Please show work, and SKIP PAGES 17 THROUGH 19

MATH 080 Final-Exam Review Revised October 2018 Can you simplify an expression using the order of operations? 1) Simplify 2) Simplify A) 32(11 - 8) - 18 32 - 3 5 - 33 - 3 6+3 5 9 B) 19 9 C) - 25 9 D) 25 9 Can you find the value of an expression when values for x and y are given? If x = -4 and y = -2, evaluate each expression. 10 - 5x 3) y- 2 4) 8 - x2 y Can you translate a phrase or sentence into symbols? Write each phrase or sentence an algebraic expression or equation. Let x represent the unknown number. 5) Three times a number decreased by 22 A) 22 - 3x B) 3x + 22 C) 3x - 22 D) 22x - 3 6) Two subtracted from a number is 0. Can you use the distributive property and combine like terms to simplify an expression? Simplify each expression. 1 7) (12x - 8) 4 A) 48x - 32 B) 3x - 2 C) 3x - 8 D) x 8) 12x - 4(7y - 10) 9) -10(7r + 4) + 6(7r + 8) 10) - 2 1 (z - 10) z 7 14 A) 5 20 z+ 14 7 B) 5 20 z14 7 C) - 1 5 20 z+ 14 7 D) 3 z + 10 14 Translate the sentence into symbols. Simplify if possible. 11) Subtract 3x - 4 from 8x - 2. Can you solve equations? Solve each equation. 12) -3 + x = 11 13) 3 1 2 1 y+ =- y5 7 5 8 14) - 1 2 k= 7 7 15) -65.7 = -7.3c 16) -29 = 7x - 1 17) 1 f-5=1 7 18) -2(3x + 1) - 3 = -3(x + 2) + 2x 1 A) 7 B) 1 5 C) 4 5 D) - 4 5 19) -7z + 1.2 = -56 - 1.8z A) -62 B) 8.2 C) 8.4 D) 11 20) -2(x - 4) - 55 = 5x - 7(x + 1) A) -62 B) -48 C) all real numbers D) no solution 21) 5(x + 2) - (5x + 10) = 0 A) 2 B) 0 C) all real numbers D) no solution 22) 2(y + 4) = 3(y - 7) A) The solution is a number less than -30 C) The solution is a number between 0 and 30 B) The solution is a number between -30 and 0 D) The solution is a number greater than 30 Can you translate a phrase or sentence into symbols? Translate each phrase or sentence. Simplify if possible. 23) A 23-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z. 24) The sum of the angles of a triangle is 180. If one angle of a triangle measures x and a second angle measures (3x + 24), express the measure of the third angle in terms of x. 2 25) If x is the first of three consecutive integers, express the sum of 23 and the third integer as an algebraic expression in terms of x. Can you solve word problems using an equation? Can you assign a variable and write the answer? Use an equation to solve each of the following. Assign a variable and write the answer. 26) The sum of four times a number and 9 is equal to the difference of twice the number and 1. Find the number. 27) The code to unlock a safety deposit box is three consecutive odd integers whose sum is 99. Find the integers. 28) Two angles are complementary if their sum is 90. If the measure of the first angle is x, and the measure of the second angle is (3x - 2), find the measure of each angle. Can you solve a formula for a specified variable? 1 for h 29) Solve A = bh 2 A) h = Ab 2 30) Solve F = 9 5 C + 32 B) h = b 2A C) h = 2A b D) h = A 2b for C Can you solve a word problem using the steps in the Blueprint for Problem Solving? 31) Ted drove to his grandparents' house for a holiday weekend. The total distance (one-way) was 379 miles and it took him 8 hours. How fast was Ted driving? (Round answer to the nearest whole number) 32) Find the height of a right circular cylinder whose volume is 225 cubic feet and whose radius is 5 feet. Can you solve a word problem involving percent, percent mark-up, discount, percent increase, or percent decrease? 