Math 46 Final Exam Review Packet

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1 Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x x Question 2. The sum of a number and its square is 72. Find the number. Question 3. Find the following product. Question 4. Find the area of the figure. (x + 1)(x 2 x + 1) Question 5. Use the point-slope form of the linear equation to find an equation of the line with the given slope and passing through the given point. Then write the equation in standard form: Question 6. Solve the equation. 8x + 1 = 39 Slope 7 ; through (5, 3). 8 Question 7. Solve the equation. x x (6x + 24) = 4 Question 8. Simplify the expression. [29 (4 + 6) 2] [ ] Question 9. Solve the system of equations. { 5x 15y = 9 x + 3y = 0 Question 10. Use the vertical line test to determine which graph is NOT a graph of a function. 1

2 Question 11. Perform the indicated operation. Simplify if possible. 2 x 2 3x x 2 1 Question 12. Use formulas to find the area of the figure. Question 13. Find the following product. 8x 2 ( 4x 2 + 3x 6) Question 14. Factor the polynomial complete. If the polynomial cannot be factored, write prime. 5x 3 + 5x 2 y 30xy 2 Question 15. Find the measures of angles 1, 2, and 3. Question 16. Find the domain and the range of the relation. {(8, 1), ( 8, 0), ( 5, 5), (13, 8)} Question 17. Write in standard notation

3 Question 18. Solve the equation. 6x 9 + 9x + 4 = 5x + 10x 8 Question 19. Factor out the GCF (greatest common factor) from the polynomial. 4m 9 + 6m 4 + 8m 2 Question 20. Solve the inequality. Graph the solution set and write it interval notation. 7 2x + 3 < 3 Question 21. Simplify the expression. Write the result using positive exponents only. 4z 3 Question 22. Factor the polynomial completely. If the polynomial cannot be factored, write prime. x 4 81 Question 23. Solve the equation. 2x + 2( 2x 4) = 10 4x Question 24. Solve the compound inequality. Graph the solution set. 6x 4 < 2x or 4x 12 Question 25. Factor the polynomial completely. If the polynomial cannot be factored, write prime. 25x 2 16 Question 26. List the elements of the set. If A = {17, 18, 19, 22} and B = {15, 17, 18, 20}, list the elements of A B. Question 27. Find the slope of the line that is perpendicular to the equation of the given line. Question 28. Multiply. ( 8)( 7)( 3) 3x 4y = 9 Question 29. Graph the linear equation. x + 8y = 8 Question 30. Factor the polynomial completely. If the polynomial cannot be factored, write prime. z 2 6z + 9 Question 31. Solve the system of equations. { y = 2x 4 4y + 20x = 72 Question 32. Factor the polynomial completely. If the polynomial cannot be factored, write prime. Question 33. Divide. Simplify if possible. x 2 x 35 z z + 24 z z + 64 z 2 + 3z z z + 48 Question 34. A 6-foot board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the shorter pice. If the shorter piece is x feet long, find the lengths of both pieces. 3

4 Question 35. Factor the polynomial completely. If the polynomial cannot be factored, write prime. x 2 8x 33 Question 36. Solve the inequality. Graph the solution set and write it in interval notation. x 9 < 4 Question 37. Simplify the expression. Write the result using positive exponents only. Question 38. Divide. Simplify if possible. ( xy 4 x 5 y ) 2 7x 7 4x 2 56x 32x 3 Question 39. The area of a circle is 49π square meters. Find its radius. Question 40. Write the sentence as an equation. Use x to represent any unknown number. Question 41. Solve the equation. b(b + 13) = 0 Question 42. Factor the polynomial completely. If the polynomial cannot be factored, write prime. 9z 2 + 6z 8 Question 43. Solve the equation. x 2 2x 63 = 0 Question 44. Simplify the expression. ( pm 4 ) 7 Question 45. Solve the absolute value equation. 3x = 8 Question 46. Factor. 64p 3 1 Question 47. Solve the system of equations. { 2x + 7y = 6 5x + 3y = 26 Question 48. Perform the indicated operations. Question 49. Factor by grouping. q 5 (6x 2 + 4) ( x 3 + 9x 2 10) 18x 2 15x + 24x 20 Question 50. Solve. Five times some number added to 4 amounts to -2 added to the product of 3 and the number. Question 51. Solve. Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 7 miles per hour and Dave bikes at 8 miles per hour. How long will it be until they are 25 miles apart from each other? Question 52. Find the perimeter of the figure named and shown. Equilateral triangle. 4

5 Question 53. Solve the system of equations. { 3x + 2y = 5 6x 4y = 10 Question 54. Graph the function. f(x) = 3 5 x 3 Question 55. Add or subtract as indicated. Write the answer in lowest terms Question 56. Find the product. (p + 7q)(p 7q) Question 57. Solve the equation. 1 x x + 3 = 4 x x + 21 Question 58. Solve the equation. 3x x = 5 Question 59. Multiply. Simplify if possible. 5p 5 p 9p 2 8p 8 Question 60. Write the algebraic expression described. Simplify if possible. If x represents the first of four consecutive odd integers, express the sum of the first integer and the fourth integer in terms of x. Question 61. Find the slope of the line that goes through the given points. (9, 2) and (5, 4) Question 62. Simplify x x Question 63. Use the quotient rule to simplify the expressions. Question 64. Evaluate the expression for the given replacement values. (x + 3y) 2 ; x = 4, y = 3 Question 65. Multiply. (3x 5y) 2 Question 66. Graph the inequality. 3x + y < 4 Question 67. Add. 2 + ( 4) Question 68. Simplify. 8 (10x + 15) 5 s 14 t 5 s 2 t Question 69. Use the Pythagorean Theorem to find the missing length in the right triangle. 5

6 Question 70. The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measure of the indicated angle. Find the measure of 3. Question 71. Perform the division. 40x 6 48x 5 48x 4 8x 5 Question 72. Solve the inequality. Graph the solution set. x < 13 Question 73. Find the product using the FOIL method. (5x 3)(6x 1) Question 74. Solve the equation. x(3x + 16) = 12 Question 75. Simplify. 16 7x 2 35x Question 76. Solve the inequality. Graph the solution set. 6x + 9 > 4 Question 77. Solve the absolute value equation. 3x Question 78. Find the x and y intercepts of the following linear equation. 6x 24y = 24 Question 79. Simplify the expression. 7 + ( 13) ( 8) Question 80. Simplify the expression by combining any like terms. 9y y 1 Question 81. Find f( 2) when f(x) = x 2 + 2x 5. Question 82. Find an equation of the line through the given points. Write the equation in standard form. Through (4, 0) and (2, 5) Question 83. Solve the system of equations by graphing the equations on the same set of axes. { y = x 5 Question 84. Find the slope of the line. x = 2 y = 2x 8 Question 85. Find the equation of the line. Write the equation using function notation. Through (2, 3); perpendicular to x + 3y = 3 Question 86. Use similar triangles and the fact that corresponding sides are proportional to find the length of the segment marked with an x. 6

7 Question 87. Simplify the rational expression. Question 88. Simplify the following. z x x x + 6 Question 89. Find the measure of angle A for the triangle shown. Question 90. Graph. y = 2x 4 7

C) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution

C) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution Sample Departmental Final - Math 46 Perform the indicated operation. Simplif if possible. 1) 7 - - 2-2 + 3 2 - A) + - 2 B) - + 4-2 C) + 4-2 D) - + - 2 Solve the problem. 2) The sum of a number and its