimination

D. elementary row operations, zeros below the diagonal

16. Solve the inequality –6 = 6x < 24. Give the result in set notation and graph it.

A.

B.

C.

D.

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

A. closed

B. dashed

C. open

D. solid

18. Solve the system of equations 2x – 2y – 2z = 3, x + 4y – z = 2, and –2x – 8y + 2z = –4.

A. There is no solution.

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

C. There is one solution, (0.1, 0.1, –1.5).

D. There are infinitely many solutions, of the form (x, 0.1, x -1.6).

19. Find the equation of the boundary line in the graph below. Then give the inequality represented by the

shaded area.

A.

B.

C.

D.

20. What is the formula for the determinant of a 3 x 3 matrix ?

A.

B.

C.

D.

21. Are the two equations –6 + y = 2x and 2y – 4x = 12 dependent?

A. Yes, because they have the same graph.

B. No, because the equations are not written the same.

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

D. No, because they are not parallel.

22. Graph the solution set of

x + 2y = 3

x + 2y = 4

A.

B.

C.

D.

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

A.

B.

C.

D.

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

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

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

D. There is no possibility for a collision.

25. 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).

Exam: 050292RR – Polynomials and Polynomial Functions

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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 a

A. (a – b)(a – 4)

B. Prime

C. (a + b)(a + 4)

D. (a + b)(a – 4)

2. Simplify the expression 2ab

A. ab

B. 2a

C. a

D. 0

2

4

2

b

– 2a

b

8

8

2

b

– 3a

– a

2

b

2

4

8

b

4

– 2a

4

b

4

3. Find the product of –3a

A. 14a

B. 12a

C. –6b

D. –6b

5

5

4

5

b

b

4

4

– 6b

– 6a

+ 12a

+ 14a

6

5

5

3

b

b

b

3

4

5

4. Solve the equation 3z

A. z = 0, z = 10, and z = –10

B. z = 0

C. Prime

D. z = –4 and z = 1

3

3

4

b(2a

– 3a

0

b

4

– 300z = 0.

2

2

+ 4b – ab – 4a.

b

2

– 4a

– ab

2

b

3

5. Completely factor the expression 7(x – y) – z(x – y).

A. (x – y)(7 + z)

B. Prime

C. (x – y)(7 – z)

D. (x – y)

2

(7 – z)

3

)

4

+ a

2

b

2

.

6. Find the product of (x – 2y)

A. x

B. x

C. x

D. x

2

2

2

2

+ 4xy + 4y

+ 4y

2

– 4xy + 4y

+ 2xy + 4y

2

2

2

2

.

7. Find the product of (2a + 3b)(2a – 3b).

A. 2a

B. 4a

C. 4a

D. 4a

2

2

2

2

– 3b

– 9b

– 6b

2

2

2

+ 12ab – 9b

2

8. Completely factor the expression 2a

A. Prime

B. 2(a – 4)(a

2

+ 4a + 16)

C. 2(a

3

– 64)

D. 2(a – 4)

3

9. Solve the equation x

A. x = 15 and x = 30

B. x = –9 and x = 5

C. No solution

D. x = 9 and x = –5

2

+ 4x – 45 = 0.

10. Completely factor the expression y

A. Prime

B. (y – 7)(y – 5)

C. (y + 7)(y – 5)

D. (y + 7)(y + 5)

11. Completely factor the expression 48u

A. 3u

2

v

2

(16u

2

v

2

– 6 – u

)

B. 3(16u

4

v

4

– 6u

2

v

2

– u

)

C. u

2

v

2

(48u

2

v

2

– 18 – 3u

)

D. Nonfactorable

6

8

v

v

6

3

5

v

3

12. Simplify the expression –2(4y

A. –21z

3

– 2y

2

– 1

2

3

2

+ 3z

– 128.

+ 12y + 35.

3

4

v

4

– 18u

+ 5) + 3(2y

2

v

2

2

– 3u

– 5z

8

3

v

5

.

+ 3).

B. 9z

3

– 14y

2

+ 19

C. –14y

2

z

3

+ 6y

2

– 1

D. 21z

3

+ 2y

2

+ 1

13. Completely factor the expression 16x

A. (4x

2

– 9y

2

)(4x

2

+ 9y

)

B. Prime

C. 0

D. (2x + 3y)(2x – 3y)(4x

2

2

+ 9y

)

2

14. Completely factor the expression 16t

A. Prime

B. 2t(8t – 25t + 18)

C. 2t(8t – 9)(t – 2)

D. 2t(8t + 9)(t + 2)

15. Completely factor the expression r

A. r(r – 2) + 1

B. (r + 1)(r – 1)

C. (r – 1)(r – 1)

D. Prime

2

4

3

– 81y

– 50t

– 2r + 1.

