Practice Test 100 - Algebra 2

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

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1. Compute the sum $2+2(1.1)+2(1.1)^2+\cdots+2(1.1)^9.$ (There are 10 terms. Use $S_n=\dfrac{a(1-r^n)}{1-r}$ for $r\ne 1$.)​​​
2. Solve the system using the elimination method: $\begin{cases} 2x + 3y = 12\\ 4x - 3y = 6 \end{cases}$ What is the solution $(x, y)$?
3. A gym charges a monthly membership fee plus a per-visit charge. The total cost is modeled by $C = 3v + 25$, where $C$ is the total cost in dollars and $v$ is the number of visits in a month. In the function $C = 3v + 25$, what does the 25 represent in this context?
4. A system consists of the equations $y = x^2 - 4x + 3$ and $y = 2x - 5$. If the solutions to this system are plotted on a coordinate plane, what is the sum of the x-coordinates of all intersection points?
5. Which choice correctly identifies $A$, $X$, and $B$ for the system written in the order shown (variable order $x, y$)? $\begin{cases} 7x+0y=-6\\ -2x+9y=15 \end{cases}$​
6. Explain why $f(x)=x^2$ (domain: all real numbers) needs a domain restriction to have an inverse. Which statement correctly uses the horizontal line test idea?
7. Convert the system to matrix form $AX=B$ using variable order $x, y$: $\begin{cases} -2x+7y=9\\ 4x+y=-6 \end{cases}$
8. A small gym charges a one-time sign-up fee plus a monthly membership fee. The total cost after $m$ months is modeled by $C(m)=25+35m$. What is the realistic domain for $m$ in this context?
9. Let $S = \{x^2 + 1, 2x - 3, x^3 - x, 4\}$. If we define a new operation $\oplus$ such that for any two polynomials $p, q \in S$, the result $p \oplus q$ is also in $S$, which operation could $\oplus$ represent?
10. A movie theater sells adult tickets and student tickets. Let $a$ = number of adult tickets and $s$ = number of student tickets. Adult tickets cost $12 and student tickets cost $8. The theater wants revenue of at least $480 from a show, but can sell at most 50 tickets total. Tickets must be whole numbers and nonnegative. Which constraint system represents this situation?
11. What are the center and radius of the circle given by $(x+5)^2+(y-1)^2=49$?
12. An infinite geometric series has first term $a = 6$ and sum $S = 15$. If instead we consider only the first 8 terms of this series, what is the sum $S_8$?
13. Multiplying by $i$ corresponds to a $90^\circ$ counterclockwise rotation on the complex plane. If $z=2+i$ (point $(2,1)$), what is the point for $iz$?​
14. Multiply and simplify using $i^2=-1$: $(2+3i)(1-2i).$
15. Let $f(x)=x^3$ and $g(x)=4x$. Use a graphing tool to find all solutions to $f(x)=g(x)$. (Exact values are expected.)
16. Consider the rational expression $R(x)=\frac{x^2+3x-2}{x-1}.$ If you view the entire numerator $(x^2+3x-2)$ as a single entity, which statement best describes the structure and dependence on $x$?
17. Find the modulus of $z = 6 - 8i$. (Recall $|a+bi| = \sqrt{a^2+b^2}$, the distance from the origin to $(a,b)$ on the complex plane.) Give your answer in simplest form.
18. A savings account balance is modeled by $B(t)=2500(1.04)^t$, where $t$ is time in years. In this model, what does the parameter $2500$ represent?
19. Condense to a single logarithm using log properties: $\log_6(x)+\log_6(y)-4\log_6(z).$
20. Find $t$ in $9\cdot 2^{4t}=100$. Express the solution as a logarithm (base 2) and approximate using a calculator.

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