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118 Intermediate Algebra
Fall 2018
Intermediate Algebra - 40428 - FNMT 118 - 122
Time: 6:30 - 9:35 pm, Thursday
Room 228
SYLLABUS
Catalog description. Real numbers, polynomials, rational expressions, algebraic expressions, linear equations and inequalities in one variable, absolute value equations and inequalities, linear equations in two variables, graphs of lines, systems of linear equations in two variables, quadratic equations in one variable, problem solving. A Departmental Exam is required with no calculators allowed. Prerequisite: FNMT 017 , or FNMT 118 (or higher) placement. Learning Outcomes.
Upon successful completion of this course, students will be able to:
1. Add, subtract, multiply, divide and factor polynomials 2. Add, subtract, multiply, divide and reduce rational expressions 3. Solve linear equations and inequalities in one variable 4. Solve absolute value equations in one variable 5. Graph linear equations and determine equations of lines 6. Solve 2 x 2 linear systems 7. Solve quadratic equations in one variable
Book: Intermediate Algebra by K. Elayn Martin-Gay, Custom edition for the Community College of Philadelphia. Web Resource: www.coursecompass.com . You will get the ID for this web resource when you buy the book. The complete procedure how to access the Web Resource is described in your book in the message to the Students. Instructor: Dr. Arkady Kitover. Email: (the best way to contact me) akitover@ccp.edu or
akitover@hotmail.com Web Page: http://faculty.ccp.edu/FACULTY/akitover The web page contains the syllabus for this course and practice tests. Office: 327 Office hours: TR 5 pm - 6:25 pm, W 5 pm – 6 pm
Course Outline:
Week # Sections Topics and Homework 1
1.1-1.4 Real Numbers (1.1-1.4) . Recommended Homework: Chapter 1 Test, p. 47
2
2.1-2.3 Equations. Recommended Homework: Chapter 2 Test, p. 116 Problems 1-6, 11-13, and 23 -28
3
2.4-2.6
Linear Inequalities; Equations and Inequalities with absolute value. Recommended Homework: Chapter 2 Test, p. 116 Problems 7-10 and 14 – 22. Review 1
4
3.1-3.3 Exam #1 (on Chapters 1 and 2). Begin: Graphs and Functions Recommended Homework: Chapter 3 Test, p. 202 Problems 1-5 and 22-23.
5
3.4 - 3.5 Equations of Straight Lines; Functions and Relations. Recommended Homework: Chapter 3 Test, p. 202 Problems 6,7, and 10 -18.
6
4.1 and 4.3 Systems of Linear Equations. Recommended Homework: Chapter 4 Test, p. 256 (except Problems 10 and 15) Review 2
7
5.1-5.2 Exponents and scientific notation. Recommended Homework: Chapter 5 Test, p. 338 Problems 1-8. Exam #2 (on Chapters 3 and 4)
8
5.3-5.7 Polynomials. Adding, subtracting, and multiplying polynomials. Dividing and Factoring Polynomials. Recommended Homework: Chapter 5 Test, p. 338 Problems 9 – 24.
9
5.8, 6.1, and 6.2 Polynomials: factoring and solving equations Begin: Rational Expressions. Recommended Homework: Chapter 5 Test, p. 338 Problems 25 – 29. Chapter 6 Test, p. 375 Problems 1-14.
10
6.3-6.6 Rational expressions. Review 3 Recommended Homework: Chapter 6 Test, p. 413 Problems 14-26.
11
7.1, 7.2 Begin: Radical Expressions Exam #3 (on Chapters 5 and 6) Recommended Homework: Chapter 7 Test, p. 478 Problems 1-8.
12
7.3-7.6
Radical Exponents, Radicals and Radical Equations Recommended Homework: Chapter 7 Test, p. 478 Problems 11-24, 31, and 32.
13
8.2 Solving Quadratic Equations by Using the Quadratic Formula. Recommended Homework: Chapter 8 Test, p. 541 Problems 1-7.