33) What number is 86% of 223? 34) 95 is 70% of what number? A) 66.5 B) 1357 C) 13.6 D) 135.7 35) 2 is what percent of 4? 36) The population of a town is currently 44,000. This represents an increase of 20% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole number if necessary. A) 220,000 B) 36,667 C) 35,200 D) 8800 37) The number of students enrolled at City College went from 7000 last year to 3000 this year. Find the percent decrease in enrollment. A) 133.3% B) 57.1% C) 42.9% D) 233.3% 3 38) Ming got a 12% raise in her salary from last year. This year she is earning $120,960. How much did she make last year? Can you solve an inequality using the multiplication and addition properties of inequality? Solve each inequality. Graph the solution set on a number line and write the answer using solution set notation. 39) -10 - 3x + 4 -4x - 9 40) -5x 95 41) -5(2y - 3) 6} Can you solve an application problem using an inequality? 42) The area of a rectangle must be at least 119 square feet. If the length is 7 feet, find the minimum for the rectangle's width. 43) Claire has received scores of 85, 88, 87, and 85 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 88? 44) An archer has $205 to spend on a new archery set. A certain set containing a bow and three arrows costs $52. With the purchase of this set, he can purchase additional arrows for $9 per arrow. Find the maximum number of arrows he could obtain, including those with the set, for his $205. Can you determine whether an ordered pair is a solution to an equation? In each case, determine whether the ordered pair is a solution of the equation. 45) x - 9y = 27; (0, 3) 4 46) x = 1 y; (4, 32) 8 Can you write a given data set using ordered pairs and create a scatter diagram? 47) The table shows the number of cookies sold at a bake sale according to their diameter in inches. Write the ordered pair data as an ordered pair of the form (diameter, number sold). Then create a scatter diagram of the ordered pairs.. Can you create a table of solutions to an equation, write these solutions as ordered pairs, and graph the linear equation by plotting the ordered-pair solutions? 48) 6x + 2y = 12 x 0 1 y 0 -6 Can you find the x- and y-intercepts of a line from its equation? 49) Determine the coordinates of the intercepts of the line 8x = -y + 4. 5 Can you identify the x- and y-intercepts of a given graph? Identify the coordinates of the intercepts of the line. 50) Can you solve an application problem that includes an equation? 51) A small-business research project estimated that for the years 1998-2003, the total number of retail bicycle stores in a particular region would grow according to the linear equation y = 20x + 800, where x is the number of years after 1998. Graph the equation and use the graph to predict the total number of retail bicycle stores in 2008. Can you graph an equation by finding and graphing intercepts? 1 52) Graph y + x = 3 by finding and graphing its intercepts. 2 6 53) Graph -4x - y = -12 by finding and graphing its intercepts. Can you identify and graph a horizontal or vertical line? 54) Graph y = -4 55) Graph x - 2 = 0 7 Can you find the slope of a line given two points on the line? In each case, find the slope of the line that passes through the points. 