Math 0312 EXAM 2 Review Questions
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1 Name Decide whether the ordered pair is a solution of the given system. 1. 4x + y = 2 2x + 4y = -20 ; (2, -6) Solve the system by graphing. 2. x - y = 6 x + y = 16 Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. 3. 5x - 2y = -1 x + 4y = 35 1
2 Solve the system by elimination. If the system is inconsistent or has dependent equations, say so x + 8y = 78 4x - 2y = x y = x y = 1 Tell how many solutions the system has. Do not actually solve. 6. 5x + 2y = -5 10x + 4y = x - y = 23 x + 3y = x = y + 3 6x - 2y = 3 Apply the product rule for exponents, if possible. 9. (-2x 3 )(9x 10 y 6 ) Evaluate the expression. 10. (-7) 0 + (-7) 0 2
3 Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary x -2 Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. 12. x-12 x -8 Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. 3x y 2 4 9xy x 3 y -3 x -3 y 2-5 Express the number in scientific notation Express the number in standard notation For the polynomial function, find the requested value. 17. f(x) = x 2-6x + 2; f(-2) For the given pair of functions, find the requested function. 18. f(x) = 5x - 3, g(x) = -9x + 9; (f - g)(x) 19. f(x) = x 2 + 4x - 3, g(x) = -8x 2 + 7x - 8; (f - g)(x) 3
4 Provide an appropriate response. 20. Let f(x) = x 2-2 and g(x) = 4x + 8. Find (f - g)(2). Find the product x 5 (-5x 6-2x 4 ) 22. (2x + 12)(x + 10) 23. (5y - 3)(25y y + 9) 24. (8y + x)(8y - x) 25. (10a - 7) t t [(4x - 3) + 3y] (x + 3y) 3 Express the area of the figure as a polynomial in descending powers of the variable x x - 3 2x + 5 Find the requested value. 30. If f(x) = x 2 + 9x + 1 and g(x) = 3x - 1, find (fg)(x). 4
5 Divide x7 + 28x x 5 7x x2 + 12x + 27 x x2 + 8x + 10 x y4 + 18y 3 + 3y - 1 6y Solve the problem. 35. A rectangular patio has an area of 3m m 2 + 9m Find the length if the width is 3m
6 36. The volume of a box is 3p p p 2. The height is p, and the width is p + 3. What is the length? For the pair of functions, find the quotient function. 37. f(x) = x 2 + 9x + 20, g(x) = x + 5 f (x) and give any x-values that are not in the domain of the quotient g Find the requested value. 38. If p(x) = 32x 5-36x x 2 and q(x) = 4x 2, find ( p q )(x). Factor out the greatest common factor. Simplify the factors, if possible wx - 8wy - 12wz 40. 5m(4 - m) + 7n(4 - m) Factor by grouping. 41. y 2 + 8y + 9y
7 Factor the trinomial completely x 2-4x z 2-8z x 3 + 2x 2 y - 12xy y 4-14y 2-8 Factor out the greatest common factor. Simplify the factors, if possible (m + p) 3-35(m + p) 2-15(m + p) 4 Factor the polynomial completely y 4-64 Factor the polynomial. 48. r 2 + 2rs + s 2-4 Factor the polynomial completely. 49. x
8 c (m + 3n) a b4-5000b3 + 54by3-135y a4b - 18b x3-20x2-4x a3-9a2b + 25ab2-15b3 Find all solutions by factoring k 2 = -24k - 64 Solve the equation. 58. (5y + 29)(4y + 11) = 0 8
9 Find all solutions by factoring. 59. x 2 + 6x - 16 = (x + 6)(x - 3) = -14 Solve the equation x x x = 0 Solve the problem. 62. The printed matter on a 14 by 18 centimeter page of a book must cover 60 square centimeters. If all margins are to be the same width, how wide should they be? 63. If an object is projected upward with an initial velocity of 64 ft per sec from a height h of 80 ft, then its height t sec after it is projected is defined by the equation h = -16t t How many sec after it is projected will it hit the ground? 9
10 Solve the equation for the specified variable k + ar = r - 8y for r 65. c = 6t + 6 t for t 10
