QUESTIONS 1-46 REVIEW THE OBJECTIVES OF CHAPTER 2.

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1 MAT 101 Course Review Questions Valid for Fall 2014, Spring 2015 and Summer 2015 MIDTERM EXAM FINAL EXAM Questions 1-86 are covered on the Midterm. There are 25 questions on the midterm, all multiple choice, and you are given 75 minutes for the exam. All questions are covered on the Final - the exam is cumulative. There are 40 questions on the final, all multiple choice, and you are give 120 minutes for the exam. QUESTIONS 1-46 REVIEW THE OBJECTIVES OF CHAPTER 2. Solve the equation. 1) 7x - 4x - 2x = ) -6(x + 10) = -42 3) -(6y - 6) - (-5y + 9) = -4 4) 2x 5 - x 3 = 5 12) Junior high classes of 25 students each met in the cafeteria to take achievement tests. If exactly 5 students sat at each table and 15 tables were used, how many classes took the tests? Solve using the five-step problem-solving process. 13) The sum of two consecutive even integers is 62. Find the larger number. 14) The sum of the page numbers on the facing pages of a book is 267. Find the larger page number. 5) x x = ) The sum of three consecutive odd integers is 267. Find the integers. Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. 6) 7(x + 5) = 7x + 35 Solve the equation. 7) -5.4m m = m ) 8x x + 5 = 9x + 6x - 7 9) 1 5 (10x - 15) = 6( 1 3 x ) + 4 Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. 10) 4(x + 4) = 4x - 32 Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the equation and find the number. 11) Three-fourths of a number is 3. Find the 16 number in lowest terms. 16) The sum of three consecutive integers is 426. Find the integers. 17) The sum of two consecutive integers is Find the larger integer. 18) A rectangular Persian carpet has a perimeter of 160 inches. The length of the carpet is 18 inches more than the width. What are the dimensions of the carpet? 19) The length of a rectangular storage room is 4 feet longer than its width. What are the dimensions of the room if the area of the room is 77 square feet? Solve the formula for the specified variable. 20) V = 1 Bh for h 3 Solve the equation for y. (You can also refer to material in 3.4 for additional examples.) 21) x = 5y + 3 Last updated Fall 2014

2 Solve the equation for y. (You can also refer to material in 3.4 for additional examples.) 22) 9x - 8y = 6 23) x - 6y = 3 Express the percent as a decimal. 24) 67.2% 25) 1 16 % Express the decimal as a percent. 26) 8 27) Due to a lack of funding, the number of students enrolled at City College went from 6000 last year to 5000 this year. Find the percent decrease in enrollment. (Round to the nearest tenth of a percent, if necessary.) 28) Sales at a local ice cream shop went up 60% in 5 years. If 37,000 ice cream cones were sold in the current year, find the number of ice cream cones sold 5 years ago. (Round to the nearest integer, if necessary.) 29) A IBM Proprinter printer priced at $538 is sold for $342. What was the percent decrease of the price? Round to the nearest tenth of a percent, if necessary. Use the percent formula, A = PB: A is P percent of B, to solve. 30) 21 is 2% of what number? 31) 10% of what number is 74? 32) 9% of students at a university attended a lecture. If 2000 students are enrolled at the university, about how many students attended the lecture? Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. 33) After a 13% price reduction, a boat sold for $ 30,450. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.) 34) Jeans are on sale at the local department store for 15% off. If the jeans originally cost $62, find the sale price. (Round to the nearest cent, if necessary.) Let x represent the number. Write the English phrase as an algebraic expression. 35) Ten times a number, decreased by ) The product of -26 and the sum of a number and 18. Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. 37) When 2 times a number is subtracted from 7 times the number, the result is 45. Find the number. 38) There are 10 more sophomores than juniors in an algebra class. If there are 80 students in this class, find the number of sophomores and the number of juniors in the class. Use the relationship among the three angles of any triangle to solve the problem. 39) One angle of a triangle is 2 times as large as another. The measure of the third angle is 120 greater than that of the smallest angle. Find the measure of each angle. Find the measure of the indicated angle. 40) The angle's measure is 40 more than triple that of its supplement. 41) Find the measure of an angle whose supplement is 9 times the measure of its complement. 2

