60 Multiple Choice Algebra Questions

Q1. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x2 – 2x – 5    a. maximum; 1    b. minimum; 1    c. maximum; – 6    d. minimum; – 6 Q2. Find the domain of the rational function. g(x) = /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.27.23 PM.png    a. all real numbers    b. {x|x ≠ -7, x ≠ 7, x ≠ -5}    c. {x|x ≠ -7, x ≠ 7}    d. {x|x ≠ 0, x ≠ -49} Q3. Solve the inequality. (x – 5)(x2 + x + 1) > 0    a. (-∞, -1) or (1, ∞)    b. (-1, 1)    c. (-∞, 5)    d. (5, ∞) Q4. Find the domain of the rational function. f(x) = /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.27.18 PM.png    a. {x|x ≠ -3, x ≠ 5}    b. {x|x ≠ 3, x ≠ -5}    c. all real numbers    d. {x|x ≠ 3, x ≠ -3, x ≠ -5} Q5. Solve the equation in the real number system. x3 + 9×2 + 26x + 24 = 0    a. {-4, -2, -3}    b. {2, 4}    c. {3, 2, 4}    d. {-4, -2} Q6. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.    a. -3    b. -2    c. 3    d. 2 Q7. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function. f(x) = x4 + 2×2 – 3    a. -4 and 4    b. -3 and 3    c. -6 and 6    d. -5 and 5 Q8. Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3×4 + 4×3 + 13×2 + 16x + 4    a. f(x) = (3x – 1)(x – 1)(x + 2)(x – 2)    b. f(x) = (3x + 1)(x + 1)(x + 2i)(x – 2i)    c. f(x) = (3x – 1)(x – 1)(x + 2i)(x – 2i)    d. f(x) = (3x + 1)(x + 1)(x + 2)(x – 2) Q9. Find the power function that the graph of f resembles for large values of |x|. f(x) = -x2(x + 4)3(x2 – 1)    a. y = x7    b. y = -x7    c. y = x3    d. y = x2 Q10. Use the Factor Theorem to determine whether x – c is a factor of f(x). 8×3 + 36×2 – 19x – 5; x + 5    a. Yes    b. No Q11. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = 9×3 + 8×2 – 6    a. No; the last term has no variable    b. Yes; degree 5    c. Yes; degree 3    d. Yes; degree 6 Q12. Solve the equation in the real number system. x4 – 3×3 + 5×2 – x – 10 = 0    a. {-1, -2}    b. {1, 2}    c. {-1, 2}    d. {-2, 1} Q13. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?    a. 25,600 ft2    b. 19,200 ft2    c. 12,800 ft2    d. 6400 ft2 Q14. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.27.10 PM.png    a. Yes; degree 3    b. No; x is a negative term    c. No; it is a ratio    d. Yes; degree 1 Q15. Give the equation of the oblique asymptote, if any, of the function. h(x) = /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.27.06 PM.png    a. y = 4x    b. y = 4    c. y = x + 4    d. no oblique asymptote Q16. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers. f(x) = 3×4 – 6×3 + 4×2 – 2x + 1    a. no real roots; f(x) = (x2 + 1)(3×2 + 1)    b. 1, multiplicity 2; f(x) = (x – 1)2(3×2 + 1)    c. -1, 1; f(x) = (x – 1)(x + 1)(3×2 + 1)    d. -1, multiplicity 2; f(x) = (x + 1)2(3×2 + 1) Q17. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) = /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.27.02 PM.png    a. symmetry with respect to the y-axis    b. symmetry with respect to the origin    c. neither Q18. Find the vertex and axis of symmetry of the graph of the function. f(x) = -3×2 – 6x – 2    a. (-1, 1) ; x = -1    b. (2, -26) ; x = 2    c. (1, -11) ; x = 1    d. (-2, -8) ; x = -2 Q19. Find the indicated intercept(s) of the graph of the function. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.26.50 PM.png Q20. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = -x2 – 2x + 2    a. minimum; – 1    b. maximum; 3    c. minimum; 3    d. maximum; – 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q1. The logistic growth function f(t) = /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.25.57 PM.png describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?    a. 480 butterflies    b. 401 butterflies    c. 244 butterflies    d. 4800 butterflies Q2. Find the present value. Round to the nearest cent. To get $10,000 after 2 years at 18% compounded monthly    a. $5000.00    b. $6995.44    c. $8363.87    d. $11,956.18 Q3. A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.    a. 3.44%    b. 3.40%    c. 36%    d. 3.04% Q4. The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 600 years? (Round your answer to three decimal places.)    a. 0    b. 0.286    c. 94.311    d. 55.668 Q5. A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.    a. 1031    b. 17,099    c. 20,040    d. 36,108 Q6. pH = -log10[H+] Find the [H+] if the pH = 8.4.    a. 3.98 x 10-8    b. 2.51 x 10-8    c. 3.98 x 10-9    d. 2.51 x 10-9 Q7. Express y as a function of x. The constant C is a positive number. ln y = ln 4x + ln C    a. y = 4Cx    b. y = 4x + C    c. y = (4x)C    d. y = x + 4C Q8. Express as a single logarithm. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.25.31 PM.png Q9. Find the amount that results from the investment. $480 invested at 16% compounded quarterly after a period of 4 years    a. $864.45    b. $419.03    c. $869.11    d. $899.03 Q10. What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.    a. $864.12    b. $1188.62    c. $1638.78    d. $627.48 Q11. Change the exponential expression to an equivalent expression involving a logarithm. 5x = 125    a. log125 x = 5    b. log5 125 = x    c. log125 5 = x    d. logx 125 = 5 Q12. Find functions f and g so that the composition of f and g is H. H(x) = |4 – 3×2|    a. f(x) = x2 ; g(x) = 4 – 3|x|    b. f(x) = 4 – 3|x|; g(x) = x2    c. f(x) = |x|; g(x) = 4 – 3×2    d. f(x) = 4 – 3×2 ; g(x) = |x| Q13. The half-life of plutonium-234 is 9 hours. If 70 milligrams is present now, how much will be present in 6 days? (Round your answer to three decimal places.)    a. 0.689    b. 44.096    c. 0.001    d. 23.091 Q14. Solve the equation. log327 = x    a. {81}    b. {9}    c. {3}    d. {30} Q15. The function f(x) = 300(0.5) x/60 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 170 years. Round to the nearest whole number.    a. 425 pounds    b. 42 pounds    c. 235 pounds    d. 53 pounds