4

2

.

+ 36t.

16. Perform the indicated operations on the expression below.

(5a

3

A. 3a

+ 3a – 2) – (4a

B. 20a

C. a

3

6

– 7

3

+ 3a

+ a

2

+ 3

D. a

3

– a

2

2

– 10

+ 3a – 7

3

+ a

2

+ 5)

17. Completely factor the expression 4q

A. 4q(q + 27r)

B. 27r

4

(4q

2

+ 1)

C. 31q

2

D. Prime

r

4

18. Graph the polynomial function f(x) = x

2

+ 27r

3

4

– 1.

.

A.

B.

C.

D.

19. Solve the equation

A.

B.

C.

D.

20. Find the value of the expression 2xy – x

A. 24

B. 6

C. –24

D. 0

Exam: 050293RR – Rational Expressions

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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. Perform the indicated operations and simplify the following expression:

A.

B.

C.

D.

2. Factor and simplify .

A.

B.

C. It is already fully simplified.

D.

3. Simplify .

A. –a

B. –a

C. –a

D. –a

4

4

8

8

b

b

b

b

3

–7

–7

3

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. Simplify the expression

A.

B.

C.

D.

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

A.

B.

C.

D.

10. Simplify the following expression:

A.

B.

C.

D.

11. Solve the following equation:

A. y = –3

B. y = 3

C. y = 4

D. y = –4

12. 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. 256 candela-square-feet

B. 128 candela-square-feet

C. 32 candela-square-feet

D. 2 candela-square-feet

13. Solve the following equation:

A. z = 6

B. z = 4

C. z = –6

D. z = –4

14. Solve this proportion for the variable:

A. x = –7

B. x = 10

C. x = –10

D. x = 7

15. Which sum yields ?

A.

B.

C.

D.

16. Divide the following expression:

(x

2

+ 10x + 21) ÷ (x + 7)

A. x + 5

B. x – 2

C. x

2

+ 3

D. x + 3

17. Solve the following equation:

A. t = 2

B. t = –1

C. t = 1

D. { }

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

A.

B.

C.

D.

19. Simplify the expression

A.

B.

C.

D.

20. Find the result of the polynomial division (3x

A.

B.

C.

D.

Exam: 050294RR – Radicals and Rational Exponents

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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

1. Which expression has the same value as 25½?

A.

B.

C.

D.

2. Solve for x.

A. x = 2 or x = 8

B. x = 4 or x = –4

C. x = 2

D. The two solutions for are complex numbers.

3. Simplify by rationalizing the denominator.

A.

B.

C.

D.

4. Simplify .

A.

B.

C.

D.

5. Solve for x.

A. 50

B. 4

C. –41

D. 40

6. Simplify .

A.

B.

C.

D.

7. Which of these expressions is in simplified form?

A.

B.

C.

D.

8. 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 and the standard deviation is approximately 5.6252.

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

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

9. Expand and simplify. Assume c = 0 and d = 0.

A.

B.

C.

D.

10. Simplify (6 – i)(2 + i).

A. 13 + 4i

B. 13 – 8i

C. 11 + 8i

D. 11 + 4i

11. Which of the following best describes imaginary numbers?

A. They are the complex numbers.

B. They are the values of expressions of the form for various real numbers a, as long as a ≠ 0.

C. They are not numbers, but are useful in solving equations.

D. They consist of two values, the principal imaginary number i and its negative –i.

12. Expand and simplify. Assume y = 0.

A.

B.

C.

D.

13. Simplify i

A. i

B. 1

C. –i

D. –1

23

.

14. Which of these expressions simplifies to ?

A.

B.

C.

D.

15. Which of these radical expressions simplifies to x?

A.

B.

C.

D.

16. Combine like radicals in .

A.

B.

C.

D.

17. Which of these phrases best describes the standard deviation?

A. It is a radical expression using n variables.

B. It is a measure of variability.

C. It is equal to the mean squared.

D. It increases as more measurements are taken.

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

D. Yes, as the distance formula indicates.

19. Compute the value of .

A.

B.

C.

D.

20. Which of these points is 5 units away from the point (6, –1)?

A.

B.

C.

D.

21. Solve for x.

A.

B.

C.

D.

22. Choose the best description of the radical expression .

A. It is in simplified form.

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

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

D. It can be simplified to –3.

23. Rationalize the denominator of .

A.

B.

C.

D.

24. Simplify .

A.

B.

C.

D.

25. Rationalize the denominator of assuming x = 0 and y = 0.

A.

B.

C.

D.

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