118 Intermediate Algebra Fall Intermediate Algebra FNMT Time: 6:30-9:35 pm, Thursday. Room 228

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1 118 Intermediate Algebra Fall 2018 Intermediate Algebra FNMT Time: 6:30-9:3 pm, Thursda Room 228

2 SYLLABUS Catalog description. Real numbers, polnomials, rational epressions, algebraic epressions, linear equations and inequalities in one variable, absolute value equations and inequalities, linear equations in two variables, graphs of lines, sstems of linear equations in two variables, quadratic equations in one variable, problem solving. A Departmental Eam 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, multipl, divide and factor polnomials 2. Add, subtract, multipl, divide and reduce rational epressions 3. Solve linear equations and inequalities in one variable 4. Solve absolute value equations in one variable. Graph linear equations and determine equations of lines 6. Solve 2 2 linear sstems 7. Solve quadratic equations in one variable Book: Intermediate Algebra b K. Elan Martin-Ga, Custom edition for the Communit College of Philadelphia. Web Resource: You will get the ID for this web resource when ou bu the book. The complete procedure how to access the Web Resource is described in our book in the message to the Students. Instructor: Dr. Arkad Kitover. (the best wa to contact me) akitover@ccp.edu or akitover@hotmail.com Web Page: The web page contains the sllabus for this course and practice tests. Office: 327 Office hours: TR pm - 6:2 pm, W pm 6 pm

3 Course Outline: Week # Sections Topics and Homework Real Numbers ( ). Recommended Homework: Chapter 1 Test, p Equations. Recommended Homework: Chapter 2 Test, p. 116 Problems 1-6, 11-13, and Linear Inequalities; Equations and Inequalities with absolute value. Recommended Homework: Chapter 2 Test, p. 116 Problems 7- and Review Eam #1 (on Chapters 1 and 2). Begin: Graphs and Functions Recommended Homework: Chapter 3 Test, p. 202 Problems 1- and Equations of Straight Lines; Functions and Relations. Recommended Homework: Chapter 3 Test, p. 202 Problems 6,7, and and 4.3 Sstems of Linear Equations. Recommended Homework: Chapter 4 Test, p. 26 (ecept Problems and 1) Review Eponents and scientific notation. Recommended Homework: Chapter Test, p. 338 Problems 1-8. Eam #2 (on Chapters 3 and 4) Polnomials. Adding, subtracting, and multipling polnomials. Dividing and Factoring Polnomials. Recommended Homework: Chapter Test, p. 338 Problems , 6.1, and 6.2 Polnomials: factoring and solving equations Begin: Rational Epressions. Recommended Homework: Chapter Test, p. 338 Problems Chapter 6 Test, p. 37 Problems Rational epressions. Review 3 Recommended Homework: Chapter 6 Test, p. 413 Problems , 7.2 Begin: Radical Epressions Eam #3 (on Chapters and 6) Recommended Homework: Chapter 7 Test, p. 478 Problems 1-8.

4 Radical Eponents, Radicals and Radical Equations Recommended Homework: Chapter 7 Test, p. 478 Problems 11-24, 31, and Solving Quadratic Equations b Using the Quadratic Formula. Recommended Homework: Chapter 8 Test, p. 41 Problems Review Onl Review for the Final Eam 1 Eam Onl Final Eam

5 Tests and Grading: Three tests in class 0 points each. Cumulative final 0 points. The final will be administered in a computer room. The details about the final will be posted b the department later in the semester. You will be able to access a practice test for the final approimatel 9 weeks after the semester starts. A: 90-0 % ( ) B: % (320 39) C: 70 79% ( ) D: 60 69% ( ) F: 0 9%(0 239) All students must take the FNMT Departmental eamination. The FNMT Departmental eamination shall count for at least 2% of each student s final grade. A student who does not take the Departmental Final Eam ma onl be assigned a grade of F or I (Incomplete). A student cannot receive an other grade (A, B, C or D) without taking the Departmental Final Eam. If a student, for a legitimate reason, does not take the final eam, his/her make-up eam should be scheduled with the FNMT Department Head, Dr. Gail Dion. Calculators are not allowed on the final eam. The final eam 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 ma not use electronic devices in the classroom for the purposes unrelated to the class material (teting, surfing the web, et cetera). I will subtract points from our total sum of points for ever violation of this rule. Put our cell phones in the vibration mode before the class starts. No use of cell phones is allowed during the tests.