14
Review Only Review for the Final Exam
15
Exam Only Final Exam
Tests and Grading: Three tests in class – 100 points each. Cumulative final – 100 points. The final will be administered in a computer room. The details about the final will be posted by the department later in the semester. You will be able to access a practice test for the final approximately 9 weeks after the semester starts. A: 90 -100 % (360 – 400) B: 80 – 89 % (320 – 359) C: 70 – 79% (280 – 319) D: 60 – 69% (240 – 279) F: 0 – 59%(0 – 239) All students must take the FNMT Departmental examination. The FNMT Departmental examination shall count for at least 25% of each student’s final grade.
A student who does not take the Departmental Final Exam may only be assigned a grade of F or I (Incomplete). A student cannot receive any other grade (A, B, C or D) without taking the Departmental Final Exam. If a student, for a legitimate reason, does not take the final exam, his/her make-up exam should be scheduled with the FNMT Department Head, Dr. Gail Dixon.
Calculators are not allowed on the final exam. The final exam shall combine multiple choice problems and open answer
problems. Class Rules: The students must attend all classes. Students missing an equivalent of two weeks without a valid reason will be dropped from the class. No food in the classroom. You may not use electronic devices in the classroom for the purposes unrelated to the class material (texting, surfing the web, et cetera). I will subtract 10 points from your total sum of points for every violation of this rule. Put your cell phones in the vibration mode before the class starts. No use of cell phones is allowed during the tests.
118 Intermediate algebra
Review 1
Find the value of the algebraic expression at the given replacement value.
1) The algebraic expression 3.9x gives the total weight in pounds of x tents of a certain type. Find the
total weight of 9 tents.
A) 12.9 lb B) 351 lb C) 3.51 lb D) 35.1 lb
1)
List all the elements of B that belong to the given set.
2) B = 6, 6, -16, 0, 4
5, -
5
4, 4.2, 9
Integers
A) 6, 0, 9 B) 6, -16, 0 C) 6, 0 D) 6, -16, 0, 9
2)
Find the value.
3) -|18|
A) -18 B) -36 C) 18 D) 0
3)
Find the opposite of the number.
4) - 11
6
A)6
11B)
11
6C) -
6
11D) -
11
6
4)
Write the phrase as a variable expression. Use x to represent ʺa number.ʺ
5) 9 more than 7 times a number
A) 7(9 + x) B) 7x + 9 C) 9x + 7 D) 16x
5)
Add or subtract as indicated.
6)1
9 - -
1
3
A)4
9B) -
4
9C)
2
9D) -
2
9
6)
Multiply or divide as indicated.
7) - 4
5 ÷ -
7
10
A) - 14
25B)
7
8C) -
8
7D)
8
7
7)
1
Evaluate.
8) - 1
2
4
A)1
4B)
1
16C) -
1
4D) -
1
16
8)
Find the indicated root.
9) - 1
16
A) - 1
7B) -
1
4
C) - 1
32D) not a real number
9)
Simplify the expression.
10)|5(-4)| - |1 - 11|
-16
A)5
8B)
15
8C) -
5
8D) -
15
8
10)
Find the value of the algebraic expression at the given replacement value.
11)y - 7x
2x + xywhen x = -2, y = 3
A)11
10B) -
9
5C) -
17
10D) -
11
2
11)
Solve the problem.
12) If c is degrees Celsius, the algebraic expression 1.8c + 32 represents the equivalent temperature in
degrees Fahrenheit. Find the Fahrenheit temperature when c = 95.
A) 203° F B) 139° F C) 71° F D) 35.4° F
12)
Write the sentence using mathematical symbols.
13) The difference of twice x and 3 is less than or equal to 11.
A) 2x - 3 ≥ 11 B) 3 - 2x ≤ 11 C) 2x - 3 ≤ 11 D) x - 2 · 3 ≥ 11
13)
Find the opposite (or additive inverse) of the number.
14) -22
A) -22 B) - 1
22C) 0 D) 22
14)
Write the reciprocal (or multiplicative inverse) of the number if it exists.
15)7
4
A)4
7B) -
4
7C) 1 D) -
7
4
15)
2
Use a commutative property to write an equivalent expression.
16)23
14 · x
5
A)23
14 · x
5B)
x
5 · 23
14C)
x
23 ·
5
14D)
5
14 ·
x
23
16)
Use an associative property to write an equivalent expression.
17) (2 · 14) · 22
A) 2 · (14 · 22) B) 22 · (2 · 14) C) (2 · 14) · 22 D) (14 · 2) · 22
17)
Use the distributive property to find the product.
