Question 1

Which of the following is the correct factorization of the quadratic expression $$x^2 - 5x + 6$?

Accepted Answer

$$ (x - 2)(x - 3) $$

Question 2

A ball is thrown upward with an initial velocity of $$32 ft/s $$from a height of $$48 ft. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t + 48. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$ t = 1 $$

Question 3

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

$$ (-\infty, 4) \cup (4, \infty) $$

Question 4

Solve the equation $$2x^2 - 8x = 0$.

Accepted Answer

$$ x = 0  or$$ $$ x = 4 $$

Question 5

Which of the following is the correct inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$ f$$^{-1}$$(x) = \dfrac{x - 7}{3} $$

Question 6

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$ 9 $$

Question 7

Which of the following is the solution set for $$|2x - 3| = 7$$?

Accepted Answer

$$ x = 5  or$$ $$ x = -2 $$

Question 8

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.2t}$$. If the initial amount is 100$ grams, how much remains after 5$ hours? (Round to the nearest gram.)

Accepted Answer

Question 9

Which of the following is the equation of a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$ (x - 2)^2$ + (y + 3)^2$ = 25 $$

Question 10

Which of the following is equivalent to $$\log_2$ 32$$?

Accepted Answer

$$ 5 $$

Question 11

Solve for $$x$$: $$3^{x} = 81$.

Accepted Answer

$$ x = 4 $$

Question 12

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$ x = 4, y = 3 $$

Question 13

Which of the following is the range of the function $$f(x) = \sqrt{x - 2}$$?

Accepted Answer

$$ [0, \infty) $$

Question 14

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is f(g(3$$))$$?

Accepted Answer

$$ 19 $$

Question 15

Which of the following is the solution to the quadratic equation $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$ x = -3 $$

Question 16

A car's value depreciates exponentially according to $$V(t) = 20000e$$^{-0.15t}$$, where t$ is in years. What is the value after 5$ years? (Round to the nearest dollar.)

Accepted Answer

$$ 9440 $$

Question 17

Which of the following is the correct solution for $$\log_{10} x = 2$$?

Accepted Answer

$$ x = 100 $$

Question 18

Which of the following is the correct equation for the tangent line to the circle $$(x - 1)^2$ + (y + 2)^2$ = 25 at $$the point $$(6, -2)$$?

Accepted Answer

$$ x = 6 $$

Question 19

Which of the following is the correct solution to $$\sqrt{x + 5} = 4$$?

Accepted Answer

$$ x = 11 $$

Question 20

Which of the following is the correct solution to the equation $$2^{x} = 1/8$?

Accepted Answer

$$ x = -3 $$

College Algebra Syllabus and Learning Goals – Baruch College MTH 1030

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