6 118 Intermediate algebra Review 1 Find the value of the algebraic epression at the given replacement value. 1) The algebraic epression 3.9 gives the total weight in pounds of tents of a certain tpe. Find the total weight of 9 tents. A) 12.9 lb B) 31 lb C) 3.1 lb D) 3.1 lb 1) List all the elements of B that belong to the given set. 2) B = 6, 6, -16, 0, 4, - 4, 4.2, 9 2) Integers A) 6, 0, 9 B) 6, -16, 0 C) 6, 0 D) 6, -16, 0, 9 Find the value. 3) - 18 A) -18 B) -36 C) 18 D) 0 3) Find the opposite of the number. 4) ) A) 6 11 B) 11 6 C) D) Write the phrase as a variable epression. Use to represent ʺa number.ʺ ) 9 more than 7 times a number A) 7(9 + ) B) C) D) 16 ) Add or subtract as indicated. 6) ) A) 4 9 B) C) 2 9 D) Multipl or divide as indicated. 7) ) A) B) 7 8 C) D) 8 7 1

7 Evaluate. 8) ) A) 1 4 B) 1 16 C) D) Find the indicated root. 9) ) A) B) C) D) not a real number Simplif the epression. (-4) ) -16 ) A) 8 B) 1 8 C) - 8 D) Find the value of the algebraic epression at the given replacement value ) when = -2, = A) 11 B) - 9 C) - 17 D) ) Solve the problem. 12) If c is degrees Celsius, the algebraic epression 1.8c + 32 represents the equivalent temperature in degrees Fahrenheit. Find the Fahrenheit temperature when c = 9. A) 203 F B) 139 F C) 71 F D) 3.4 F 12) Write the sentence using mathematical smbols. 13) The difference of twice and 3 is less than or equal to 11. A) B) C) D) ) Find the opposite (or additive inverse) of the number. 14) -22 A) -22 B) C) 0 D) 22 14) Write the reciprocal (or multiplicative inverse) of the number if it eists. 1) 7 4 1) A) 4 7 B) C) 1 D)

8 Use a commutative propert to write an equivalent epression. 16) A) B) C) D) ) Use an associative propert to write an equivalent epression. 17) (2 14) 22 A) 2 (14 22) B) 22 (2 14) C) (2 14) 22 D) (14 2) 22 17) Use the distributive propert to find the product. 18) -(s - 2) A) s - 2 B) -s - 2 C) s + 2 D) -s ) Write the following as an algebraic epression. 19) If 6 is an even integer, represent the net even integer as an epression in. A) 12 B) C) D) 8 19) Simplif the epression. 20) (6-4) A) -6 - B) C) -6 + D) ) 21) 4(62-2) - 3(2-3) A) B) C) D) ) 22) A) B) C) D) ) 23) 1 3 (1-3) - 1 (72-9) 8 23) A) B) C) D) ) The of a number a is -a. A) reciprocal B) opposite C) inequalit D) absolute value 24) 2) The numbers 0, 1, 2, 3,... are called numbers A) eponent B) whole C) variable D) real 2) Solve the equation. 26) -1 = -9-6 A) -36 B) -32 C) D) 11 26) 27) (7 - ) + 4 = 7( - 4) + 27) A) B) 6 C) - 2 D)

