BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 012/051 Final Examination Review Form H Multiple Choice Problems 1. If a = -1 and b = -2, find the value of!3a2 b + 2b 3 a. a) -2 b) 22 c) -22 d) 40 2. If x = 2 and y = -2, find the value of x 2! 2y 2. a) 0 b) 2 c) 4 d) -4 3. Subtract!4x 2! 4x! 5 from 2x 2! x + 3. a)!6x 2 + 5x!8 b) 6x 2 + 3x! 2 c) 6x 2! 5x +8 d) 6x 2 + 3x +8 4. Solve the equation x 3 +1= x 6 for x. a) 0 b) 1 c) -3 d) -6 5. Solve the equation 2(3x!1)! (4x! 5) = 4x! 7 for x. a) -5 b) 0 c) 5 d) 1 2 6. Solve the inequality 7(y + 4) > 3(y!8) for y. a) y < 13 b) y < -13 c) y > 13 d) y > -13 7. Solve the inequality 4(x + 5)! 4(2x +1) for x. a) x! 4 b) x! "4 c) x! 4 d) x! "4 8. Solve the equation w = 4x + 4y for y. a) y = w! x b) y = w! 4x c) y = w! 4x 4 d) y = w + 4x 4 9. What is the slope of the line given by the equation 6x! y = 5? 6 a) 6 b) -6 c) -1 d) 5 Updated: 11/12/2012 1
10. Find the equation of the line passing through the points (-3,0) and (1,-2), in slope-intercept form. a) y =! 1 2 x! 3 2 b) y =! 1 2 x + 3 2 c) y = 1 2 x! 3 2 d) y = 1 2 x + 3 2 11. Find the equation of the line passing through the points (0,1) and (-1,0), in slope-intercept form. a) y = x +1 b) y = x!1 c) y =!x +1 d) y =!x!1 12. Find the equation of the line passing through the points (0,2) and (3,-6), in slope-intercept form. a) y =!x + 2 b) y = 2x!1 c) y =! 8 3 x + 2 d) y =! 4 3 x + 2 13. Solve the system of equations for x and y. 3x! y = 4 x + 2y = 6 a) (-14, 20) b) (2, 2) c) (-2, -2) d) (4, -8) 14. Solve the system of equations for x and y. 4x + 3y =11 3x! 7y =!1 a) (-14, 20) b) (-2, -1) c) (2, 1) d) (4, -8) 15. Simplify the expression and write the answer with positive exponents. " 1 % 3 $ 2 x!1 y 2 ' # & a) 1 8 x3 y 6 b) 1 8 x2 y 5 c) y 6 8x 3 d) y 5 8x 2 Updated: 11/12/2012 2
16. Simplify the expression and write the answer with positive exponents. ( 3x!2 c 3 ) 3 a) 27c 9 b) 27c6 x 6 x 4 c) 27c 6 x d) 27c 9 x 6 17. Simplify the expression and write the answer with positive exponents. x 3 y!4 w 3 x 4 y!5 w 3 a) xy b) 1 xy c) y x d) xyw 18. Find the product and simplify. (2x + 2)(3x 2! x!1) a) 6x 3! 2 b) 6x 3 + 6x 2! 4x! 2 c) 6x 3 + 6x 2! 4x! 2 d) 6x 3 + 4x 2! 4x! 2 19. Find the product and simplify. (2x! 2) 2 a) 4x 2! 4 b) 4x 2 + 4 c) 4x 2! 4x! 9 d) 4x 2!8x + 4 20. Find the product and simplify. (4x! 2)(x 2! 2x + 3) a) 4x 3 +10x 2 +8x! 6 b) 4x 3!10x 2 +16x! 6 c) 4x 3!10x 2! 6x! 6 d) 4x 3 +10x 2!16x! 6 Updated: 11/12/2012 3
21. Factor Completely. 5x 3 + 25x 2 + 30x a) 5x(x 2 + 5x + 6) b) x 2 + 5x + 6 c) (x + 3)(x + 2) d) 5x(x + 3)(x + 2) 22. What is the sum of the solutions to the equation x 2!8x +15 = 0? a) 8 b) - 2 c) 15 2 d) 15 23. Reduce to lowest terms. x 2! 9 x 2 + 6x + 9 a) x + 3 x! 3 b) x! 3 x + 3 c) - 1 d) 1 6x 24. Simplify. 24b5! 36b 3 6b 3 a) 24b 5! 6 b) 4b 2! 36b 3 c) 4b 2! 6 d) 4b 2! 6b 25. Simplify. 20x5 + 30x 8! 40x 9 10x 7 a)! 2 x 2 + 3x + 4 x 2 b) 2x2 + 3x! 4x 2 c) 2 x!2 + 3x! 4x2 d) 2 + 3x! 4x2 2 x 26. Simplify. 3c 12c 5 a) 6c 3 3c b) 36c 3 c c) 12c 6 3 d) 3c 11 12 27. Simplify. 6x 3 9x 7 a) 36x 10 b) 18x 6 x c) 54x 9 x d) 6x 5 9x Updated: 11/12/2012 4
