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MATH 45, Elementary Algebra 12) Given that a = 2, b = 3, and c = 1, evaluate Review Problems for Comprehensive b 2 4ac . Final Exam {Scientific Calculators allowed, No Graphing Calculators} 13) Given that x = 2, y = 1, evaluate xy y 2 x 2 . 3 5 3 1) 7 14 4 14) Given that x = 1, y = 1, evaluate 3x 2y. 2) (13 4) + (7 + 2) = 15) Write an algebraic expression to represent 2 "11 more than one half of a number k." 10 5(2) 2 3) 52 16) Translate the following into an algebraic 78 78 expression: "The quotient of a number x 4) divided by 5 is decreased by 15." 5 17) Name the property illustrated by the 8 4(2) 2 2 statement: 3 (5 + 9) = (5 + 9) 3 5) 4 22 18) Name the property illustrated by the statement: (x + y) + 4 = x + (y + 4) 5 1 2 6) 19) Name the property illustrated by the 6 3 5 statement: 7 (a − w) = 7a − 7w 5 5 2 7) 3 6 a3 6a9 8 20) Simplify: 8) You have 60 ounces of dough to make 21) Simplify: 5y 6 2y 3 5 breadsticks. If each breadstick requires 4 ounces of dough, how many breadsticks can you make? 22) Simplify: xz 2y 2 z 4 2 9) 2 6 5 3 23) Simplify: 5y 3 y 10) In the following figure, what is the total area in square feet? 3 ft 24) Solve for the variable h in the expression: 1 A bh 6 ft 2 3 ft 9 ft 25) Solve for the variable x in the expression: ax + by = c 11) In the expression 25y, what is the coefficient? 26) Write the number 1,637,000,000 in scientific notation. 2 27) Solve for x in the equation: 5x 10 = 4x 10 39) Greg has three times as many pencils as he has erasers and five fewer rulers than 28) Solve for x in the equation: pencils. He has 30 items in all. How many 1 2 3 1 rulers does he have? x x 4 3 4 3 40) William has 20 coins. All are nickels and 29) Solve for x in the equation: dimes. The combined value is $1.60. How 6(2 3x) = 5(2x 8) many nickels does he have? 30) Solve for x in the equation: 5x 3 = 13 41) Find h. 31) Solve for x in the inequality, then graph the solution. 7 3x 22 h 32) Solve for z in the inequality, then graph the solution. 6 ft 2 (z 1) 3 (z 1) | 100 ft | 8 ft | 33) Solve for x in the equation: 10 x x4 42) Graph the equation y = 2 2 5 43) Graph the equation y = 6 34) What is the area of a circle that has a 44) Graph the equation x = 3 diameter of 18 feet? (round to nearest tenth) 45) Graph the equation y 5x = 1 35) Eight is subtracted from five times a number. 46) Graph. x y 2 The result is two more than six times the number. What is the number? 47) Graph. 2x y 6 48) Determine the slope and y-intercept of the line 3x + 4y + 12 = 0. 36) The width of a swimming pool is four feet less than its length. The perimeter of the 49) Given 2x + y = 5, determine the slope and y- pool is 112 feet. What is the width of the intercept. pool? 50) Find the equation (in slope-intercept form) of the line that passes through the points (2, 3) 37) Two cars start at the same point and travel in (4, 6). opposite directions at average speeds of 40 and 55 miles per hour. How much time must 51) Write an equation of the line perpendicular to elapse before the two cars are 170 miles the line y = 6x 1 which has y-intercept 8. apart? 52) Find the equation (in slope-intercept form) of 38) The price of a pair of ski boots is $98. What the line that passes through the point (5, 1) will be the sale price of the boots during a and has slope 2. 