Practice Test 8 - AP Precalculus

20 questions. Answer them in any order, then submit to see your score and every explanation.

For $s(x)=\dfrac{x^2-5x+6}{x^2-9}$ , which $x$ -value is a vertical asymptote?
### Semi-Log Plots and Exponential Growth (Population Growth) A semi-log plot uses a logarithmic scale on one axis and a linear scale on the other. For population growth, it is typical to plot time $t$ on the linear $x$ -axis and population $N$ on the logarithmic $y$ -axis. If a population follows an exponential pattern, the semi-log plot can display the points in a straight-line pattern. This helps planners determine whether the growth rate is stable without being misled by the rapidly increasing scale of the raw population values. Why semi-log is used: - It linearizes exponential growth. - It highlights constant percent change. Interpreting a straight line: - Straight line $\rightarrow$ constant growth factor per year. Based on the passage, why is a semi-log plot used instead of a regular linear plot in this context?
Using the provided logarithmic data, determine $t$ if $P(t)=P_0\cdot 2^{t/5}$ and $\log_{10}(P/P_0)=\log_{10}(8)$ .
A sound wave's displacement is modeled by $y=\sin(\theta)$ , where $\theta$ is the phase angle on the unit circle. At a particular time, the phase is $\theta=90^\circ=\pi/2$ , measured counterclockwise from the positive $x$ -axis. The unit circle has radius 1, so sine equals the $y$ -coordinate. Use an exact value consistent with standard special angles. What is the sine of an angle measuring $\pi/2$ radians on the unit circle?
A projectile is modeled by $x(t)=12t$ and $y(t)=5+8t-4.9t^2$ ; determine the coordinates at $t=1$ .
A ball is launched from $(0,2)$ with $V_0=25\text{ m/s}$ at $30^\circ$ ; $x(t)=21.65t$ , $y(t)=2+12.5t-4.9t^2$ . Using $y(t)$ , find the maximum height.
Which of the following expressions is equivalent to $\tan(\arccos(x))$ for $0 < x < 1$ ?
A city compares two projected input-output tables (same two sectors) to see which plan requires more Manufacturing input per dollar of output. Plan A uses $\mathbf{A}=\begin{bmatrix}0.18&0.12\\0.08&0.22\end{bmatrix}$ and Plan B uses $\mathbf{B}=\begin{bmatrix}0.20&0.10\\0.07&0.24\end{bmatrix}.$ Matrices organize the coefficients, and subtraction highlights differences entry-by-entry. Multiplication would be used later to compute intermediate demand from an output vector. Using the matrix model described, which entry of $\mathbf{B}-\mathbf{A}$ gives the change in Manufacturing input per $1 of Services output?
A scientist has collected five distinct data points from an experiment. Assuming there is no experimental error, what is the minimum degree of a single polynomial function that is guaranteed to be able to pass through all five of these points?
According to the model, what is the approximate number of people who have heard the rumor after 4 hours?
A $\$20{,}000$ certificate of deposit grows 4.2% annually, modeled by $A(t)=20000\cdot(1.042)^t$ . How long will it take to reach $\$25{,}000$ ?
Based on the passage, let $f(x)=x^3+2x^2+5x+10$ , a degree $3$ polynomial. Factor by grouping: $x^3+2x^2+5x+10=x^2(x+2)+5(x+2)=(x+2)(x^2+5)$ . The real zero is $x=-2$ , and the remaining zeros satisfy $x^2=-5$ , so $x=\pm\sqrt{5}\,i$ . In the complex plane, $\pm\sqrt{5}i$ lie on the imaginary axis, symmetric about the real axis. What are the complex zeros of the polynomial function $f(x)=x^3+2x^2+5x+10$ ?
What is the value of $\arccos(\cos(\frac{7\pi}{6}))$ ?
Using the polynomial provided, consider $p(x)=x^3+3x^2+4x+12$ , a degree $3$ polynomial. Factor by grouping: $x^2(x+3)+4(x+3)=(x+3)(x^2+4)$ . The real root is $x=-3$ , and $x^2+4=0$ yields $x=\pm 2i$ . Complex conjugates correspond to symmetric points in the complex plane, while only real zeros appear as $x$ -intercepts. What are the complex zeros of the polynomial function $p(x)$ ?
Consider the functions $f(x) = (1.5)^x$ and $g(x) = (2.5)^x$ . Which statement best compares the behavior of these two functions for $x > 0$ ?
For an angle $\theta$ in standard position, its terminal ray intersects the unit circle at point $(a, b)$ . Which of the following expressions is always equal to 1?
Consider the function $r(x)=\dfrac{x^2-16}{x+4}$ for a travel-time formula; what is the location of the hole in the function $r(x)$ ?
Which of the following statements accurately compares the values of the two investments over time?
The function $f$ is given by $f(x) = 15(0.82)^x$ . Which of the following statements best describes the function $f$ ?
A sinusoidal function has an amplitude of 4, a period of $\pi$ , a midline of $y=-1$ , and a phase shift of $\frac{\pi}{2}$ to the right. Which of the following equations could represent this function?

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