3 Use both the addition and multiplication properties of inequality to solve the inequality. Graph the solution set on a number line. 42) 8x - 7 4x ) 5x - 6 < 6(x + 5) Solve the linear inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 44) 5(4x + 4) - 4x < 4(5 + 4x) ) -4x -4(x - 6) 46) 3(x + 4) 2(x - 3) + x 52) A certain car has a weight limit for all passengers and cargo of 1065 pounds. The four passengers in the car weigh an average of 165 pounds. Use an inequality to find the maximum weight of the cargo that the car can handle. 53) When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.05. After that, each additional minute or portion of a minute of that call costs $0.35. Use an inequality to find the maximum number of minutes one can call long distance for $2.75. ADDITIONAL REVIEW SUGGESTIONS: Chapter Two Review Exercises pg 204 #1-87 Chapter Two Test pg 207 #1-34 Cumulative Review Exercises pg QUESTIONS COVER THE OBJECTIVES FOR CHAPTER 3 UP TO SECTION 3.4 Complete the ordered pair for the equation. 54) y = -6x - 23 (, -23) Solve the inequality, then graph the solution. 47) 4x x < 6-7x ) y = -3x + 21 (9, ) Find a solution to the equation using the value given for x. 56) y = -7x - 4; x = -3 Solve the inequality. 48) 7x + 13 > 7(x + 11) Graph the linear equation in two variables. 57) y = x ) x + 8 x ) -3(-3 - x) < 5x x 51) 4x - 7 > 4(x - 5) 3

4 58) y = -2x - 4 Find the y- and x-intercepts for the equation. Then graph the equation. 62) 6y - 3x = -9 59) y = 1 6 x ) -6x - 12y = 36 Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept. 60) Graph the equation. 64) x = 0 Find the x-intercept and the y-intercept of the graph of the equation. Do not graph the equation. 61) 2x + y = -6 Find the slope of the line passing through the pair of points or state that the slope is undefined. 65) (-6, 5), (7, -9) 4

5 Find the slope of the line that passes through the two given points. 66) (2, 0), (0, 6) Find the slope of the line. Interpret the slope in terms of rise and run. 72) Find the slope of the line passing through the pair of points or state that the slope is undefined. 67) (-3, -2) and (-3, 6) 68) (9, -1) and (-2, -1) Determine the slope and the y-intercept. Then graph the equation. 69) y = 4x - 7 Determine the slope and the y-intercept. Then graph the equation. 73) 2x - 4y = 14 Determine whether the lines through each pair of points are parallel. 70) (10, -7) and (2, 7); (8, -6) and (12, 1) By observing the vertical and horizontal change of the line between the two points indicated, determine the slope of the line. 71) Determine whether the lines through each pair of points are parallel. 74) (-3, 5) and (13, 23); (9, 10) and (17, 19) Determine whether the lines through each pair of points are parallel, perpendicular, or neither. 75) (-10, 9) and (-18, 7); (7, 10) and (6, 14) 5

6 Find the slope of the line, or state that the slope is undefined. 76) Graph the linear equation. 81) y = 2 5 x - 2 Find the slope of the line. 77) x = 4 78) y = 2 Put the equation in slope-intercept form by solving for y. Use the slope and y-intercept to graph the equation. 82) 7x + 3y = 21 Find the slope and the y-intercept of the line with the given equation. 79) 8x + y = 6 Graph the linear equation using the slope and y-intercept. 80) y = x Interpret the linear equation. 83) The altitude above sea level of an airplane just after taking off from an airport on a high plateau is given by the linear function y = 600x , where y is in feet and x is the time in minutes since take-off. Find and interpret the slope and y-intercept. 84) The monthly cost of a certain long distance service is given by the linear function y = 0.04x where y is in dollars and x is the amount of time in minutes called in a month. Find and interpret the slope and y-intercept of the linear equation. 6