56) (-1, 17) and (3, 7) 5 A) B) 12 2 57) (-4, -10) and (-4, -6) A) undefined B) 1 2 C) - 5 2 D) - C) 0 2 5 D) 2 58) (-10, 1) and (6, 1) Can you rewrite the equation of a line in slope-intercept form? 59) Write -x + 5y = 60 in slope-intercept form. 60) Write x = -7y in slope-intercept form. Can you find the slope of a line given its equation? 61) Find the slope of the line y = 4.9x - 9.6 62) Find the slope of the line -x + 11y = 88 A) m = 11 B) m = 1 11 C) m = - 1 11 D) m = -1 Can you determine whether two lines are parallel, perpendicular, or neither by comparing their slopes? Determine whether each pair of lines is parallel, perpendicular, or neither. 63) y = 2x + 5 y = -2x + 1 64) 3x - 6y = 20 18x + 9y = 9 65) 6x + 2y = 8 12x + 4y = 17 Can you solve an application problem by identifying slope as a rate of change? 66) The approach ramp used by a daredevil motorcyclist for flying over a pit of venomous snakes has a rise of 52 feet for every 80 feet in horizontal distance. Find the grade of the ramp. Round to the nearest whole percent. 8 67) To the nearest dollar, the average tuition at a public four-year college was $3013 in 1998 and $3327 in 2000. Use the ordered pairs (1998, $3013) and (2000, $3327) to find and interpret the slope of the line representing the change in tuition. A) tuition increased $174 per year B) tuition decreased $157 per year C) tuition increased $168 per year D) Tuition increased $157 per year. Can you write the equation of a line in slope-intercept form given its slope and y-intercept? 68) Write the equation of the line with slope = 4 , and y-intercept (0,0). 5 69) Write the equation of the line with slope = -2, and y-intercept (0, 1 ) 3 Can you write the equation of a line in slope-intercept form given information about the line? 70) Slope = -3, through (-3, -6) A) y = -3x + 15 B) y = -3x - 15 C) y = 3x + 3 D) y = -3x - 3 C) x = 3 D) x = 9 71) Through (-2, -5) and (-4, -2) Can you write the equation of a horizontal or vertical line? 72) Write the equation of the vertical line through (9, 3) A) y = 9 B) y = 3 73) Write the equation of the line with slope 0, through - 74) Through (-6, 7) and parallel to the x-axis. Can you graph a linear equation? 75) Graph y = -3x + 7 using the slope and y-intercept. 9 1 ,6 8 76) Graph 5x + 4y = 20 77) Find the slope and y-intercept of the line. Then write the equation of the line in slope-intercept form. A) y = - 2 9 x+ 3 2 B) y= - 2 x +3 3 C) y = 2 x+3 3 Can you answer questions about a given graph? 78) Does the graph given below have a positive or negative slope? Does the graph given below have a positive or negative y-intercept? Can you determine whether an ordered pair satisfies a system of linear equations? 79) (5, -2) x + y = -7 x - y = -3 10 D) y = - 3 x+3 2 Can you solve a system of linear equations by graphing? 80) 2x + 3y = 24 2x + 2y = 20 81) x = -y y+ x= 6 82) y = -2x + 1 x = -3 A) (-3, 7) B) (2, -3) C) no solution 11 D) infinite solutions Can you solve a system of equations using the substitution by solving one equation for x or y and then using the substitution method? 83) x + 6y = 6 7x - 5y = -5 84) -6x + y = 32 -7x + 5y = 45 A) (2, -5) B) (-5, 2) C) (-4, 1) D) no solution 85) y - 4x = 3 5y = 20x + 15 Can you solve a system of equations using the elimation method? 