Practice Test 86 - Algebra 2

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

Complex numbers correspond to points $(a,b)$ in the plane. Using the midpoint formula $\dfrac{z_1+z_2}{2}=\dfrac{a+c}{2}+\dfrac{b+d}{2}i$ , find the midpoint of the segment from $z_1=7-3i$ to $z_2=-1+5i$ .
A theater is selling two types of tickets: adult and student. Let $a$ = number of adult tickets and $s$ = number of student tickets. Constraints: - The theater can seat at most 180 people: $a+s\le 180$ . - At least 40 student tickets must be sold: $s\ge 40$ . - Revenue goal: adult tickets are $15 and student tickets are $10; total revenue must be at least $2200. - Nonnegativity: $a\ge 0,\ s\ge 0$ . Which of the following points is viable?
A function is defined by $g(x)=2\cdot 3^x$ . Consider equal intervals of length 1. Which set of values and ratios correctly demonstrates that $g$ has a constant ratio (and therefore forms a geometric sequence when sampled at integers)?
What is the coefficient of $x^3y^3$ in the expansion of $(x+y)^6?$ (You may use Pascal's Triangle row 6: $1,6,15,20,15,6,1$ .)
The formula relating pressure, volume, and temperature for an ideal gas is $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ . A chemistry student needs to find the final temperature $T_2$ when the pressure doubles and volume is halved. Which setup is correct?
A rectangular garden has an area of 150 m $^2$ . Its length is 5 meters more than its width. Write and solve an equation to find the garden's dimensions. Let $w$ = width (in meters).
A student attempts to solve $2x^2 - 12x + 10 = 0$ by factoring. After factoring out the GCF, what quadratic expression remains, and what is the most appropriate next method to find the solutions?
Consider the functions $p(x) = \frac{x + 3}{2x - 1}$ and $q(x) = \frac{x + 3}{2x - 1}$ . A student observes that $p(x) = q(x)$ for all $x$ and concludes that they must be inverse functions since $p(q(x)) = p(p(x))$ and $p$ composed with itself might equal $x$ . Which statement best evaluates this reasoning?
A student claims that $\frac{x^3 + 4x^2 + x - 6}{x^2 + 3x - 2} = x + 1 + \frac{3x - 4}{x^2 + 3x - 2}$ . To verify this algebraically, which of the following equations must be satisfied?
The volume of a cylinder is given by $V=\pi r^2h$ , where $V$ is volume (cm $^3$ ), $r$ is radius (cm), and $h$ is height (cm). If the height is fixed at $h=10$ cm, what equation models $V$ as a function of $r$ , and what graph setup is appropriate for $0\le r\le 8$ ?
A loan is repaid with 10 end-of-month payments. The monthly interest rate is $2\%$ . If each payment is $P$ dollars, the value of all payments at the time of the last payment is $P + P(1.02) + P(1.02)^2 + \cdots + P(1.02)^9.$ Which expression correctly represents this sum in closed form?
A bakery sells cupcakes in boxes. The profit (in dollars) from selling $n$ boxes is modeled by $P(n)=4n-30$ . The bakery can sell at most 120 boxes in a day. What is an appropriate domain for $n$ ?
Convert $3\big(\cos 270^\circ+i\sin 270^\circ\big)$ from polar form to rectangular form $a+bi$ . Use $a=r\cos\theta$ and $b=r\sin\theta$ .
Convert $5\left(\cos 60^\circ+i\sin 60^\circ\right)$ from polar form to rectangular form $a+bi$ . Use $a=r\cos\theta$ and $b=r\sin\theta$ . (Argument is measured from the positive real axis.)
Solve by taking square roots: $(x-3)^2 = 5$ .
Write matrices $A$ , $X$ , and $B$ for the system (use variable order $x, y$ ): $\begin{cases} -2x+7y=4\\ 5x+y=9 \end{cases}$ Which choice correctly gives $AX=B$ ?
Two lines are $f(x)=1.5x-2$ and $g(x)=-0.5x+6$ . Solve $f(x)=g(x)$ by interpreting the solution as the $x$ -coordinate of the intersection of $y=f(x)$ and $y=g(x)$ .
The expression $(x + 3)(x - 2) + 5x$ can be written as $ax^2 + bx + c$ . Which of the following correctly identifies the factors of the coefficient $b$ ?
A printing company's weekly cost is modeled by $C = 150 + 0.08n$ , where $C$ is the total cost in dollars and $n$ is the number of pages printed that week. In the function, what does the parameter $0.08$ represent in context?
A student claims the system (variable order $x, y$ ) $\begin{cases} 2x-3y=4 \\ -x+5y=1 \end{cases}$ can be written as $\begin{bmatrix} 2 & -3 \\ -1 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 1 \end{bmatrix}.$ Which choice correctly explains why this matrix equation matches the system?

Practice tests