18) -(s - 2y)
A) s - 2y B) -s - 2y C) s + 2y D) -s + 2y
18)
Write the following as an algebraic expression.
19) If 6x is an even integer, represent the next even integer as an expression in x.
A) 12x B) 6x + 2 C) 6x + 1 D) 8x
19)
Simplify the expression.
20) -14 - (6y - 4)
A) -6y - 10 B) -6y - 18 C) -6y + 10 D) -6y + 18
20)
21) 4(6x2 - 2) - 3(x2 - 3)
A) 21x2 - 5 B) 21x2 - 17 C) 12x2 + 1 D) 21x2 + 1
21)
22) 5.5x - 1.9 - 3.6x + 7 + 2.7x
A) 4.6x + 8.9 B) 4.6x - 5.1 C) 4.6x + 5.1 D) 11.8x + 5.1
22)
23)1
3(15x - 3) -
1
8(72x - 9y)
A) -4x + 1
8y B) -4x +
9
8y - 1 C) 4x +
1
8y D) 4x +
9
8y - 1
23)
24) The of a number a is -a.
A) reciprocal B) opposite C) inequality D) absolute value
24)
25) The numbers 0, 1, 2, 3, ... are called numbers
A) exponent B) whole C) variable D) real
25)
Solve the equation.
26) -51 = -9x - 6
A) -36 B) -32 C) 5 D) 11
26)
27) x(7x - 5) + 4 = 7x(x - 4) + x
A) - 4
23B) 6 C) - 2 D) -
2
11
27)
3
28) - 1
8(x - 16) -
1
8(x - 8) = x + 5
A) - 16
5B) -
8
5C) -
32
5D) -
24
5
28)
Solve.
29) The sum of three consecutive even integers is 318. Find the integers.
A) 104, 106, 108 B) 106, 108, 110 C) 102, 104, 106 D) 105, 106, 107
29)
Solve the formula for the specified variable.
30) S = 2πrh + 2πr2 for h
A) h = S
2πr - 1 B) h = S - r C) h = 2π(S - r) D) h =
S - 2πr2
2πr
30)
Solve the inequality. Write the solution set in interval notation and graph the solution set.
31) 3z - 1 ≥ 2z + 4
A) (5, ∞)
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
B) (-∞, 5]
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
C) [5, ∞)
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
D) (3, ∞)
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
31)
Write the solution set using interval notation.
32) 15(14x + 1) > 15
A)1
210, ∞ B)
1
210, ∞ C) (0, ∞) D) [0, ∞)
32)
List the elements of the set.
33) If A = {7, 8, 9, 12} and B = {5, 7, 8, 10}, list the elements of A ∩ B.
A) { } B) {5, 9, 10, 12}
C) {7, 8} D) {5, 7, 8, 9, 10, 12}
33)
4
Solve the compound inequality. Graph the solution set.
34) 7x < 35 and x + 7 > 4
A) [-3, 5]
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
B) (-∞, -3) ∪ (5, ∞)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
C) (-3, 5)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
D) ∅
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
34)
List the elements of the set.
35) If A = {x|x is an even integer} and B = {-11, -9, -7, -5}, list the elements of A ∪ B.
A) {x|x is an even integer}
B) { }
C) {x|x is an even integer or x = -11 or x = -9 or x = -7 or x = -5}
D) {-11, -9, -7, -5}
35)
Solve the compound inequality. Graph the solution set.
36) 9x - 6 < 3x or -2x ≤ -6
A) (-∞, 1) ∪ [3, ∞)
1 2 3 4 5 6 7 81 2 3 4 5 6 7 8
B) [1, 3]
1 2 3 4 5 6 7 81 2 3 4 5 6 7 8
C) (1, 3)
1 2 3 4 5 6 7 81 2 3 4 5 6 7 8D) ∅
-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3
36)
Solve the absolute value equation.
37)5x + 10
2 = 5
A) 4, 0 B) -4, 4 C) -4, 0 D) ∅
37)
5
38) |7x - 5| = |-6 - 8x|
A) - 1
15, 11 B) -
1
15, - 11 C) -
1
15D) ∅
38)
Solve the inequality. Graph the solution set.
