0.0/ 2.5 Points 1. Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 31-x = 1/27 A. {2} B. {-7} C. {4} D. {3} 2.5 Points 2. Perform the long division and write the partial fraction decomposition of the remainder term. x4 - x2 + 2/x3 - x2 A. x + 3 - 2/x - 1/x2 + 4x - 1 B. 2x + 1 - 2/x - 2/x + 2/x + 1 C. 2x + 1 - 2/x2 - 2/x + 5/x - 1 D. x + 1 - 2/x - 2/x2 + 2/x - 1 2.5 Points 3. Solve each equation by either substitution or addition method. x2 + 4y2 = 20 x + 2y = 6 A. {(5, 2), (-4, 1)} B. {(4, 2), (3, 1)} C. {(2, 2), (4, 1)} D. {(6, 2), (7, 1)} 2.5 Points 4. 5. Solve the following system by the addition method. {2x + 3y = 6 {2x - 3y = 6 A. {(4, 1)} B. {(5, 0)} C. {(2, 1)} D. {(3, 0)} 0.0/ 2.5 Points 6. Find the domain of following logarithmic function. f(x) = ln (x - 2)2 A. (, 2) (-2, -) B. (-, 2) (2, ) C. (-, 1) (3, ) D. (2, -) (2, ) 0.0/ 2.5 Points 7. Find the domain of following logarithmic function. f(x) = log (2 - x) A. (, 4) B. (, -12) C. (-, 2) D. (-, -3) 0.0/ 2.5 Points 8. Perform the long division and write the partial fraction decomposition of the remainder term. x5 + 2/x2 - 1 A. x2 + x - 1/2(x + 1) + 4/2(x - 1) B. x3 + x - 1/2(x + 1) + 3/2(x - 1) C. x3 + x - 1/6(x - 2) + 3/2(x + 1) D. x2 + x - 1/2(x + 1) + 4/2(x - 1) 0.0/ 2.5 Points 9. Solve each equation by the substitution method. x2 - 4y2 = -7 3x2 + y2 = 31 A. {(2, 2), (3, -2), (-1, 2), (-4, -2)} B. {(7, 2), (3, -2), (-4, 2), (-3, -1)} C. {(4, 2), (3, -2), (-5, 2), (-2, -2)} D. {(3, 2), (3, -2), (-3, 2), (-3, -2)} 0.0/ 2.5 Points 10. Write the partial fraction decomposition for the following rational expression. 1/x2 - c2 (c 0) A. 1/4c/x - c - 1/2c/x + c B. 1/2c/x - c - 1/2c/x + c C. 1/3c/x - c - 1/2c/x + c D. 1/2c/x - c - 1/3c/x + c 0.0/ 2.5 Points 11. Write the partial fraction decomposition for the following rational expression. ax +b/(x - c)2 (c 0) A. a/a - c +ac + b/(x - c)2 B. a/b - c +ac + b/(x - c) C. a/a - b +ac + c/(x - c)2 D. a/a - b +ac + b/(x - c) 0.0/ 2.5 Points 12. Write the form of the partial fraction decomposition of the rational expression. 5x2 - 6x + 7/(x - 1)(x2 + 1) A. A/x - 2 + Bx2 + C/x2 + 3 B. A/x - 4 + Bx + C/x2 + 1 C. A/x - 3 + Bx + C/x2 + 1 D. A/x - 1 + Bx + C/x2 + 1 0.0/ 2.5 Points 13. Solve the following system. 3(2x+y) + 5z = -1 2(x - 3y + 4z) = -9 4(1 + x) = -3(z - 3y) A. {(1, 1/3, 0)} B. {(1/4, 1/3, -2)} C. {(1/3, 1/5, -1)} D. {(1/2, 1/3, -1)} 0.0/ 2.5 Points 14. Write the partial fraction decomposition for the following rational expression. 4/2x2 - 5x - 3 A. 4/6(x - 2) - 8/7(4x + 1) B. 4/7(x - 3) - 8/7(2x + 1) C. 4/7(x - 2) - 8/7(3x + 1) D. 4/6(x - 2) - 8/7(3x + 1) 15. Use properties of logarithms to expand the following logarithmic expression as much as possible. Logb (xy3 / z3) A. 1/2 logb x - 6 logb y + 3 logb z B. 1/2 logb x - 9 logb y - 3 logb z C. 1/2 logb x + 3 logb y + 6 logb z D. 1/2 logb x + 3 logb y - 3 logb z 2.5 Points 16. Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. 3 ln x - 1/3 ln y A. ln (x / y1/2) B. lnx (x6 / y1/3) C. ln (x3 / y1/3) D. ln (x-3 / y1/4) 2.5 Points 17. Evaluate the following expression without using a calculator. Log7 7 A. 1/4 B. 3/5 C. 1/2 D. 2/7 2.5 Points 18. Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution. 2 log x = log 25 A. {12} B. {5} C. {-3} D. {25} 2.5 Points 19. Write the following equation in its equivalent exponential form. 4 = log2 16 A. 2 log4 = 16 B. 22 = 4 C. 44 = 256 D. 24 = 16 2.5 Points 20. Find the domain of following logarithmic function. f(x) = log (2 - x) A. (, 4) B. (, -12) C. (-, 2) D. (-, -3) 2.5 Points 21. Find the domain of following logarithmic function. f(x) = log5 (x + 4) A. (-4, ) B. (-5, -) C. (7, -) D. (-9, ) 2.5 Points 22. Consider the model for exponential growth or decay given by A = A 0ekt. If k __________, the function models the amount, or size, of a growing entity. If k __________, the function models the amount, or size, of a decaying entity. A. > 0; < 0 B. = 0; 0 C. 0; < 0 D. < 0; 0 2.5 Points 23. You have $10,000 to invest. One bank pays 5% interest compounded quarterly and a second bank pays 4.5% interest compounded monthly. Use the formula for compound interest to write a function for the balance in each bank at any time t. A. A = 20,000(1 + (0.06/4))4t; A = 10,000(1 + (0.044/14))12t B. A = 15,000(1 + (0.07/4))4t; A = 10,000(1 + (0.025/12))12t C. A = 10,000(1 + (0.05/4))4t; A = 10,000(1 + (0.045/12))12t D. A = 25,000(1 + (0.05/4))4t; A = 10,000(1 + (0.032/14))12t 2.5 Points 24. The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds? A. 10 grams after 10 seconds; 6 grams after 20 seconds B. 12 grams after 10 seconds; 7 grams after 20 seconds C. 4 grams after 10 seconds; 1 gram after 20 seconds D. 8 grams after 10 seconds; 4 grams after 20 seconds 2.5 Points 25. Solve each equation by the substitution method. x2 - 4y2 = -7 3x2 + y2 = 31 A. {(2, 2), (3, -2), (-1, 2), (-4, -2)} B. {(7, 2), (3, -2), (-4, 2), (-3, -1)} C. {(4, 2), (3, -2), (-5, 2), (-2, -2)} D. {(3, 2), (3, -2), (-3, 2), (-3, -2)} 2.5 Points 26. Solve the following system. x+y+z=6 3x + 4y - 7z = 1 2x - y + 3z = 5 A. {(1, 3, 2)} B. {(1, 4, 5)} C. {(1, 2, 1)} D. {(1, 5, 7)} 2.5 Points 27. Solve the following system. 2x + 4y + 3z = 2 x + 2y - z = 0 4x + y - z = 6 A. {(-3, 2, 6)} B. {(4, 8, -3)} C. {(3, 1, 5)} D. {(1, 4, -1)} 2.5 Points 28. Solve the following system by the addition method. {2x + 3y = 6 {2x - 3y = 6 A. {(4, 1)} B. {(5, 0)} C. {(2, 1)} D. {(3, 0)} 2.5 Points 29. Write the partial fraction decomposition for the following rational expression. x2 - 6x + 3/(x - 2)3 A. 1/x - 4 - 2/(x - 2)2 - 6/(x - 2) B. 1/x - 2 - 4/(x - 2)2 - 5/(x - 1)3 C. 1/x - 3 - 2/(x - 3)2 - 5/(x - 2) D. 1/x - 2 - 2/(x - 2)2 - 5/(x - 2)3 2.5 Points 30. Write the partial fraction decomposition for the following rational expression. 1/x2 - c2 (c 0) A. 1/4c/x - c - 1/2c/x + c B. 1/2c/x - c - 1/2c/x + c C. 1/3c/x - c - 1/2c/x + c D. 1/2c/x - c - 1/3c/x + c 2.5 Points 31. Write the form of the partial fraction decomposition of the rational expression. 5x2 - 6x + 7/(x - 1)(x2 + 1) A. A/x - 2 + Bx2 + C/x2 + 3 B. A/x - 4 + Bx + C/x2 + 1 C. A/x - 3 + Bx + C/x2 + 1 D. A/x - 1 + Bx + C/x2 + 1 2.5 Points 32. Write the partial fraction decomposition for the following rational expression. 6x - 11/(x - 1)2 A. 6/x - 1 - 5/(x - 1)2 B. 5/x - 1 - 4/(x - 1)2 C. 2/x - 1 - 7/(x - 1) D. 4/x - 1 - 3/(x - 1)