9 28) ( - 16) - 1 ( - 8) = ) A) - 16 B) - 8 C) - 32 D) - 24 Solve. 29) The sum of three consecutive even integers is 318. Find the integers. A) 4, 6, 8 B) 6, 8, 1 C) 2, 4, 6 D), 6, 7 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 - 2πr 2 2πr 30) Solve the inequalit. Write the solution set in interval notation and graph the solution set. 31) 3z - 1 2z ) A) (, ) B) (-, ] C) [, ) D) (3, ) Write the solution set using interval notation. 32) 1(14 + 1) > 1 1 A) 2, B) 1, C) (0, ) D) [0, ) 2 32) List the elements of the set. 33) If A = {7, 8, 9, 12} and B = {, 7, 8, }, list the elements of A B. A) { } B) {, 9,, 12} C) {7, 8} D) {, 7, 8, 9,, 12} 33) 4

10 Solve the compound inequalit. Graph the solution set. 34) 7 < 3 and + 7 > 4 34) A) [-3, ] B) (-, -3) (, ) C) (-3, ) D) List the elements of the set. 3) If A = { is an even integer} and B = {-11, -9, -7, -}, list the elements of A B. A) { is an even integer} B) { } C) { is an even integer or = -11 or = -9 or = -7 or = -} D) {-11, -9, -7, -} 3) Solve the compound inequalit. Graph the solution set. 36) 9-6 < 3 or ) A) (-, 1) [3, ) B) [1, 3] C) (1, 3) D) Solve the absolute value equation. + 37) = 2 A) 4, 0 B) -4, 4 C) -4, 0 D) 37)

11 38) 7 - = ) A) - 1 1, 11 B) - 1 1, - 11 C) D) Solve the inequalit. Graph the solution set. 39) 2k < 13 39) A) -, , B) , C) -, D) -,

12 40) k > 4 40) A) - 14, B) -, , C) - 4, D) -, ,

13 Answer Ke Testname: REVIEW 1 1) D 2) D 3) A 4) B ) B 6) A 7) D 8) B 9) B ) C 11) C 12) A 13) C 14) D 1) A 16) B 17) A 18) D 19) B 20) A 21) D 22) C 23) B 24) B 2) B 26) C 27) D 28) B 29) A 30) D 31) C 32) C 33) C 34) C 3) C 36) A 37) C 38) B 39) B 40) B 8

14 Review 2 Determine the coordinates of the indicated point on the graph. D A B E C M G F - L J H K I - 1) G A) (-3, 0) B) (0, 3) C) (0, -3) D) (3, 0) 1) Name the quadrant or ais 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) (-, 4) 3) A) B)

15 C) D) Determine whether the ordered pair is a solution of the given equation. 4) = -4-6; (-2, 14) A) No B) Yes 4) Graph the equation. ) -9 - = -4 ) A) B)

16 C) D) Find the domain and range. 6) {(-8, -2), (-4, 1), (11, -), (-6, -1), (12, 4)} A) domain = {12, 4, -, -2, -4}; range = {-6, 1, -1, 11, -8} B) domain = {1, -8, -, 11, -2}; range = {-6, -1, 12, 4, -4} C) domain = {4, -2, 1, -1, -}; range = {12, -8, -4, -6, 11} D) domain = {-8, -4, 11, -6, 12}; range = {1, -, -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 allerg 7) Alice Brad Carl fur dust milk A) domain: {Alice, Brad, Carl} range: {fur, dust, milk} function C) domain: {fur, dust, milk} range: {Alice, Brad, Carl} function B) domain: {Alice, Brad, Carl} range: {fur, dust, milk} not a function D) domain: {fur, dust, milk} range: {Alice, Brad, Carl} not a function 3

17 Use the vertical line test to determine whether the graph is the graph of a function. 8) 8) A) function B) not a function 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) 9) 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 Find the indicated value. ) Find f(-6) when f() = -4.8( +.3) A) 33.9 B) 3.36 C) 3.16 D) 34.1 ) Solve. 11) The monthl cost of a certain long distance service is given b the linear function C(t) = 0.04t 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) $12.1 B) $3.20 C) $17.9 D) $ ) 4

