Question 1

Solve the quadratic equation $$2x^2 - 3x - 5 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = \dfrac{3 \pm \sqrt{49}}{4}$$

Question 2

Given the equation $$\sqrt{2(x+16)} - 4 = x$$, which of the following is a solution?

Accepted Answer

$$x = 8$$

Question 3

A population of mosquitoes grows according to $$P = P_0$ e$$^{kt}$$. If P_0$ = 1000$$ and $$P = 1800$$ after 1 day, what is the population after 3 days (rounded to the nearest whole number)?

Accepted Answer

$$P \approx 3240$$

Question 4

Given the function $$f(x) = -2x^2$ + 4x - 9$$, what are the coordinates of the vertex?

Accepted Answer

$$(1, -7)$$

Question 5

Find the complex zeros of $$f(x) = x^3$ - 8x^2$ + 25x - 26.$$

Accepted Answer

$$x = 2,\ 3+2i,\ 3-2i$$

Question 6

Solve the logarithmic equation $$\log(8x + 1) = 1 + \log(x - 8). $$What is the value of $$x$$?

Accepted Answer

$$x = 9$$

Question 7

Given the exponential growth model $$P = P_0$ e$$^{kt}$$ with P_0$ = 1000$$ and $$P = 1800$$ after 1 day, how long will it take for the population to reach $$70,000$$ mosquitoes? (Round to the nearest tenth)

Accepted Answer

$$t \approx 6.7$$ days

Question 8

Which of the following is the line of best fit for the data set: $$(1, 4), (2, 6), (3, 8)$$?

Accepted Answer

$$y = 2x + 2$$

Question 9

Solve the system of equations using row operations:

$$\begin{cases} 4x + 7y = 22 \ 2x - y = 1 \end{cases}$$
What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 10

Determine the complex zeros of $$f(x) = x^4$ + 4x^3$ + 4x + 36x - 45.$$

Accepted Answer

$$x = 1, -5, 3i, -3i$$

Question 11

Which of the following best describes the effect of increasing the value of $$k in $$the exponential growth model $$P = P_0$ e$$^{kt}$$?

Accepted Answer

The population grows faster as $$k$$ increases.

Question 12

If $$f(x) = -2x^2$ + 4x - 9$$ models the height (in meters) of a projectile after $$x$$ seconds, what is the maximum height reached by the projectile?

Accepted Answer

$$-7$$ meters

Question 13

Solve for $$x$$: $$x^2 - 8x = 7$

Accepted Answer

$$x = 4 \pm \sqrt{23}$$

Question 14

A scientist records the following data for a chemical reaction: $$(1, 2.5), (2, 5.1), (3, 7.6). $$Which equation best models the line of best fit?

Accepted Answer

$$y = 2.55x$$

Question 15

Which of the following is a solution to $$\sqrt{2(x+16)} - 4 = x$$?

Accepted Answer

$$x = 8$$

Question 16

If $$\log(8x + 1) = 1 + \log(x - 8)$$, what is the value of $$x$$?

Accepted Answer

$$x = 9$$

Question 17

Given $$f(x) = x^3$ - 8x^2$ + 25x - 26$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 18

Solve the system using row operations:

$$\begin{cases} 4x + 7y = 22 \ 2x - y = 1 \end{cases}$$
What is the value of $$y$$?

Accepted Answer

$$y = 2$$

Precalculus Study Notes: Equations, Functions, and Applications

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