Arizona Western College Math 81 Course Review. Name Class Time

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1 Arizona Western College Math 81 Course Review Name Class Time Questions from Chapter 1 Simplify. 1) (-0.9) ) ) (-4) 3 2) (-11) 8) (2.8) 3 3) (- 2) 4) -4(-4)(5)(-4) 9) ) -85 (-5) 10) (2) 3 (-2) 1

2 11) ( ) 2 17) 5(9a + 6) - (4a - 2) Simplify. 12) -2x(8x + 4y + 6) Evaluate for the value of the variable(s) indicated. 18) x 3 + 4x 2 y - 5y + 6 for x = 3 and y = -2 13) 3xy 2 (-5x - 4y - 4xy) 19) 2x2 + 3x + 5 for x = -2 14) 4ab a2 b ab a2 b 20) -2a + 3b for a = 1 4 and b = ) 5.7x 2 y - 1.3xy 2-3.8x 2 y + 6xy x 2 y Solve. 21) If you are traveling 70 miles per hour on a highway in Canada, how fast are you traveling in kilometers per hour? (Use k = 1.61r, where r = rate in miles per hour and k = rate in kilometers per hour.) 16) 2(8 - x) - 5(5 + 6x) 2

3 22) A window is in the shape of a trapezoid. The altitude of the window is 40 inches. One base measures 24 inches, and the other base measures 52 inches. What is the area of the window? Questions from Chapter 2 Solve for the variable. 27) -6y + 1-4(y + 1) = -5y ) 2x = ) Find the total cost of tiling a triangular area having a base length of 9 meters and a height of 5 meters if it costs $6.65 to tile one square meter. Round to the nearest cent. 29) -5x + 9 = x 24) You wish to apply blacktop sealer to your driveway, but do not know how much to buy. If your rectangular driveway measures 45 feet long by 10 feet wide, and a can of blacktop sealer claims to cover 150 square feet, how many cans should you buy? 30) 5(y + 4) = 6(y - 4) Simplify. 25) 5[a - b(5a + 6b) + 6b 2 ] 31) 2 5 y - 4 = 1 3 y 32) 2(x + 2) = 3(x - 8) 26) 5a - {5b - 3[a - (b - 2a)]} 3

4 33) x x = x ) 2 5 x x = 3 34) 3 5 y = y ) 3 4 x = x ) 6y + 2-5(y + 1) = -5y ) (x - 4) - 1 (x - 7) = x ) 12(9x - 8) = 5x - 8 Solve and graph the inequality. 42) -6(2x - 3) < -18x - 18 Solve for the variable. 37) 3(2x - 5) = 5(x + 5) 43) 24x + 8-4(5x + 3) 0 Solve for x. 38) -4(x + 8) - (-5x + 7) = -7 4

5 44) 12x - 7 > 11x ) In a triangle, the measure of the first angle is four times the measure of the second angle. The measure of the third angle is 150 degrees more than the second angle. What is the measure of the first angle? Write an equation and then solve. 45) A number is doubled and then decreased by 14. The result is 72. What is the original number? 46) One number is 8 less than three times a second number. The sum of the two numbers is 16. Find each number. 49) Gary has a budget of $1930 to rent a computer for his company office. The computer company he wants to rent from charges $250 for installation and service as a one-time fee. Then they charge $105 per month rental for the computer. How many months will Gary be able to rent a computer with this budget? 47) Josh and Sam traveled in separate cars from their apartment to a ski resort 360 miles away. Sam wanted to get there early, so he traveled the maximum speed limit, 60 mph. Josh just bought a new car, so he drove a little slower at exactly 40 mph. If they both left at the same time, how much sooner did Sam arrive at the ski resort than Josh? 50) Nancy has $1.80 in change. She has three times as many nickels as quarters. She has two more quarters than dimes. How many coins of each type does he have? 5

6 Chapter 3 questions. Plot and label the points. 51) E: (1, 8) F: (2, 0) G: (-3, 5) H: (6, -4) 53) -x + 8 = 3x 54) y = x + 4 Graph. 52) 7x - 8 = 6x + 2y 6

7 Provide an appropriate response. 55) Complete (a) and (b) for the equation x - 3y = -6 (a) State the x- and y-intercepts. (b) Use the intercept method to graph. 58) Find an equation of the line with slope 3 5 and y-intercept (0, -4). 59) (a) Write an equation for the line f that passes through (4, 4) and has a slope of (b) What is the slope of a line perpendicular to line f? 56) Find the slope of the line that passes through (5, -6) and (4, -4). 60) Find an equation for the line passing through (-7, 3) and (4, -3). 57) What is the slope and y-intercept of the line 10x - 11y - 3 = 0? 61) Is this relation a function? {(-3, -8), (4, -4), (4, -3)} Why? 7

8 62) Look at the relation graphed below. Is this relation a function? Why? Chapter 4 questions. Solve by the method specified. 65) Graphing method 5x + y = -22 2x + 6y = 8 63) For f(x) = x 2 + 4x - 3: (a) Find f(0). (b) Find f(4). 66) Substitution method x - 7y = 31-2x - 8y = 48 64) For f(x) = x 2 + 3x - 6: (a) Find f(0). (b) Find f(-1). 8