39) |2k + 7| + 9 < 13
A) -∞, - 11
2 ∪ -
3
2, ∞
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
B) - 11
2, -
3
2
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
C) -∞, - 11
2
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
D) -∞, - 3
2
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
39)
6
40) |5k + 9| - 1 > 4
A) - 14
5, -
4
5
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
B) -∞, - 14
5 ∪ -
4
5, ∞
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
C) - 4
5, ∞
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
D) -∞, - 14
5 ∪ -
4
5, ∞
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
40)
7
Answer KeyTestname: REVIEW 1
1) D
2) D
3) A
4) B
5) B
6) A
7) D
8) B
9) B
10) C
11) C
12) A
13) C
14) D
15) A
16) B
17) A
18) D
19) B
20) A
21) D
22) C
23) B
24) B
25) B
26) C
27) D
28) B
29) A
30) D
31) C
32) C
33) C
34) C
35) C
36) A
37) C
38) B
39) B
40) B
8
Review 2
Determine the coordinates of the indicated point on the graph.
x-5 5
y
5
-5
C
F
A BD
E
G
HI
JK
L
M
x-5 5
y
5
-5
C
F
A BD
E
G
HI
JK
L
M
1) G
A) (-3, 0) B) (0, 3) C) (0, -3) D) (3, 0)
1)
Name the quadrant or axis in which the point lies.
2) (9, -3)
A) quadrant I B) quadrant II C) quadrant III D) quadrant IV
2)
Plot the point.
3) (-5, 4)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
A)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
B)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
3)
1
C)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
D)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
Determine whether the ordered pair is a solution of the given equation.
4) y = -4x - 6; (-2, 14)
A) No B) Yes
4)
Graph the equation.
5) -9x - y = -4
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
5)
2
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Find the domain and range.
6) {(-8, -2), (-4, 1), (11, -5), (-6, -1), (12, 4)}
A) domain = {12, 4, -5, -2, -4}; range = {-6, 1, -1, 11, -8}
B) domain = {1, -8, -5, 11, -2}; range = {-6, -1, 12, 4, -4}
C) domain = {4, -2, 1, -1, -5}; range = {12, -8, -4, -6, 11}
D) domain = {-8, -4, 11, -6, 12}; range = {1, -5, -1, 4, -2}
6)
Find the domain and the range of the relation. Then determine whether the relation is a function.
7)
Input: Output:
patient allergy
Alice
Brad
Carl
fur
dust
milk
A) domain: {Alice, Brad, Carl}
range: {fur, dust, milk}
function
B) domain: {Alice, Brad, Carl}
range: {fur, dust, milk}
not a function
C) domain: {fur, dust, milk}
range: {Alice, Brad, Carl}
function
D) domain: {fur, dust, milk}
range: {Alice, Brad, Carl}
not a function
7)
3
Use the vertical line test to determine whether the graph is the graph of a function.
8)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A) function B) not a function
8)
Find the domain and the range of the relation. Use the vertical line test to determine whether the graph is the graph of a
function.
9)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A) domain: [-4, 4]
range: [-9, 9]
not a function
B) domain: [-9, 9]
range: [-4, 4]
not a function
C) domain: [-4, 4]
range: [-9, 9]
function
D) domain: [-9, 9]
range: [-4, 4]
function
9)
Find the indicated value.
10) Find f(-6) when f(x) = -4.8(x + 5.3)
A) 33.9 B) 3.36 C) 3.16 D) 34.1
10)
Solve.
11) The monthly cost of a certain long distance service is given by the linear function C(t) = 0.04t + 9.95
where C(t) is in dollars and t is the amount of time in minutes called in a month. Find the cost of
calling long distance for 80 minutes in a month.
A) $12.15 B) $3.20 C) $17.95 D) $13.15
11)
4
Graph the function by finding x- and y-intercepts.
12) x + 3y = 15
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
12)
5
Graph the equation.
13) y + 2 = 0
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
13)
6
14) x + 4 = 0
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
14)
Find the slope of the line that goes through the given points.
15) (5, 0), (0, 3)
A)3
5B) -
5
3C) -
3
5D)
5
3
15)
Find the slope of the line.
16) 3x + 2y = 13
A) - 3
2B)
2
3C)
13
2D)
3
2
16)
7
Solve the problem.
