Q: A chemist mixes two solutions, one with a concentration of $$30\%$$ and another with $$50\%$$, to obtain $$10$$ liters of a $$40\%$$ solution. Which system of equations represents this scenario if $$x is $$the amount (in liters) of the $$30\%$$ solution and $$y is $$the amount of the $$50\%$$ solution?

$$ \begin{cases} x + y = 10 \\ 0.3x + 0.5y = 0.4 \times 10 \end{cases} $$

Q: A population of bacteria triples every $$4$$ hours. If the initial population is $$200$$, which equation models the population $$P$$ after $$t$$ hours?

$$ P = 200 \times 3$$^{t/4}$$ $$

Question 1

Which of the following is the correct equation of a circle with center at $$(-3, 4)$$ and radius $$5$$?

Accepted Answer

$$ (x + 3)^2$ + (y - 4)^2$ = 25 $$

Question 2

A chemist mixes two solutions, one with a concentration of $$30\%$$ and another with $$50\%$$, to obtain $$10$$ liters of a $$40\%$$ solution. Which system of equations represents this scenario if $$x is $$the amount (in liters) of the $$30\%$$ solution and $$y is $$the amount of the $$50\%$$ solution?

Accepted Answer

$$ \begin{cases} x + y = 10 \ 0.3x + 0.5y = 0.4 	imes 10 \end{cases} $$

Question 3

Given the function $$f(x) = 2x^2$ - 8x + 6$$, what is the vertex of the parabola?

Accepted Answer

$$ (2, -2) $$

Question 4

Which of the following expressions is equivalent to $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

$$ 7\sqrt{2} $$

Question 5

If $$f(x) = 3x - 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$ 7 $$

Question 6

A ball is thrown upward from the top of a $$20$$ meter building with an initial velocity of $$15 m/s. $$Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 15t + 20. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$ t = 1.53 $$

Question 7

Which of the following is the inverse function of $$f(x) = 2x + 7$$?

Accepted Answer

$$ f$$^{-1}$$(x) = \frac{x - 7}{2} $$

Question 8

Which of the following is the correct solution to the equation $$x^2 - 6x + 13 = 0$?

Accepted Answer

$$ x = 3 \pm 2i $$

Question 9

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

$$ (-\infty, -3) \cup (-3, 3) \cup (3, \infty) $$

Question 10

A population of bacteria triples every $$4$$ hours. If the initial population is $$200$$, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$ P = 200 	imes 3$$^{t/4}$$ $$

Question 11

Which of the following is the correct solution to $$\log_2$(x - 1) = 3$$?

Accepted Answer

Question 12

Which of the following is the correct solution to $$\log_2$(x - 1) = 3$$?

Accepted Answer

$$ x = 9 $$

Question 13

Which of the following is the correct factorization of $$x^2 - 10x + 25$?

Accepted Answer

$$ (x - 5)^2$ $$

Question 14

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

Accepted Answer

$$ 13 $$

Question 15

Which of the following is the correct solution to the inequality $$2x - 5 \u003e 7$$?

Accepted Answer

$$ x \u003e 6 $$

Question 16

Which of the following is the correct simplified form of $$(2x - 3)(x + 4)$$?

Accepted Answer

$$ 2x^2$ + 5x - 12 $$

Question 17

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for driving $$x$$ miles?

Accepted Answer

$$ C(x) = 0.20x + 25 $$

Question 18

Which of the following is the correct solution to $$2x^2 - 8x = 0$?

Accepted Answer

$$ x = 0, 4 $$

Question 19

Which of the following is the correct simplified form of $$\frac{2x^2$ - 8}{2x}$$ for $$x 
eq 0$$?

Accepted Answer

$$ x - 2 + \frac{4}{x} $$

Precalculus Study Guide: Corequisite College Algebra (Math 030/130) - Course Topics and Concepts

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