Q: A population of bacteria doubles every 4 hours. If the initial population is 500, what will the population be after 12 hours?

$$500 \times 2$$^{3}$$ = 4000$$

Q: A triangle has sides of length 7, 24, and 25. What is the measure of the largest angle?

$$\cos$$^{-1}$$\left(\frac{7^2$ + 24^2$ - 25^2$}{2 \times 7 \times 24}\right) \approx 90^\circ$$

Q: A car travels along a circular track of radius 100 meters. If it completes a quarter of the circle, what is the distance traveled?

$$\frac{1}{4} \times 2\pi \times 100 = 50\pi \approx 157.08$$ meters

Question 1

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream over time $$t (in $$hours) by the function $$C(t) = 5e$$^{-0.4t}$$. What is the concentration after 3 hours?

Accepted Answer

$$C(3) = 5e$$^{-1.2}$$ \approx 1.51$$

Question 2

Which of the following is the correct factorization of the polynomial $$f(x) = x^3$ - 4x^2$ + 5x - 2$$?

Accepted Answer

$$(x-1)(x-2)(x-1)$$

Question 3

A population of bacteria doubles every 4 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$$500 	imes 2$$^{3}$$ = 4000$$

Question 4

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

Accepted Answer

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

Question 5

A triangle has sides of length 7, 24, and 25. What is the measure of the largest angle?

Accepted Answer

$$\cos$$^{-1}$$\left(\frac{7^2$ + 24^2$ - 25^2$}{2 	imes 7 	imes 24}ight) \approx 90^\circ$$

Question 6

Which of the following is the correct solution to the equation $$2^{x+1} = 32$?

Accepted Answer

$$x = 4$$

Question 7

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 20x + 100$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue?

Accepted Answer

$$R(5) = -2(5)^2$ + 20(5) + 100 = 150$$

Question 8

Which of the following is the correct expression for the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r$$?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

Question 9

A vector $$	extbf{v}$$ has initial point $$(2, -1)$$ and terminal point $$(5, 3). $$What is $$	extbf{v} in $$component form?

Accepted Answer

$$(3, 4)$$

Question 10

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 11

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How many years will it take for only 60 grams to remain?

Accepted Answer

$$t = -\frac{1}{0.05} \ln\left(\frac{60}{100}\right) \approx 10.22$$

Question 12

Which of the following is the correct formula for the area $$A of a $$triangle given two sides $$a$$, $$b$$ and the included angle $$C$$?

Accepted Answer

$$A = \frac{1}{2}ab\sin C$$

Question 13

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 14

A car travels along a circular track of radius 100 meters. If it completes a quarter of the circle, what is the distance traveled?

Accepted Answer

$$\frac{1}{4} 	imes 2\pi 	imes 100 = 50\pi \approx 157.08$$ meters

Question 15

Which of the following is the correct expression for the sum $$\sum_{k=1}^{5} (2k-1)$$?

Accepted Answer

$$1 + 3 + 5 + 7 + 9 = 25$$

Question 16

Which of the following is the correct solution to the equation $$|3x - 7| = 5$$?

Accepted Answer

$$x = 4 or$$ $$x = \frac{2}{3}$$

Question 17

Which of the following is the correct formula for the period of the function $$y = 3\sin(2x)$$?

Accepted Answer

$$\frac{2\pi}{2} = \pi$$

Question 18

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

Accepted Answer

$$\sqrt{6^2$ + 8^2$} = 10$$

Question 19

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Precalculus and College Algebra Assessment Exam Topics: Structured Study Guide

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