 

 

 

 

 

 

 

 

 

 

 

 

Q16. Change the logarithmic expression to an equivalent expression involving an exponent. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.24.50 PM.png Q17. The function f is one-to-one. Find its inverse. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.24.26 PM.png Q18. If the following defines a one-to-one function, find the inverse. {(6, 6), (12, 7), (10, 8), (8, 9)}    a. {(7, 6), (9, 10), (6, 10), (7, 8)}    b. {(7, 6), (6, 10), (6, 12), (7, 8)}    c. Not a one-to-one function    d. {(6, 6), (7, 12), (8, 10), (9, 8)} Q19. Change the exponential expression to an equivalent expression involving a logarithm. ex = 25    a. log 25 x = e    b. log x e = 25    c. ln x = 25    d. ln 25 = x Q20. Express as a single logarithm. 3log6x + 5log6(x – 6)    a. log6x3(x – 6)5    b. log6x(x – 6)15    c. log6x(x – 6)    d. 15 log6x(x – 6)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q1. Rob bought 2 pairs of shorts, 3 shirts and a pair of shoes for $146.64. Jessie bought 3 pairs of shorts, 5 shirts and 2 pairs of shoes for $256.35. Allen bought a pair of shorts and 4 shirts for $104.07. What is the price of a pair of shorts? Express answer rounded to two decimal places.    a. $14.55    b. $50.40    c. $22.38    d. $10.30 Q2. An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?    a. 153 miles    b. 168 miles    c. 147 miles    d. 132 miles Q3. A retired couple has $190,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 7%. The rest they want to invest in AA bonds yielding 10% per year. How much should they invest in each to realize exactly $17,200 per year?    a. $120,000 at 7% and $70,000 at 10%    b. $130,000 at 7% and $60,000 at 10%    c. $130,000 at 10% and $60,000 at 7%    d. $140,000 at 10% and $50,000 at 7% Q4. Verify that the values of the variables listed are solutions of the system of equations. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.23.03 PM.png x = 5, y = 5    a. not a solution    b. solution Q5. Use Cramer’s rule to solve the linear system.    a. x = 2, y = 4    b. x = 4, y = 2    c. x = -2, y = 4    d. x = -4, y = -2

Q6. A flat rectangular piece of aluminum has a perimeter of 62 inches. The length is 15 inches longer than the width. Find the width.    a. 31 inches    b. 38 inches    c. 8 inches    d. 23 inches Q7. Verify that the values of the variables listed are solutions of the system of equations. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.22.52 PM.png x = 0, y = -5, z =-4    a. solution    b. not a solution Q8. Write the partial fraction decomposition of the rational expression. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.22.39 PM.png Q9. Solve the system using the inverse method. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.22.19 PM.png    a. x = -36, y = -38, z = -14    b. x = -14, y = 88, z = -32    c. x = -60, y = 82, z = -34    d. x = 8, y = 24, z = 10 Q10. Solve the system using the inverse method. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.22.04 PM.png    a. x = -19, y = -61, z = -35    b. x = -1, y = -3, z = -2    c. x = 15, y = -49, z = 27    d. x = -2, y = -28, z = 20 Q11. Perform the indicated operations and simplify. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.21.06 PM.png

Q12. Write the partial fraction decomposition of the rational expression. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.20.26 PM.png Q13. Solve the system. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.19.33 PM.png    a. inconsistent (no solution)    b. (-9, 0)    c. (0, 0)    d. y = – x/2 – 9, where x is any real number Q14. Find the inverse of the matrix. A= /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.18.13 PM.png Q15. A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?    a. 16 adults    b. 10 adults    c. 29 adults    d. 24 adults Q16. The Family Fine Arts Center charges $21 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 486 people paid admission, the total receipts were $6894. How many who paid were senior citizens?    a. 208 senior citizens    b. 368 senior citizens    c. 118 senior citizens    d. 278 senior citizens

 

 

Q17. Use the elimination method to solve the system. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.17.40 PM.png    a. x = 11, y = -11    b. x = -2, y = 9    c. x = 9, y = -9    d. x = -9, y = 9 Q18. Use the properties of determinants to find the value of the second determinant, given the value of the first. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.16.49 PM.png&    a. -44    b. 44    c. 88    d. -88 Q19. Jenny receives $1270 per year from three different investments totaling $20,000. One of the investments pays 6% , the second one pays 8%, and the third one pays 5%. If the money invested at 8% is $1500 less than the amount invested at 5%, how much money has Jenny invested in the investment that pays 6%?    a. $8500    b. $4500    c. $10,000    d. $1500 Q20. Solve the system of equations. /Users/Schugg/Desktop/Screen Shot 2016-02-24 at 5.16.20 PM.png

a. x = 0, y = 1, z = 0    b. x = 1, y =1, z = 1    c. x = 0, y = 1, z = -1    d. x = 0, y = 0, z = 1

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