9 67) Addition method 8x + 5y = -70 4x - 3y = -2 71) 1 2 x y = 1 x - y = 14 68) Any method x - 7y = 49 6x - 6y = 42 72) 8x - 5y = 10 24x - 15y = 20 73) y - 3x = 5 3y = 9x + 15 Solve by any method. If there is not one solution to a system, state why. 69) x + 5y = -16 4x + 4y = 0 70) -7x + 7y = 35 4x + 5y = 25 74) 0.2x - 0.6y = x - 0.6y = 3.2 9

10 75) 1 (x + y) = (x - y) = ) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $ Another customer buys 5 hot dogs and 3 bags of potato chips for $ Find the cost of each item. Write a system of equations and then solve. 76) One number is four more than a second number. Two times the first number is 12 more than four times the second number. Find the numbers. 79) A twin-engined aircraft can fly 1440 miles from city A to city B in 5 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind? 77) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $10 each and a number of necklaces at $13 each. She wrote a check for $1350 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase? 10

11 Chapter 5 Questions Simplify. Leave your answer in exponent form. 80) (5 10 )(5 22 ) 85) 5a 3 b 3 3c ) (2 4 ) 2 86) (3x2 ) 3 (6x) 2 Simplify. 82) (-8x 3 y)(-2x 6 y 5 ) Simplify and write with only positive exponents. 87) 4a -3 b -5 c 6 83) -10x7 y 3 35x 4 y 12 88) 5x-2 y -6 x -3 y ) (-4x 6 y 8 ) 2 Write in scientific notation. 89)

12 Write in decimal notation. 90) ) (5a + 5b)(6a - 7b) Multiply using the exponent rules. Leave your answer in scientific notation. 91) ( )( )( ) 96) (2x y 2 )2 97) (3s - 5t)(3s + 5t) Combine. 92) (5x 3-14x 2-12) - (9x x + 6) 98) (8x 2-10xy)(x 2-3xy) Multiply. 93) -5x 3 (2x 3 + 4x 2 + 7x - 2) Divide. 99) (30x x x 2 ) 6x 2 94) (6x 2 y 2-5xy + 11)(-5x 2 y) 100) (128x x x 2 ) 32x 2 12

13 Answer Key Testname: FINALEXAMREVIEWMATH81FALL2017 1) ) -3 3) 8 7 4) ) 17 6) -30 7) -64 8) ) ) 86 11) ) -16x 2-8xy - 12x 13) -15x 2 y 2-12xy 3-12x 2 y 3 14) 13 4 ab a2 b 15) 4.8x 2 y + 4.7xy 2 16) -32x ) 41a ) ) 7 20) ) km/hr 22) 1520 in. 2 23) $ ) 3 cans 25) 5a - 25ab 26) 14a - 8b 27) y = ) x = 4 29) x = ) y = 44 31) y = 60 32) x = 28 33) x = ) y = ) y = ) x = ) x = 40 38) x = 32 39) x = 45 13

14 Answer Key Testname: FINALEXAMREVIEWMATH81FALL ) x = ) x = ) x < -6 43) x 1 44) x > ) 43 46) 6 and 10 47) 3 hours sooner 48) 20 49) 16 months 50) 4 quarters, 2 dimes, 12 nickels 51) 14

15 Answer Key Testname: FINALEXAMREVIEWMATH81FALL ) 53) 54) 15

16 Answer Key Testname: FINALEXAMREVIEWMATH81FALL ) x-intercept: (-6, 0) y-intercept: (0, 2) 56) -2 57) m = ; 0, ) y = 3 5 x ) (a) y = x ; (b) ) y = x ) No; two different ordered pairs have the same first coordinate. 62) Yes; any vertical line passes through no more than one point on the graph. 63) (a) -3; (b) 29 64) (a) -6; (b) -8 65) (-5, 3) 66) (-4, -5) 67) (-5, -6) 68) (0, -7) 69) (4, -4) 70) (0, 5) 71) (8, -6) 72) No solution, inconsistent system 73) Infinite number of solutions, dependent equations 74) (1, -4) 75) (3, 6) 76) 2 and ) 70 bracelets and 50 necklaces 78) $2.00 for a hot dog; $1.50 for a bag of potato chips 79) 54 mph 16

17 Answer Key Testname: FINALEXAMREVIEWMATH81FALL ) ) 28 82) 16x 9 y 6 83) - 2x3 7y 9 84) 16x 12 y 16 85) 125a9 b ) 3x4 4 4c 87) 6 a 3 b 5 88) 5xy 4 89) ) 73,500 91) ) -4x 3-14x 2-15x ) -10x 6-20x 5-35x x 3 94) -30x4y x3y 2-55x 2 y 95) 30a2-5ab - 35b2 96) 4x4 + 44x 2 y y4 97) 9s 2-25t 2 98) 8x 4-34x 3 y + 30x 2 y 2 99) 5x x ) 4x 7 + 3x