18 Graph the function b finding - and -intercepts. 12) + 3 = 1 12) A) B) C) D)

19 Graph the equation. 13) + 2 = 0 13) A) B) C) D)

20 14) + 4 = 0 14) A) B) C) D) Find the slope of the line that goes through the given points. 1) (, 0), (0, 3) 1) A) 3 B) - 3 C) - 3 D) 3 Find the slope of the line. 16) = 13 A) B) 2 3 C) 13 2 D) ) 7

21 Solve the problem. 17) When a tow truck is called, the cost of the service is given b the linear function = , where is in dollars and is the number of miles the car is towed. Find and interpret the slope and -intercept of the linear equation. A) m = 3; The number of miles the car is towed increases 3 miles for ever 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 ever 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 ever 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 ever 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) B) 0 C) D) undefined 18) Find the slope of the line. 19) + 2 = 0 A) 0 B) -2 C) 2 D) undefined 19) Determine whether the lines are parallel, perpendicular, or neither. 20) f() = -6-8 g() = A) parallel B) perpendicular C) neither 20) Solve the problem. 21) Find the slope of a line perpendicular to the line = 3. 21) A) 3 B) 6 C) undefined D) - 6 Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and -intercept. 22) Slope 2 ; -intercept (0, 1) 22) A) = B) = C) = D) = 2-1 Find an equation of the line. Write the equation in standard form. 23) Through (9, -28) and (1, 4) A) - 4 = 8 B) 4 + = 8 C) + 4 = 8 D) -4 + = 8 23) Find an equation of the line. Write the equation using function notation. 24) Through (3, -4); perpendicular to + = - A) f() = - 11 B) f() = 1-23 C) f() = - 19 D) f() = ) 8

22 Find an equation of the line. Write the equation in standard form. 2) Through (3, 3); parallel to = 2 A) = 33 B) = 33 C) 2-9 = 33 D) 9-2 = 33 2) Determine whether the ordered pair is a solution of the sstem of linear equations. 26) (4, -6), + =- - = 2 A) Yes B) No 26) Solve the sstem b graphing. 27) - = =-13 27) A) (-, 4) B) (-4, ) C) (-4, -) D) (-, -4) 28) = 0-3 =-1 28) A) (-1, -4) B) (-4, -1) C) (-1, 4) D) (-4, 1) Solve the sstem of equations. 29) + =-2 =-3 A) (-1, 3) B) (1, 3) C) (1, -3) D) (-1, -3) 29) 9

23 30) - 2 = =-63 A) (-9, 4) B) (8, 4) C) (9, 3) D) 30) 31) - = =-28 A) (8, 6) B) (6, 8) C) (-8, 6) D) 31) 32) 1 + = = 6 32) A) 1 6, -29 B) - 1 6, -29 C) 29, 1 6 D) 1 6, 29 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) and 6 B) 6 and 7 C) -7 and -6 D) 7 and 8 33) 34) Two cars leave a cit 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 2 mph C) 44 mph and 47 mph D) 47 mph and 0 mph 34) 3) The manager of a bulk foods establishment sells a trail mi for $7 per pound and premium cashews for $1 per pound. The manager wishes to make a 480-pound trail mi-cashew miture that will sell for $8 per pound. How man pounds of each should be used? A) 420 pounds of trail mi B) 60 pounds of trail mi 60 pounds of cashews 420 pounds of cashews C) 240 pounds of trail mi 240 pounds of cashews D) 270 pounds of trail mi 2 pounds of cashews 36) A vendor sells hot dogs and bags of potato chips. A customer bus 2 hot dogs and bags of potato chips for $8.00. Another customer bus 3 hot dogs and 3 bags of potato chips for $7.0. Find the cost of each item. A) $1.0 for a hot dog; $1.00 for a bag of potato chips B) $1.00 for a hot dog; $1.0 for a bag of potato chips C) $1.0 for a hot dog; $1.2 for a bag of potato chips D) $1.7 for a hot dog; $1.2 for a bag of potato chips 3) 36) Given the cost function, C(), and the revenue function, R(), find the number of units that must be sold to break even. 37) C() = ,000 37) R() = 000 A) 11 units B) 13 units C) 12 units D) units