7 85) When a tow truck is called, the cost of the service is given by the linear function y = 3x + 75, 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. Interpret the linear equation. 86) The amount of water in a leaky bucket is given by the linear function y = 127-8x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation. ADDITIONAL PRACTICE SUGGESTIONS: Chapter Three Review Exercises pg Chapter Three Test pg 272 #1-14 and 19 Cumulative Review Exercises pg 273 #1 = 20 STOP HERE FOR MIDTERM QUESTIONS REVIEW THE OBJECTIVES FROM CHAPTER 5 Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. 87) -8y7-3 Add the polynomials. 88) (7x3 + 2x - 2) + (9x2 + 4x + 7) Subtract the polynomials. 89) (9x5 + 3x x6) - (3 + 5x6 + 7x7-7x5) Perform the indicated operations. 90) Subtract -1-8x7 + 6x8 + 2x6 + 3x from the sum of -9x6 + 3x + 6 and 3x8-3x7. Multiply the expression using the product rule. 91) y3 y4 y6 Simplify the expression using the power rule. 92) (-7)9 10 Simplify the expression using the products-to-powers rule. 93) (-2x4) 4 Multiply the monomials. 94) x x 9 Find the product. 95) -10x2(-10x6 + 2x4-4) 96) (9x - 1)(x2-2x + 1) Use the FOIL method to find the product. Express the product in descending powers of the variable. 97) (4x + 1)(6x + 9) Multiply using the rule for finding the product of the sum and difference of two terms. 98) (9x + 8)(9x - 8) Multiply by using the rule for the square of a binomial. 99) (x3 + 5) 2 100) (11-10x)2 Divide using the quotient rule. 101) x 12y11 x9y6 Use the zero-exponent rule to simplify the expression. 102) (-3)0 Simplify the expression using the quotients-to-powers rule. 2p4v ) s2 Divide the monomials. 104) -8x 10 56x6 Divide the polynomial by the monomial. 105) 6x 8 + 8x6-6x2 2x2 Divide as indicated. 106) p 2 + 3p - 25 p + 7 7

8 107) 4m 3 + 6m2 + 2m + 12 m + 2 Simplify the expression. Write the result using positive exponents only. 108) y -9 y4 109) (-4x4y-5)(2x-1y) 110) -4z-3 111) m-4 m3 m-8 m Write the expression with positive exponents only. Then simplify, if possible ) 4x-4 Simplify the exponential expression. 113) (3x3) 3 x-15 Write the number in decimal notation without the use of exponents. 114) x 10-5 Write the number in scientific notation. 115) 13,000,000 Perform the indicated computations. Write the answer in scientific notation. 116) (3 109)(6 10-7) Perform the indicated operation by first converting the numbers to scientific notation. Write the answer in scientific notation. 117) ( )(0.0004) Solve. 118) A particle is observed moving at meters per second. Find the distance the particle would travel in seconds. 119) NEW The national debt of a small country is $ 6,780,000,000 and the population is 2,236,000. What is the amount of debt per person? 120) The sun radiates energy into space at the rate of joules per second. How many joules are emitted in three weeks? Express the answer in scientific notation to two decimals. 121) A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels miles/second. Solve. 122) Approximately employees of a certain company average $30,000 each year in salary. What is the total amount earned by all the employees of this company per year? Write your answer in scientific notation. ADDITIONAL PRACTICE SUGGESTIONS: Chapter Five Review Exercises pg 421 #1-73, Chapter Five Test pg 423 #1-18, Cumulative Review pg 424 #1-12, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ QUESTIONS REVIEW THE OBJECTIVES FROM CHAPTER 6 Factor out the GCF from the polynomial. 123) 120x6y9-36x4y6-60x2y4 Factor by grouping. 124) 6x6-15x3 + 10x3-25 Factor completely. 125) x7-11x6 + 24x5 Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. 126) 8z2 + 6z - 9 8

9 Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. 127) 12z2-7z - 12 Factor completely. If unfactorable, indicate that the polynomial is prime. 128) 25k2-81m2 129) z2 + 14z + 49 Factor completely, or state that the polynomial is prime. 130) 25x Factor the polynomial completely. If the polynomial cannot be factored, write "prime." 131) x4-81 Factor completely. If the polynomial is prime, say so. 132) x2 + 59x + 60 Factor the polynomial completely. If the polynomial cannot be factored, write "prime." 133) 12(a + 5) - y(a + 5) 142) 3x2-27x + 60 = 0 143) 36x2 = ) 16x2-5x = 0 145) x2 = -16x ) x(x - 24) = ) (x + 2)(x2 + 2x - 24) = 0 148) The width of a rectangle is 6 kilometers less than twice its length. If its area is 176 square kilometers, find the dimensions of the rectangle. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ADDITIONAL PRACTICE SUGGESTIONS: Chapter Six Review Exercises pg 485 #1-95 Chapter Six Test pg 487 #1-30 Cumulative Review pg 488 #1-8, ) x Factor completely. If prime, so state. 135) w4 - s4 136) 2x2-20x ) 17x2 + 17xy + y2 Factor the polynomial completely. If the polynomial cannot be factored, write "prime." 138) 256-4x2 Factor. 139) t Factor completely. 140) 64 - t3 Solve the equation. 141) (9x + 23)(3x + 22) = 0 9