60% off sale? 3 53) Determine whether the lines given by the 68) Simplify and write with no negative equations y = 1/3x 1 and y = 3x + 7 are xy 2 parallel, perpendicular or neither. exponents. y 3 x 3 54) Find the sum of 7x 2 3x 10 and 69) Simplify and write with no negative 9x 2 4x 6. 2 exponents. 4z 6 5z3 55) Subtract and simplify. 5x 2 4x 3 x 2 3x 5 70) Simplify and write with no negative 1 exponents. 2s1t 2 56) Multiply and simplify. (6 2x) (4x + 3) 71) Simplify and write with no negative 57) Expand and simplify. 5 x 2 3 x 3 y 4 exponents. 58) Multiply and simplify. 5 . 3x 2 y 6xy 4xy 5 7z 72) Simplify and write with no negative 2x 3 exponents. 59) Simplify. 4x 2 y 3 5x 1 6 xy 9 73) Factor completely, if possible. 7f 2 7f 60) Divide and simplify. 74) Factor completely, if possible. 4x 3 36x 4a 9b 2 2 12ab 75) Factor completely, if possible. 100 49x 2 61) Divide and simplify. 76) Factor completely, if possible. x 2 25 30a 2 b 2 15a 2 b 10ab 2 77) A binomial factor of both 10ab x2 x 6 and x 2 x 12 is 62) Divide and simplify. 78) Factor completely, if possible. x 3 x 2 2x 6x 11x 2 2 3x 1 79) Factor completely, if possible. c 2 6c 10 63) Divide and simplify. 80) Factor completely, if possible. 2x 7 x 4x 3 3 2 6y 2 5 y 6 2x 3 81) Factor completely, if possible. 64) Write in Scientific Notation. .000000302 3z 2 8z 5 65) Evaluate. 50 82) Factor completely, if possible. 4z 2 12z 40 4 66) Evaluate. 1 83) Factor completely, if possible. 0 1 67) Evaluate. 7 6 x 2 5x x 5 4 84) Factor completely, if possible. 98) Solve for x and y. 2x 5y = 1 xy + 3y + 2x + 6 x+ y= 3 99) Students can buy tickets to a basketball 85) Factor completely, if possible. game for $1. The admission for non- students is $2. If 350 tickets are sold and the x3 8 total receipts are $450, how many student tickets are sold? 86) Factor completely, if possible. 100) Simplify and reduce to lowest terms (if 125a 3 27 possible): 9 3t t 3 87) Factor completely, if possible. 101) Simplify and reduce to lowest terms (if 2t 128t 5 2 x4 possible): x 88) Solve for x. x (x 3) (x + 25) = 0 102) Simplify and reduce to lowest terms (if 89) Solve for x. 2 3x x x2 9 possible): x 2 4x 3 90) Solve for x. x 2 x 20 103) Simplify and reduce to lowest terms (if 91) Solve for x. 4x 2 1 0 x 2 7x possible): x 2 8x 7 92) Solve for x. 3x 2 8x 5 0 25 x 2 8xy 2 104) Multiply and simplify: 93) Find two consecutive positive odd integers 8xy 10 5x whose product is 323. 94) The length of a rectangle is 1 centimeter x x 7 x 1 105) Multiply and simplify: more than 3 times its width. If its area is 52 7 x x 7 square centimeters, find the dimensions of the rectangle. 106) Multiply and simplify: y 2 8y 7 y 2 3y 10 95) Solve. x 2y = 1 y 2 3y 4 y 2 9y 14 6x + 4y = 3 x2 x 2 107) Divide and simplify: (2 x ) x2 96) Solve for y. xy=6 x 2 y 2 x y 2 108) Divide and simplify: x+y=2 xy xy 2y 2 6y 109) Divide and simplify: 97) Solve for x. x y = 6 y3 y 2 3y x + y = 2 3y 2 2 y 5 110) Add: y3 y3 7 x 7 2x 7 111) Subtract: 5y 5y 5 112) Add and subtract: 3y x yx x 5 x 5 x 5 113) Find the length of x of the triangle shown. 3 in 5 in x 114) What is the slope of the line shown? 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10

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posted: | 11/24/2011 |

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