24 The figure shows the graphs of the cost and revenue functions for a compan that manufactures and sells binoculars. Use the information in the figure to answer the question. 38) How man binoculars must be produced and sold for the compan to break even? A) 0 binoculars B) 70 binoculars C) 2700 binoculars D) 220 binoculars 38) 39) At the break-even point both cost and revenue are what? A) $2700 B) $0 C) $220 D) $70 39) Fill in the blank with one of the words or phrases listed below. matri consistent sstem of equations solution inconsistent square 40) A(n) sstem of equations has at least one solution. A) consistent B) inconsistent C) matri D) square 40) 11

25 Answer Ke Testname: REVIEW 2 1) A 2) D 3) C 4) A ) B 6) D 7) B 8) B 9) B ) B 11) D 12) C 13) B 14) B 1) C 16) A 17) B 18) D 19) A 20) C 21) B 22) B 23) B 24) C 2) A 26) B 27) D 28) B 29) C 30) C 31) B 32) D 33) B 34) D 3) A 36) A 37) A 38) B 39) C 40) A 12

26 Review 3 Simplif. Write the answer with positive eponents. 1) 4 47 A) 163 B) 43 C) 1612 D) 412 1) 2) A) B) 3232 C) D) ) Simplif. Assume that variables in the eponent represent nonzero integers. 3) 2a 9a 8a + 2 A) a144a+2 B) a19a + 2 C) 144a + 2 D) 19a + 2 3) Simplif. Write the answer with positive eponents. 4) (-8)0-80 A) -9 B) -7 C) D) -16 4) ) A) 36 B) 46 C) 6 D) 3 ) 6) z4 833z3 6) A) -86 B) 86z C) -7z D) -86z Simplif. Assume that variables in the eponent represent nonzero integers. 7) a + 7 3a a A) 9a B) 7a + 7 C) 2a + 7 D) 1a 7) Simplif. Write the answer with positive eponents. 1 8) 2-3 8) A) -8 B) 1 8 C) 1 6 D) 8 9) ) A) 1 2 B) 2 C) D) -2 1

27 -7 ) -2-4 ) A) 1 33 B) 3 3 C) 11 3 D) 311 Write the number in scientific notation. 11) In a certain cit, the bus sstem carried a total of 12,700,000,000 passengers. A) 1.27 B) C) 12.7 D) ) Write the number in standard notation. 12) A) B) C) -,482,000 D) ) Simplif. Write the answer with positive eponents. 13) (34) -2 A) -162 B) C) D) ) 14) 442 z4 3 14) A) z12 B) 64 7 z7 C) z7 D) z12 Perform the indicated operations. 1) ( ) - ( ) A) B) C) D) ) Multipl. 16) (4 + 11)( ) A) B) C) D) ) 17) (8-9)2 A) B) C) D) ) Simplif. Write the answer with positive eponents ) 3 18) A) 1 8 B) 6 4 C) 4 6 D) 1 9 2