28. Maria received $150 in simple annual interest at a rate of 5% on her CD. How much did she invest in the CD? a) $300 b) $30,000 c) $3000 d) $30 29. To enter a museum, adult visitors pay $7 each and children pay $3 each. In one day the museum collected a total of $348 from 60 visitors. How many visitors were adults and how many were children? a) 42 adults, 18 children b) 27 adults, 33 children c) 28 adults, 32 children d) 30 adults, 30 children Short Answer Problems 1. Perform the indicated operations and simplify: a. (!4) 3 + 3"(!5) = b.! 2 $ # " 3% &! 6 $ # " 7 & = % c.!7+ 20 (!10)+ 5 = 2. Evaluate:!a 2 + a 3 b 2, when a = -3 and b = -4. 3. Translate each phrase into an expression in terms of x: a. 6 less than the number x b. 10 more than the product of 4 and x c. Five times the difference of twice x and 8 4. Find the sum of!y! 3x and 4 x + y. 5. Simplify the expression 9! 3( 5x! 4) +8. 6. Simplify: 6( 2x + y)! 3( 2x! 4y) 7. Solve for y : 4(2y +1)! (y! 3) = 2y + 6 8. Solve the inequality for, x and graph the solution on the real number line. 8 6( x 3) 4x + 12 9. Solve the inequality for!, and graph the solution on the number line: 3(x!8) " 6(x! 5) 10. Solve the inequality for!, and graph the solution on the number line.!!! 2 >!!! +!! 11. The length of a rectangle is 5 inches less than 3 times the width. If the perimeter is 54 inches, find the length and width. Updated: 11/12/2012 5
12. One number is four more than three times another. If their sum is increased by five, the result is twenty nine. Find the numbers. 13. If 4! 5 = 23, then 4! =? 14. The sum of three consecutive even integers is 108. Find the numbers. 15. The sum of two consecutive integers is 93. Find the numbers. 16. Michael has $2.35 in dimes and nickels. He has a total of 29 coins. How many of each does he have? 17. Shahin is twice as old as his sister. In 10 year s time the sum of their ages will be 44 years. How old is each of them now? 18. Using the formula,!" =!"#, solve for r. 19. Find the x- and y-intercepts for 4x! 2y =!8, and then use them to draw the graph. 20. Sketch the graph of the equation!8x + 6y = 24 on the rectangular coordinate system using the grid below. Updated: 11/12/2012 6
21. Sketch the graph of the equation y =! 2 x + 2 on the rectangular coordinate system using the grid below. 3 22. Sketch the graph of the equation y = 1 x! 4 on the rectangular coordinate system using the grid below. 2 23. Sketch the graph of the equation y = 3on the rectangular coordinate system using the grid below. Updated: 11/12/2012 7