86) x + 6y = -8 -4x + 5y = -26 87) 9x - 3y = 4 18x - 6y = 20 88) 5x + 1 y = -13 2 2x + 5 y=- 1 4 Can you use a system of equations to solve a word problem using the Blueprint for Problem Solving? 89) The sum of two numbers is -2, and their difference is 4. Find the two numbers. 90) One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers. 91) A flat rectangular piece of aluminum has a perimeter of 64 inches. The length is 8 inches longer than the width. Find the width. A) 20 in. B) 32 in. C) 28 in. D) 12 in. 12 92) The Little Town Fine Arts Center charges $24 per adult and $14 per senior citizen for its performances. On a recent weekend evening when 484 people paid admission, the total receipts were $8486. How many who paid were senior citizens? 93) Aviva has a total of 52 coins, all of which are either dimes or nickels. The total value of the coins is $4.70. Find the number of each type of coin. Write a system of equations to describe the situation. Do not solve the system. Let x = the cost of one bag of chips and y = the cost of one container of dip. 94) At the local convenience store, 7 bags of chips and 6 containers of dip cost $33. However, 6 bags of chips and 4 containers of dip cost $26. What is the cost of one bag of chips and one container of dip? A) B) C) D) 13xy = 33 x + 7 + 6 + y = 33 7x - 6y = 33 7x + 6y = 33 6x + 4y = 26 10xy = 26 6 + x + 4 + y = 26 6x - 4y = 26 Can you evaluate an expression with exponents? Evaluate each expression. 95) -5 2 A) 10 B) 25 C) -25 D) -10 96) 4 5 3 Can you use the rules of exponents to simplify an expression? Simplify each expression. Write each result using positive exponents only. 97) (-9p3 )(3p5 ) 98) 40m 19n 10 8m 18n 7 A) 5mn 3 99) B) 5n 3 C) 5m 37n 17 D) 32mn 3 B) 1 C) -7 D) -6 4x2 y2 4 z3 100) 5x0 + 5x 0 101) -7y0 A) 0 102) y-9 y2 13 103) 6 -1 + 8-1 24 A) 7 B) 7 24 C) - B) -3x4 y5 C) 104) (-5x5 y-6 )(2x-1 y) A) -10x4 y7 1 2 -10x4 y5 D) 2 D) -10x6 y7 105) (x-4 y4 )-1 106) -2 xy5 x3y Can you determine the degree and coefficient of a term, and the degree of a polynomial? Find the degree and coefficient of each term of each of the following polynomials, and then determine the degree of the polynomial. 107) -17y4 + 2 108) 4q2 r2 + rs3 - qr2 s2 Can you use the vocabulary for polynomials? Find the degree of the following polynomial and identity each as a monomial, binomial, trinomial, or none of these. 109) -13s7 - 5s + 4 110) 15z + 9 Can you evaluate a polynomial? 111) Evaluate -10 - x3 - x2 when x = -1 A) -12 B) 8 C) -10 D) -8 112) The height of a new building in China will be 905 feet. Neglecting air resistance, the height of an object dropped from this building at time t seconds would be given by the polynomial -16t2 + 905. Find the height of the object at time t = 4 seconds. Can you simplify a polynomial by adding or subtracting? Simplify each by adding or subtracting. 113) -10r - 9r4 - 3r4 + 7r B) -15r4 A) -15r C) -3r - 12r4 D) cannot be simplified 14 114) 2 2 2 1 1 1 1 x - x - + x2 - x 3 3 3 4 5 3 Can you write a polynomial so the powers are in descending order? 115) Write in descending order: 7 + 8x3 - 4x - 3x2 Can you add and subtract polynomials? 116) (3x2 - 10x + 4) - (x2 - 5x + 2) + (7x2 + 5) A) -5x2 - 15x + 11 B) 9x2 - 5x + 11 C) 9x2 - 5x + 7 D) 9x2 + 5x + 7 B) -30x11 C) 30x11 D) 30x30 B) 6x2 + 10x + 10 C) 6x2 + 10x - 12 D) 8x2 + 10x + 10 B) x + 121 C) 121x2 + 22x + 121 D) x2 + 121 B) x4 - 169y2 C) x4 - 26x2 y - 169y2 D) x4 - 26y2 117) Subtract (-9x2 - 3x + 1) from (-x2 - 7x + 6). Can you multiply polynomials? 