40 algebra multiple choice questions

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Home>Mathematics homework help>Algebra homework help>40 algebra multiple choice questions

Question 1 of 40

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution. 32x + 3x - 2 = 0

A. {1}

B. {-2}

C. {5}

D. {0}

Question 2 of 40

Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log x + 3 log y

A. log (xy)

B. log (xy3)

C. log (xy2)

D. logy (xy)3

Question 3 of 40

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)

Question 4 of 40

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}

Question 5 of 40

Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log2 96 – log2 3

A. 5

B. 7

C. 12

D. 4

Question 6 of 40

Write the following equation in its equivalent logarithmic form. 2-4 = 1/16

A. Log4 1/16 = 64

B. Log2 1/24 = -4

C. Log2 1/16 = -4

D. Log4 1/16 = 54

Question 7 of 40

Approximate the following using a calculator; round your answer to three decimal places. e-0.95

A. .483

B. 1.287

C. .597

D. .387

Question 8 of 40

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution. ex = 5.7

A. {ln 5.7}; ≈1.74

B. {ln 8.7}; ≈3.74

C. {ln 6.9}; ≈2.49

D. {ln 8.9}; ≈3.97

Question 9 of 40

Evaluate the following expression without using a calculator. 8log8 19

A. 17

B. 38

C. 24

D. 19

Question 10 of 40

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

Question 11 of 40

The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.

A. bx; (∞, -∞); (1, ∞)

B. bx; (-∞, -∞); (2, ∞)

C. bx; (-∞, ∞); (0, ∞)

D. bx; (-∞, -∞); (-1, ∞)

Question 12 of 40

Evaluate the following expression without using a calculator. Log7 √7

A. 1/4

B. 3/5

C. 1/2

D. 2/7

Question 13 of 40

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, ∞)

Question 14 of 40

Find the domain of following logarithmic function. f(x) = log (2 - x)

A. (∞, 4)

B. (∞, -12)

C. (-∞, 2)

D. (-∞, -3)

Question 15 of 40

Consider the model for exponential growth or decay given by A = A0ekt. 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

Question 16 of 40

Find the domain of following logarithmic function. f(x) = log5 (x + 4)

A. (-4, ∞)

B. (-5, -∞)

C. (7, -∞)

D. (-9, ∞)

Question 17 of 40

Use properties of logarithms to expand the following logarithmic expression as much as possible. logb (x2y)

A. 2 logy x + logx y

B. 2 logb x + logb y

C. logx - logb y

D. logb x – logx y

Question 18 of 40

Write the following equation in its equivalent logarithmic form. 3√8 = 2

A. Log2 3 = 1/8

B. Log8 2 = 1/3

C. Log2 8 = 1/2

D. Log3 2 = 1/8

Question 19 of 40

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. ex+1 = 1/e

A. {-3}

B. {-2}

C. {4}

D. {12}

Question 20 of 40

Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k.

A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t

B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t

C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t

D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe

Question 21 of 40

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)

Question 22 of 40

Solve the following system.

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2x + y = 2 x + y - z = 4 3x + 2y + z = 0

A. {(2, 1, 4)}

B. {(1, 0, -3)}

C. {(0, 0, -2)}

D. {(3, 2, -1)}

Question 23 of 40

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)

Question 24 of 40

Solve the following system.

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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)}

Question 25 of 40

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

Question 26 of 40

Solve each equation by the substitution method.

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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)}

Question 27 of 40

Write the partial fraction decomposition for the following rational expression.   x + 4/x2(x + 4)

A. 1/3x + 1/x2 - x + 5/4(x2 + 4)

B. 1/5x + 1/x2 - x + 4/4(x2 + 6)

C. 1/4x + 1/x2 - x + 4/4(x2 + 4)

D. 1/3x + 1/x2 - x + 3/4(x2 + 5)

Question 28 of 40

On your next vacation, you will divide lodging between large resorts and small inns. Let x represent the number of nights spent in large resorts. Let y represent the number of nights spent in small inns. Write a system of inequalities that models the following conditions: You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts average $200 per night and small inns average $100 per night. Your budget permits no more than $700 for lodging.

A.

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y ≥ 1 x + y ≥ 5 x ≥ 1 300x + 200y ≤ 700

B.

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y ≥ 0 x + y ≥ 3 x ≥ 0 200x + 200y ≤ 700

C.

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y ≥ 1 x + y ≥ 4 x ≥ 2 500x + 100y ≤ 700

D.

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y ≥ 0 x + y ≥ 5 x ≥ 1 200x + 100y ≤ 700

Question 29 of 40

Solve the following system by the substitution method. {x + 3y = 8 {y = 2x - 9

A. {(5, 1)}

B. {(4, 3)}

C. {(7, 2)}

D. {(4, 3)}

Question 30 of 40

Solve the following system.

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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)}

Question 31 of 40

Many elevators have a capacity of 2000 pounds. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x children and y adults will cause the elevator to be overloaded.

A. 50x + 150y > 2000

B. 100x + 150y > 1000

C. 70x + 250y > 2000

D. 55x + 150y > 3000

Question 32 of 40

A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions. Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.

A. z = 200x + 125y

B. z = 125x + 200y

C. z = 130x + 225y

D. z = -125x + 200y

Question 33 of 40

Solve each equation by the addition method.

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x2 + y2 = 25 (x - 8)2 + y2 = 41

A. {(3, 5), (3, -2)}

B. {(3, 4), (3, -4)}

C. {(2, 4), (1, -4)}

D. {(3, 6), (3, -7)}

Question 34 of 40

Find the quadratic function y = ax2 + bx + c whose graph passes through the given points. (-1, 6), (1, 4), (2, 9)

A. y = 2x2 - x + 3

B. y = 2x2 + x2 + 9

C. y = 3x2 - x - 4

D. y = 2x2 + 2x + 4

Question 35 of 40

Solve each equation by the substitution method.

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y2 = x2 - 9 2y = x – 3

A. {(-6, -4), (2, 0)}

B. {(-4, -4), (1, 0)}

C. {(-3, -4), (2, 0)}

D. {(-5, -4), (3, 0)}

Question 36 of 40

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

Question 37 of 40

Solve the following system by the substitution method. {x + y = 4 {y = 3x

A. {(1, 4)}

B. {(3, 3)}

C. {(1, 3)}

D. {(6, 1)}

Question 38 of 40

Solve each equation by either substitution or addition method.

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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)}

Question 39 of 40

Solve the following system.

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x = y + 4 3x + 7y = -18

A. {(2, -1)}

B. {(1, 4)}

C. {(2, -5)}

D. {(1, -3)}

Question 40 of 40

Solve the following system.

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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)}