11 Answer Key Testname: MATH EXAM 2 - REVIEW QUESTIONS 1. Yes Objective: (3.1) Decide If Ordered Pair Is Solution of System (Y/N) 2. {(11, 5)} Objective: (3.1) Solve Linear System by Graphing 3. {(3, 8)} Objective: (3.1) Solve System of Linear Equations by Substitution 4. {(-5, )} Objective: (3.1) Solve Linear System by Elimination , -1 Objective: (3.1) Solve Linear System by Elimination 6. Infinitely many Objective: (3.1) Determine Number of Solutions of Linear System 7. One solution Objective: (3.1) Determine Number of Solutions of Linear System 8. No solution Objective: (3.1) Determine Number of Solutions of Linear System x 13 y 6 Objective: (4.1) Simplify Using Product Rule Objective: (4.1) Evaluate Expression with Exponent of Zero x 2 Objective: (4.1) Write Expression with Only Positive Exponents 1 x 4 Objective: (4.1) Simplify Using Quotient Rule 13. 9x 11 y 6 Objective: (4.1) Simplify Using Power, Product, and Quotient Rules 14. y 25 32x 30 Objective: (4.1) Simplify Using Power, Product, and Quotient Rules Objective: (4.1) Write Number in Scientific Notation ,920 Objective: (4.1) Write Number in Standard Notation Objective: (4.3) Evaluate Polynomial Function x - 12 Objective: (4.3) Find Sum or Difference of Polynomial Functions 19. 9x 2-3x + 5 Objective: (4.3) Find Sum or Difference of Polynomial Functions Objective: (4.3) Evaluate Sum/Diff of Polynomial Functions 21. x x 9 Objective: (4.4) Multiply Monomial by Polynomial 22. 2x x Objective: (4.4) Multiply Two Binomials y 3-27 Objective: (4.4) Multiply Polynomials y 2 - x 2 Objective: (4.4) Multiply Conjugate Binomials a 2-140a + 49 Objective: (4.4) Square Binomial 26. 9t Objective: (4.4) Multiply Polynomials (Fractions and Decimals) x 2-24x xy - 18y + 9y 2 Objective: (4.4) Find Product of Special Trinomials 28. x 3 + 9x 2 y + 27xy y 3 Objective: (4.4) Find Third or Fourth Power of Binomial 29. 6x 2 + 9x - 15 Objective: (4.4) Express Area as Polynomial 30. 3x x 2-6x - 1 Objective: (4.4) Evaluate Product of Polynomial Functions 31. 3x x Objective: (4.5) Divide Polynomial by Monomial 32. x + 3 Objective: (4.5) Divide Polynomial by Binomial 33. x x + 6 Objective: (4.5) Divide Polynomial by Binomial 34. 6y 2 + 3y - 1 Objective: (4.5) Divide Polynomial by Binomial
12 Answer Key Testname: MATH EXAM 2 - REVIEW QUESTIONS 35. m 2 + 4m - 9 Objective: (4.5) Solve Apps: Dividing Polynomials 36. 3p 2 + 5p Objective: (4.5) Solve Apps: Dividing Polynomials 37. x + 4; x -5 Objective: (4.5) Find Quotient Function and State Domain 38. 8x 3-9x Objective: (4.5) Evaluate Quotient of Polynomial Functions 39. 4w(5x - 2y - 3z) Objective: (5.1) Factor Out Greatest Common Factor 40. (5m + 7n)(4 - m) Objective: (5.1) Factor Out Greatest Common Factor 41. (y + 8)(y + 9) Objective: (5.1) Factor by Grouping 42. -(x - 6)(x + 10) Objective: (5.2) Factor Trinomial with Lead Coefficient 1 or (3z - 4)(5z + 4) Objective: (5.2) Factor Trinomial with Lead Coefficient Not 1 or x(x - 2y)(x + 3y) Objective: (5.2) Factor Trinomial with Common Factor 45. (3y 2-4)(5y 2 + 2) Objective: (5.2) Factor Trinomial Using Substitution 46. 5(m + p) 2 (m + p - 7-3m 2-6mp - 3p 2 ) Objective: (5.1) Factor Out Greatest Common Factor 47. (3y 2 + 8)(3y 2-8) Objective: (5.3) Factor Difference of Two Squares 48. (r + s + 2)(r + s - 2) Objective: (5.3) Factor Perfect Square Trinomial 49. (x - 3)(x 2 + 3x + 9) Objective: (5.3) Factor Sum or Difference of Cubes 50. (9c + 5)(81c 2-45c + 25) Objective: (5.3) Factor Sum or Difference of Cubes 51. (6 + m + 3n)(6 - m - 3n) Objective: (5.3) ^Factor Complicated Expression 52. (7a 3-2)(7a 3 + 2) Objective: (5.3) Use Special Factoring with Higher Exponents 53. (10b + 3y)(2b - 5)(100b2-30by + 9y2) Objective: (5.3) Factor by Grouping and Then Use Special Factoring 54. 2b(2a2 + 3b)(2a2-3b) Objective: (5.4) Factor Binomial x(2x + 1)(3x + 1) Objective: (5.4) Factor Trinomial 56. (3a2 + 5b2)(5a - 3b) Objective: (5.4) Factor Polynomial with Four Terms , -8 Objective: (5.5) Solve Quadratic Equation by Factoring , Objective: (5.5) Solve Factored Equation Using Zero-Factor Property 59. {-8, 2} Objective: (5.5) Solve Quadratic Equation by Factoring 60. {, -4} Objective: (5.5) Solve Quadratic Equation by Factoring , - 4 3, 0 Objective: (5.5) Solve Cubic Equation by Factoring cm Objective: (5.5) Solve Apps: Factoring and Zero-Factor Property sec Objective: (5.5) Solve Apps: Factoring and Zero-Factor Property 64. r = 7k - 8y a - 1-7k + 8y or r = 1 - a Objective: (5.5) Solve for Specified Variable 65. t = 6-6 or t = c - 6 -c + 6 Objective: (5.5) Solve for Specified Variable 2
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