118) 6x5 (-5x6 ) A) -30x30 119) 1 9 x 3 1 6 x 8 120) -4x(3x2 - 3x - 5) 121) (2x + 4)(4x - 3) A) 8x2 + 10x - 12 122) (x + 8)(x3 + 4x - 6) 123) (x + 11)2 A) x2 + 22x + 121 124) (8a - 5)2 125) (a - 11)(a + 11) 126) (x2 + 13y)(x2 - 13y) A) x4 + 26x2 y - 169y2 Can you divide a polynomial by a monomial? 127) 20x2 + 24x - 12 12 15 128) 2x3 y3 + 10xy + x2 2xy A) x2 y2 + 5 + xy x B) x2 y2 + 5 + 2y C) xy + 5 + x 2y2 2 D) x2 y2 + 5 + 2xy Can you change a number from standard notation to scientific notation and vice versa? Write each number in scientific notation. 129) 150,000 130) 0.00007701 A) 7.701 105 B) 7.701 104 C) 7.701 10-4 D) 7.701 10-5 B) 70,860 C) 283.44 D) 7086 Write each number in standard notation. 131) 4.99 10-4 132) 7.086 104 A) 708,600 Can you multiply and divide numbers given in scientific notation? Simplify each expression and write each answer in standard notation. 133) (5 102 ) (6 104 ) 134) 35 105 5 108 16 Answer Key Testname: MATH 080 FINAL-EXAM REVIEW - OCT2018 1) 13 2) B 15 3) 2 4) 5) 6) 7) 8) 9) 10) 11) 12) -4 C x-2=0 B 12x - 28y + 40 -28r + 8 C 5x + 2 14 15 13) 56 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) -2 9 -4 42 B D D C C (23 - z) cm (156 - 4x) x + 25 Let x be the number. Equation: 4x + 9 = 2x - 1 x=-5 The number is - 5. Let x be the smallest of the consecutive odd integers. Equation: x + (x + 2) + (x + 4) = 99 x = 31 The code is 31, 33, 35. Let x be the degree measure of the first angle. Equation: x + (3x - 2) = 90 x = 23 The first angle measures 23; the second angle measures 67. C 5 C = (F - 32) 9 33) 34) 35) 36) 37) 38) 39) 191.8 D 50% B B $108,000 {x x -3} 48) x y 0 6 2 0 1 3 4 -6 40) {x x 19} 41) 42) 43) 44) 45) 46) 47) B The minimum width is 17 ft. The minimum score is 95. at most 20 arrows no yes 49) x-intercept (1, 150) (1.5, 300) (2, 450) (2.5, 250) (3, 350) 1 , 0 ; y-intercept 2 (0, 4) 50) x-intercept: (3, 0); y-intercept (0, -6) 51) 1000 stores 31) Ted was driving at a rate of 47 mph. 32) The height is 9 ft. 17 Answer Key Testname: MATH 080 FINAL-EXAM REVIEW - OCT2018 52) 55) 75) 53) 76) 56) C 57) A 58) 0 59) y = 1 x + 12 5 60) y = - 54) 1 x 7 61) 62) 63) 64) 65) 66) 67) m = 4.9 B neither perpendicular parallel 65% D 4 68) y = x 5 69) y = -2x + 70) B 71) y = - 1 3 3 x-8 2 72) D 73) y = 6 74) y = 7 77) B 78) Positive Slope & Negative y-intercept 79) No 80) (6, 4) 81) inconsistent 82) A 83) (0, 1) 84) B 85) infinite number of solutions 86) (4, -2) 87) no solution 88) (-3, 4) 89) 1 and - 3 90) 6 and 8 91) D 92) 313 senior citizens 93) 10 nickels; 42 dimes 94) D 95) C 96) 500 97) -27p8 98) A 18 Answer Key Testname: MATH 080 FINAL-EXAM REVIEW - OCT2018 99) 256x8 y8 z 12 100) 6 101) C 1 102) y11 131) 132) 133) 134) 0.000499 B 30,000,000 0.007 103) B 104) C x4 105) y4 106) x4 y8 107) -17y4 : degree 4; coefficient -17 2: degree 0; coefficient 2 polynomial degree: 4 108) 4q2 r2 : degree 4; coefficient 4 rs3 : degree 4; coefficient 1 - qr2 s2 : degree 5; coefficient -1 polynomial degree: 5 7; trinomial 1; binomial C 649 ft C 11 2 13 2 x x114) 12 15 3 109) 110) 111) 112) 113) 115) 8x3 - 3x2 - 4x + 7 116) C 117) 8x2 - 4x + 5 118) B 1 15 x 119) 24 120) -12x3 + 12x2 + 20x 121) A 122) x4 + 8x3 + 4x2 + 26x - 48 123) A 124) 64a 2 - 80a + 25 125) a 2 - 121 126) B 5 127) x2 + 2x - 1 3 128) B 129) 1.5 105 130) D 19