Practice Test 10 - AP Precalculus

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

Based on the information above, how does matrix multiplication affect $\mathbf{v}$ if $\mathbf{A}=\begin{pmatrix}3&0\\0&1\end{pmatrix}$ and $\mathbf{v}=\begin{pmatrix}2\\-4\end{pmatrix}$ ?
Describe the symmetry of the polar graph $r=2\cos(\theta)$ in standard position.
A rectangular garden has a length that is 4 meters more than twice its width. If the width is $w$ meters, which function represents the area $A$ of the garden in square meters?
Two transforms are $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}2&4\\1&2\end{bmatrix}$ . Since invertible means $\det\neq0$ , which of these matrices is invertible?
A bacteria culture is $B(t)=900\cdot 1.25^t$ (t in hours). Solve for $t$ when $B(t)=5000$ .
Let $\vec{v} = \langle -3, 6 \rangle$ and $\vec{w} = \langle 2, 4 \rangle$ . What is the dot product $\vec{v} \cdot \vec{w}$ ?
A spacecraft's orbit is modeled by an ellipse, as in Kepler's Laws. The standard form is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1.$ Here, $(h,k)$ is the center, $a$ is the semi-major axis, and $b$ is the semi-minor axis. Engineers adjust $a$ to widen or tighten the orbit while keeping the center fixed. Refer to the equation provided in the passage: how does increasing $a$ affect the ellipse's horizontal extent?
A projectile is launched at 50 m/s at a 40° angle above horizontal. Based on the scenario described, what is its initial vertical speed (nearest tenth)?
The rational function $h(x) = \frac{x^2 + 5x + 6}{x^2 + 3x + 2}$ has how many vertical asymptotes?
In an engineering control system, a steady-state vector $\vec s=\langle x,y\rangle$ satisfies $x^2+ay^2=9$ , where $a>0$ is a tunable gain parameter. As $a$ changes, $y$ changes with $x$ held constant. Using the information provided, how does the parameter $a$ affect the derivative $\dfrac{dy}{da}$ (with $x$ constant)? Assume $y\neq 0$ .
Matrices organize information and help solve real problems. A theater sells Adult and Student tickets. Revenue is found by multiplying a price row vector by a sales column vector. If prices are $\mathbf{p}=\begin{bmatrix}12&8\end{bmatrix}$ (dollars) and sales are $\mathbf{s}=\begin{bmatrix}150\\200\end{bmatrix},$ then multiplication combines prices and quantities, while addition/subtraction compares sales across days. Using the matrix model described, what operation gives total revenue?
For market index $f(x)=(x-2)(x+1)(x^3-4)$ , how does end behavior relate to its graph?
Let $P$ be the point where the terminal ray of an angle $\theta$ in standard position intersects the unit circle. What are the coordinates of point $P$ ?
Using the equation $y=\cos(3x)$ for a circuit, what is the period?
A computer scientist models processing time using $T(n) = 0.5 + 0.12\log_2(n)$ , where $n$ is the input size and $T(n)$ is time in seconds. If the processing time is 1.94 seconds, what is the input size?
Based on the discussion of inverse functions, which function is the inverse of $f(x)=e^{x-4}$ ?
Which of the following is a parametrization for the right half of the circle $x^2 + y^2 = 9$ , traced in a counterclockwise direction?
Let $f(x) = -x^3 + 12x + 1$ . On which of the following intervals is $f(x)$ increasing at a decreasing rate?
A botanist proposes a linear function $H(d) = 0.5d + 2$ to model the height of a sunflower, in centimeters, $d$ days after it sprouted. What is a key assumption made in this linear model?
The rational function $h(x)$ has a single vertical asymptote at $x=5$ . The function $k(x)$ is defined by $k(x) = h(2x) - 3$ . What is the vertical asymptote of the graph of $k(x)$ ?

Practice tests