 # [Solved] Maths

1.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

2.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

3.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

4.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}

5.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

6.An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. 7 grams
B. 8 grams
C. 23 grams
D. 4 grams

7.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 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, ∞)

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)

9.Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.
(-1, -4), (1, -2), (2, 5)
A. y = 2×2 + x – 6
B. y = 2×2 + 2x – 4
C. y = 2×2 + 2x + 3
D. y = 2×2 + x – 5

10.Solve the following system by the addition method.
{4x + 3y = 15
{2x – 5y = 1
A. {(4, 0)}
B. {(2, 1)}
C. {(6, 1)}

11.Write the partial fraction decomposition for the following rational expression.
4/2×2 – 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)
D. {(3, 1)}

12.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

13.Solve each equation by the substitution method.
x2 – 4y2 = -7
3×2 + 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)}

14.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)}

15.Solve the following system.
x = y + 4
3x + 7y = -18
A. {(2, -1)}
B. {(1, 4)}
C. {(2, -5)}
D. {(1, -3)}
B. {(1/4, 1/3, -2)}

16.Solve the following system.
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)}
C. {(1/3, 1/5, -1)}
D. {(1/2, 1/3, -1)}

17.Solve each equation by the substitution method.
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)}

18.Write the partial fraction decomposition for the following rational expression.
1/x2 – c2 (c ≠0)
A. 1/4c/x
B. 1/2c/x – c – 1/2c/
C. 1/3c/x – c – 1/2c/x + c
D. 1/2c/x – c – 1/3c/x +

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