28 19) z ) A) z B) z8 C) z D) z6 Perform the indicated operation. Write the answer in scientific notation. 20) 270,000,000, A) 24 1 B) C) 9 1 D) ) Solve. Write the answer in scientific notation. 21) If the mass of an object is tons and its densit is tons per cubic foot, find the volume of this object. (Use the formula D = M V.) 21) A) cubic feet B).26-1 cubic feet C).26-3 cubic feet D).26-2 cubic feet Find the degree of the polnomial and indicate whether the polnomial is a monomial, binomial, trinomial, or none of these. 22) ) A) degree 2; trinomial B) degree ; trinomial C) degree 3; trinomial D) degree 2; none of these Perform the indicated operations. 23) ) A) C) B) D) Multipl. 24) (2 + 12)(2-12) A) B) C) D) ) ( - 3)( + 1)(4-3) A) B) C) D) ) 2) Factor the polnomial completel. 26) A) 832( ) B) 32( ) C) 83( ) D) 8( ) 26) 3

29 27) - 4z z A) ( - 4)( + 11z) B) ( + 4)( - 11z) C) ( + 11)( - 4z) D) ( - 11)( + 4z) 27) 28) A) ( - 3)( + 1) B) ( - )( + 7) C) ( + )( - 7) D) prime polnomial 28) 29) A) (20 + 3)( - 2) B) (4 + 3)( - 2) C) (4-3)( + 2) D) prime polnomial 29) 30) A) (7-6)2 B) (492 + )( + 362) C) (7-6)(7 + 6) D) (7 + 6)2 30) 31) A) 2(6 + 7)2 B) 2(6 + 7)(6-7) C) 2(6-7)2 D) prime polnomial 31) 32) A) (12-7)( ) B) (8-7)( ) C) (8 + 7)( ) D) (8 + 7)( ) 32) 33) A) 3(12-3)( ) B) 3( + 32)( ) C) 3( - 3)( ) D) (1-92)( ) 33) Solve the equation. 34) 3 - = A) 1, - 7, 7 B) - 7, 7 C) 49 D) -1, 1, ) Solve. 3) Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hpotenuse is 6 more than twice the shorter leg. A) 9 m B) 17 m C) 18 m D) m 3) Find the domain of the rational function ) f() = ) A) is a real number and 8, -4, 1 6 B) is a real number and 8, -4, 1 6, 0 C) { is a real number and -8, -4} D) { is a real number and 8, -4} 4

30 Simplif the rational epression. 37) ) A) B) C) D) Multipl or divide as indicated. Simplif completel. 38) ) A) B) C) + 4 D) ) ) A) B) C) D) Perform the indicated operation. Simplif if possible ) ) A) 8 B) 8-1 C) 0 D) 8( + 1) - 1 Solve the equation. + 41) = A) -1 B) -3 C) 3 D) 0 41) Perform the indicated operation. Simplif if possible. m - 42) m2-7m m + 1 m2 - m + 4 3m - 4 A) 2m2-12m + C) 3m - 4 D) B) 3m2-20m + 14 (m + 1)(m + 6)(m + 4) 3m2-20m + 14 (m - 1)(m - 6)(m - 4) 42) Divide. 43) ( ) (-4 + 1) A) B) C) D) )

31 Use snthetic division to divide. 44) ) A) B) C) D) Solve. 4) One conveor belt can move 00 boes in minutes. Another can move 00 boes in 11 minutes. If another conveor belt is added and all three are used, the boes are moved in 3 minutes. How long would it take the third conveor belt alone to do the same job? A) minutes B) minute C) 1 minutes D) minute 4) 46) The pressure of a gas varies jointl as the amount of the gas (measured in moles) and the temperature and inversel as the volume of the gas. If the pressure is 14 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 80 cc. A) 1768 B) 780 C) 832 D) ) 6

32 Answer Ke Testname: REVIEW 3 1) D 2) C 3) D 4) B ) B 6) D 7) B 8) D 9) B ) C 11) A 12) A 13) B 14) D 1) B 16) D 17) C 18) C 19) B 20) D 21) D 22) C 23) D 24) B 2) D 26) A 27) C 28) D 29) B 30) A 31) B 32) D 33) C 34) D 3) D 36) D 37) D 38) C 39) C 40) A 41) B 42) D 43) C 44) D 4) A 46) C 7

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