17) When a tow truck is called, the cost of the service is given by the linear function y = 3x + 80, where
y is in dollars and x is the number of miles the car is towed. Find and interpret the slope and
y-intercept of the linear equation.
A) m = 3; The number of miles the car is towed increases 3 miles for every dollar spent on the
service. b = 80; The tow truck will tow the car 80 miles for no cost.
B) m = 3; The cost of the service increases $3 every mile the car is towed. b = 80; The cost of the
service is $80 if the car is not towed.
C) m = 80; The cost of the service increases $80 every mile the car is towed. b = 3; The cost of
the service is $3 if the car is not towed.
D) m = 80; The number of miles the car is towed increases 80 miles for every dollar spent on the
service. b = 3; The tow truck will tow the car 3 miles for no cost.
17)
Find the slope of the line that goes through the given points.
18) (3, -3), (3, 8)
A)5
6B) 0 C) -
11
6D) undefined
18)
Find the slope of the line.
19) y + 2 = 0
A) 0 B) -2 C) 2 D) undefined
19)
Determine whether the lines are parallel, perpendicular, or neither.
20) f(x) = -6x - 8
g(x) = 6x + 7
A) parallel B) perpendicular C) neither
20)
Solve the problem.
21) Find the slope of a line perpendicular to the line -5x - 6y = 3.
A) 3 B)6
5C) undefined D) -
6
5
21)
Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y -intercept.
22) Slope 2
5; y-intercept (0, 1)
A) y = - 5
2x + 1 B) y =
2
5x + 1 C) y = -
5
2x - 1 D) y =
2
5x - 1
22)
Find an equation of the line. Write the equation in standard form.
23) Through (9, -28) and (1, 4)
A) x - 4y = 8 B) 4x + y = 8 C) x + 4y = 8 D) -4x + y = 8
23)
Find an equation of the line. Write the equation using function notation.
24) Through (3, -4); perpendicular to x + 5y = -5
A) f(x) = 5x - 11 B) f(x) = 1
5x -
23
5
C) f(x) = 5x - 19 D) f(x) = - 1
5x -
23
5
24)
8
Find an equation of the line. Write the equation in standard form.
25) Through (3, 3); parallel to 9x + 2y = 2
A) 9x + 2y = 33 B) 2x + 9y = 33 C) 2x - 9y = 33 D) 9x - 2y = 33
25)
Determine whether the ordered pair is a solution of the system of linear equations.
26) (4, -6), x + y = -10
x - y = 2
A) Yes B) No
26)
Solve the system by graphing.
27)
x - y = -1
x + 2y = -13
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A) (-5, 4) B) (-4, 5) C) (-4, -5) D) (-5, -4)
27)
28)
4y + 4 = 0
x - 3y = -1
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A) (-1, -4) B) (-4, -1) C) (-1, 4) D) (-4, 1)
28)
Solve the system of equations.
29)
x + y = -2
y = -3x
A) (-1, 3) B) (1, 3) C) (1, -3) D) (-1, -3)
29)
9
30)
x - 2y = 3
-6x - 3y = -63
A) (-9, 4) B) (8, 4) C) (9, 3) D) ∅
30)
31)
x - 5y = -34
2x - 5y = -28
A) (8, 6) B) (6, 8) C) (-8, 6) D) ∅
31)
32)
1
x + y = 35
6
x + y = 65
A)1
6, -29 B) -
1
6, -29 C) 29,
1
6D)
1
6, 29
32)
Solve.
33) One number is 1 less than a second number. Twice the second number is 4 less than 3 times the
first. Find the two numbers.
A) 5 and 6 B) 6 and 7 C) -7 and -6 D) 7 and 8
33)
34) Two cars leave a city and head in the same direction. After 6 hours, the faster car is 18 miles ahead
of the slower car. The slower car has traveled 282 miles. Find the speeds of the two cars.
A) 30 mph and 33 mph B) 49 mph and 52 mph
C) 44 mph and 47 mph D) 47 mph and 50 mph
34)
35) The manager of a bulk foods establishment sells a trail mix for $7 per pound and premium
cashews for $15 per pound. The manager wishes to make a 480-pound trail mix-cashew mixture
that will sell for $8 per pound. How many pounds of each should be used?