24. Sketch the graph of the equation x =!2 on the rectangular coordinate system using the grid below. 25. Given the equation!3x + 4y =!12, determine the slope and y-intercept. 26. Find the slope of a line which is parallel to 2! + 4! = 6. 27. Find y if the line through ( 2, 4) and (6, y) has a slope of 1 2. 28. Find y if the line through (3, 6) and (6, y) has a slope of 7. 1 29. Find the equation of the line through ( 2, 1) with slope. Write the answer in slope-intercept form. 2 30. Find the slope of a line which is perpendicular to! = 2! + 8. 31. Given f (x) = 2 + x 2, evaluate f (7). 32. Given g(x) = 1 + 4, evaluate and simplify g(3). x! 2 33. Given h(x) = x, evaluate and simplify h(5). x + 9 34. Given t(x) = 2x 2 + 2x!10, evaluate t(!1). 35. Is the ordered pair (4,5) a solution to the system? 2! 3! = 7 4!! = 0 36. Is the ordered pair ( 2,1) a solution to the system? 2! + 3! = 1 3!! = 7 37. Solve the system of equation by any convenient method. 5x 4y = 7 6x + 8y = 2 Updated: 11/12/2012 8
38. Solve by elimination. 2x + 3y = 4 5x + 4y = 3 39. Solve by substitution. 3x! 3y = 7 y =!1+ 2x 40. Simplify the expression and write the answer with positive exponents only. 41. What is the product of 8!!!! and 5!!!? 5 2 4 ( 3y ) ( 2y ) 3 42. Perform the indicated operations and simplify: 2x 2 y 3xy( x 1) 43. Express in scientific notation: a. 3,460,000 b. 0.00568 44. Express in standard notation: a. 2.094!10 "6 b. 5 7 10 45. Multiply or divide as indicated. Reduce all answers to lowest terms. a.!!!!!!!!!!!!!!!!! b.!!!!!!!"!!!!!!!! 46. Simplify the radicals. a. 18 + 8 b. 5 12! 2 75 c. 54 + 4 24 d. e. 5m 640m9!6y 50y3 47. If a right triangle has base equal to 5 feet and height equal to 3 feet, find the hypotenuse. Simplify your answer. 48. If a right triangle has base equal to 6 feet and hypotenuse equal to 11 feet, find the height. Simplify your answer. Updated: 11/12/2012 9
MAT 012/051 Practice Final Answer Key Multiple Choice Answers 1. b 2. d 3. d 4. d 5. c 6. d 7. c 8. c 9. a 10. a 11. a 12. c 13. b 14. c 15. c 16. a 17. c 18. d 19. d 20. b 21. d 22. a 23. b 24. c 25. d 26. a 27. b 28. c 29. a Short Answer Solutions 1. a. 79 b.!! c. 4 2. 441 3. a.! 6 b. 4! + 10 c. 5 2! 8 4.! 5. 15! + 29 6. 6! + 18! 7. y =! 1 5 8. x! 7 9. x! 2 10. x > 39 20 11. L = 19 inches, W = 8 inches 12. 5 and 19 13. 4x = 28 14. 38, - 36, and 34 15. 46 and 47 16. 11 nickels and 18 dimes 17. Shahin is 16 years old and his Sister is 8 years old. 18. r = Pv nt 19. 20. (0,4) (0,4) (-2,0) (-3,0) Updated: 11/12/2012 10
21. 23. (0,2) (0,3) (3,0) 22. 24. (-2,0) (0,-4) (2,-3) 25. m = 3 4,b = - 3 26. m =! 1 2 27. y = 8 28. y = 15 29. y = 1 2 x + 2 30. m = 1 2 31. f(7) = 51 32. g(3) = 5 42.!x 2 y + 3xy 33. h(5) = 5 14 34. t(-1) = -10 35. No 36. Yes 37. x = -3, y = -2 38. x =-1, y = 2 39. x = 4 3, y = 5 3 40. 8 9y 22 41. 40 p 3 q 7 Updated: 11/12/2012 11
43. a. 3.46!10 6 b. 5.68!10 "3 44. a..000002094 b. 700,000 45. a. x x + 3 b. x! 5 2x 2 (x! 3) 46. a. 5 2 b. 0 c. 11 6 d. 40m 5 10m e.!30y 2 2y 47. 34 48. 85 Updated: 11/12/2012 12