A) 420 pounds of trail mix
60 pounds of cashews
B) 60 pounds of trail mix
420 pounds of cashews
C) 240 pounds of trail mix
240 pounds of cashews
D) 270 pounds of trail mix
210 pounds of cashews
35)
36) A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 5 bags of potato
chips for $8.00. Another customer buys 3 hot dogs and 3 bags of potato chips for $7.50. Find the
cost of each item.
A) $1.50 for a hot dog; $1.00 for a bag of potato chips
B) $1.00 for a hot dog; $1.50 for a bag of potato chips
C) $1.50 for a hot dog; $1.25 for a bag of potato chips
D) $1.75 for a hot dog; $1.25 for a bag of potato chips
36)
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
37) C(x) = 2000x + 33,000
R(x) = 5000x
A) 11 units B) 13 units C) 12 units D) 5 units
37)
10
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars.
Use the information in the figure to answer the question.
38) How many binoculars must be produced and sold for the company to break even?
A) 1500 binoculars B) 750 binoculars C) 2700 binoculars D) 2250 binoculars
38)
39) At the break-even point both cost and revenue are what?
A) $2700 B) $1500 C) $2250 D) $750
39)
Fill in the blank with one of the words or phrases listed below.
matrix consistent system of equations
solution inconsistent square
40) A(n) system of equations has at least one solution.
A) consistent B) inconsistent C) matrix D) square
40)
11
Answer KeyTestname: REVIEW 2
1) A
2) D
3) C
4) A
5) B
6) D
7) B
8) B
9) B
10) B
11) D
12) C
13) B
14) B
15) C
16) A
17) B
18) D
19) A
20) C
21) B
22) B
23) B
24) C
25) A
26) B
27) D
28) B
29) C
30) C
31) B
32) D
33) B
34) D
35) A
36) A
37) A
38) B
39) C
40) A
12
Review 3
Simplify. Write the answer with positive exponents.
1) 45 · 47
A) 1635 B) 435 C) 1612 D) 412
1)
2) 8x4 · -4x8
A) -32x32 B) 32x32 C) -32x12 D) 32x12
2)
Simplify. Assume that variables in the exponent represent nonzero integers.
3) x2a · x9a · x8a + 2
A) ax144a+2 B) ax19a + 2 C) x144a + 2 D) x19a + 2
3)
Simplify. Write the answer with positive exponents.
4) (-8x)0 - 8x0
A) -9 B) -7 C) -8x + 1 D) -16
4)
5)x9y13
x5y7
A) x3y6 B) x4y6 C) xy6 D) x3y5
5)
6)-40x11y9z4
8x3y3z3
A) -5x8y6 B) x8y6z C) -5x7y5z D) -5x8y6z
6)
Simplify. Assume that variables in the exponent represent nonzero integers.
7)x5a + 7 · x3a
xa
A) x9a B) x7a + 7 C) x2a + 7 D) x15a
7)
Simplify. Write the answer with positive exponents.
8)1
2-3
A) -8 B)1
8C)
1
6D) 8
8)
9)x-7
x-9
A)1
x2B) x2 C) -
1
x2D) -x2
9)
1
10)x-5y7
x-2y-4
A)1
x3y3B)
x3
y3C)
y11
x3D) x3y11
10)
Write the number in scientific notation.
11) In a certain city, the bus system carried a total of 12,700,000,000 passengers.
A) 1.27 × 1010 B) 1.27 × 109 C) 12.7 × 1010 D) 1.27 × 1011
11)
Write the number in standard notation.
12) 5.482 × 10-6
A) 0.000005482 B) 0.00005482 C) -5,482,000 D) 0.0000005482
12)
Simplify. Write the answer with positive exponents.
13) (34)-2
A) -162 B)1
6561C)
1
729D) -24
13)
14)4x4y2
z4
3
A)4x12y6
z12B)
64x7y5
z7C)
4x12y6
z7D)
64x12y6
z12
14)
Perform the indicated operations.
15) (9x5 + 9x4 + 9x3 - 4) - (5x5 - 6x4 - 2x3 + 6)
A) 14x5 + 3x4 + 7x3 - 10 B) 4x5 + 15x4 + 11x3 - 10
C) 14x5 + 3x4 + 7x3 + 2 D) 4x5 + 3x4 + 7x3 + 2
15)
Multiply.
16) (4y + 11)(3y2 - 2y - 7)
A) 12y3 + 41y2 + 50y + 77 B) 12y3 - 8y2 - 28y + 11
C) 45y2 - 30y - 105 D) 12y3 + 25y2 - 50y - 77
16)
17) (8x - 9y)2
A) 8x2 + 81y2 B) 64x2 + 81y2
C) 64x2 - 144xy + 81y2 D) 8x2 - 144xy + 81y2
17)
Simplify. Write the answer with positive exponents.
18)xy4
x3y
-2
A)1
x8y10B)
y6
x4C)
x4
y6D)
1
x5y9
18)
2
19)3-1x-4y-4
z-2
-4
A)z8
81x16y16B)
81x16y16
z8C)
z8
3x16y16D)
3x16y16
z6
19)
Perform the indicated operation. Write the answer in scientific notation.
20)270,000,000,000
0.000003
A) 24 × 1015 B) 24 × 1016 C) 9 × 1015 D) 9 × 1016
20)
Solve. Write the answer in scientific notation.
21) If the mass of an object is 2.45116 × 10-8 tons and its density is 4.66 × 10-7 tons per cubic foot, find
the volume of this object. (Use the formula D = M
V.)
A) 52.6 × 10-2 cubic feet B) 5.26 × 10-1 cubic feet
C) 5.26 × 10-3 cubic feet D) 5.26 × 10-2 cubic feet
21)
Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
22) -8x2 + 8x2y + 7
A) degree 2; trinomial B) degree 5; trinomial
C) degree 3; trinomial D) degree 2; none of these
22)
Perform the indicated operations.
23) - 2
3x2 -
2
5x +
1
3 +
1
3x2 -
4
5x +
1
2
A) - 1
3x4 -
6
5x2 +
5
6B) -
1
3x2 -
6
5x -
5
6
C) - 23
15x6 +
5
6D) -
1
3x2 -
6
5x +
5
6
23)
Multiply.
24) (x2 + 12y)(x2 - 12y)
A) x4 - 24y2 B) x4 - 144y2
C) x4 - 24x2y - 144y2 D) x4 + 24x2y - 144y2
24)
25) (x - 3)(x + 1)(4x - 3)
A) 4x3 - 6x2 - 11x + 9 B) 4x3 + 9
C) 4x3 + 11x2 + 6x + 9 D) 4x3 - 11x2 - 6x + 9
25)
Factor the polynomial completely.
26) 24x9y9 - 32x7y5 + 64x3y2
A) 8x3y2(3x6y7 - 4x4y3 + 8) B) x3y2(24x6y7 - 32x4y3 + 64)
C) 8x3(3x6y9 - 4x4y5 + 8y2) D) 8(3x9y9 - 4x7y5 + 8x3y2)
26)
3
27) xy - 4yz + 11x - 44z
A) (y - 4)(x + 11z) B) (y + 4)(x - 11z) C) (y + 11)(x - 4z) D) (y - 11)(x + 4z)
27)
28) x2 - x - 35
A) (x - 35)(x + 1) B) (x - 5)(x + 7)
C) (x + 5)(x - 7) D) prime polynomial
28)
29) 20x2 + 7x - 6
A) (20x + 3)(x - 2) B) (4x + 3)(5x - 2)
C) (4x - 3)(5x + 2) D) prime polynomial
29)
30) 49x3y - 84x2y2 + 36xy3
A) xy(7x - 6y)2 B) (49x2y + xy)(x + 36y2)
C) xy(7x - 6y)(7x + 6y) D) xy(7x + 6y)2
30)
31) 72x2y - 98y
A) 2y(6x + 7)2 B) 2y(6x + 7)(6x - 7)
C) 2y(6x - 7)2 D) prime polynomial
31)
32) 512y3 + 343
A) (512y - 7)(y2 + 56y + 49) B) (8y - 7)(64y2 + 56y + 49)
C) (8y + 7)(64y2 + 56y + 49) D) (8y + 7)(64y2 - 56y + 49)
32)
33) 375x3y - 81y4
A) 3y(125x - 3y)(x2 + 15xy + 9y2) B) 3y(5x + 3y2)(25x2 - 15xy + 9xy2)
C) 3y(5x - 3y)(25x2 + 15xy + 9y2) D) (15xy - 9y2)(25x2 + 9y2)
33)
Solve the equation.
34) x3 - x = -7x2 + 7
A) 1, - 7, 7 B) - 7, 7 C) 49 D) -1, 1, - 7
34)
Solve.
35) Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the
hypotenuse is 6 more than twice the shorter leg.
A) 9 m B) 17 m C) 18 m D) 10 m
35)
Find the domain of the rational function.
36) f(x) = 1 - 6x
x2 - 4x - 32
A) x|x is a real number and x ≠ 8, x ≠ -4, x ≠ 1
6
B) x|x is a real number and x ≠ 8, x ≠ -4, x ≠ 1
6, x ≠ 0
C) {x|x is a real number and x ≠ -8, x ≠ -4}
D) {x|x is a real number and x ≠ 8, x ≠ -4}
36)
4
Simplify the rational expression.
37)x2 + 11x + 30
x2 + 12x + 35
A) - x2 + 11x + 30
x2 + 12x + 35B)
11x + 30
12x + 35C)
11x + 6
12x + 7D)
x + 6
x + 7
37)
Multiply or divide as indicated. Simplify completely.
38)x2 + 8x + 15
x2 + 10x + 21 ·
x2 + 7x
x2 + 9x + 20
A)x2 + 7x
x + 4B)
1
x + 4C)
x
x + 4D)
x
x2 + 10x + 21
38)
39)x2 + 5x - 6
x2 + 9x + 18 ÷
x2 - 1
x2 + 7x + 12
A)x + 4
x - 1B)
x + 1
x + 4C)
x + 4
x + 1D)
x - 1
x + 4
39)
Perform the indicated operation. Simplify if possible.
40)8x2
x - 1 +
-8x
x - 1
A) 8x B)8x
x - 1C) 0 D)
8x(x + 1)
x - 1
40)
Solve the equation.
41)x + 5
x2 + 3x + 2 -
5
x2 + 4x + 4 =
x - 5
x2 + 3x + 2
A) -15 B) -3 C) 3 D) 0
41)
Perform the indicated operation. Simplify if possible.
42)m - 5
m2 - 7m + 6 +
2m + 1
m2 - 5m + 4
A)3m - 4
2m2 - 12m + 10B)
3m2 - 20m + 14
(m + 1)(m + 6)(m + 4)
C) 3m - 4 D)3m2 - 20m + 14
(m - 1)(m - 6)(m - 4)
42)
Divide.
43) (-8x3 + 14x2 - 15x + 3) ÷ (-4x + 1)
A) x2 - 3x + 3 B) 2x2 + 3 C) 2x2 - 3x + 3 D) x2 + 3x - 3
43)
5
Use synthetic division to divide.
44)3x3 + 10x2 + 13x - 14
x - 2
3
A) 3x2 + 8x + 23
3 +
2
3
x - 2
3
B) 3x2 - 12x + 21
C) 3x2 + 12x + 21 - 28
x - 2
3
D) 3x2 + 12x + 21
44)
Solve.
45) One conveyor belt can move 1000 boxes in 10 minutes. Another can move 1000 boxes in 11
minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3
minutes. How long would it take the third conveyor belt alone to do the same job?
A) 71
47 minutes B)
47
330 minute C) 1
157
173 minutes D)
173
330 minute
45)
46) The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the
temperature and inversely as the volume of the gas. If the pressure is 1014 kPa (kiloPascals) when
the number of moles is 8, the temperature is 260° Kelvin, and the volume is 640 cc, find the
pressure when the number of moles is 9, the temperature is 320° K, and the volume is 1080 cc.
A) 1768 B) 780 C) 832 D) 1664
46)
6
Answer KeyTestname: REVIEW 3
1) D
2) C
3) D
4) B
5) B
6) D
7) B
8) D
9) B
10) C
11) A
12) A
13) B
14) D
15) B
16) D
17) C
18) C
19) B
20) D
21) D
22) C
23) D
24) B
25) D
26) A
27) C
28) D
29) B
30) A
31) B
32) D
33) C
34) D
35) D
36) D
37) D
38) C
39) C
40) A
41) B
42) D
43) C
44) D
45) A
46) C
7
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