Practice Test 43 - Algebra 1

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

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1. A movie theater charges $9 for a ticket plus $3 for each snack you buy. Let $C$ be the total cost (in dollars) and let $s$ be the number of snacks. What equation represents this relationship?
2. The expression $3x^2 - 21x + 36$ represents the area of a rectangle where both dimensions are linear expressions in $x$. After factoring completely, if the dimensions are $(x - a)$ and $3(x - b)$ where $a$ and $b$ are positive constants, what is the value of $a \cdot b$?
3. A phone battery percentage is modeled by $B(t)=100(0.97)^t$, where $t$ is measured in hours. What is the percent decay rate per hour?
4. Which property justifies the step from $\frac{x-1}{4}=3$ to $x-1=12$?​
5. A discounted price can be modeled by $S = P(1 - r)$, where $P$ is the original price, $r$ is the discount rate (as a decimal), and $S$ is the sale price. Solve for $r$ in terms of $P$ and $S$.
6. Write both a recursive formula and an explicit formula for the arithmetic sequence $4, 9, 14, 19, \dots$.
7. A bouncing ball rises to $80\%$ of its previous height after each bounce. The first bounce rises to $10$ ft. The total of the first $5$ bounce heights is $10 + 10(0.8) + 10(0.8)^2 + 10(0.8)^3 + 10(0.8)^4.$ Using $S_n = \frac{a(1-r^n)}{1-r}$ with $a=10$, $r=0.8$, $n=5$, what is the sum of these bounce heights?
8. In geometry, the volume of a rectangular prism is $V = lwh$, where $V$ is volume, $l$ is length, $w$ is width, and $h$ is height. Solve $V = lwh$ for $h$.
9. For $h(x) = 2x + 1$, what is $h(a + 3)$?
10. The revenue function for selling $x$ items is $R(x)=x^2-6x+5$. Break-even occurs when $R(x)=0$. What are the solutions to $x^2-6x+5=0$?
11. A ball's height (in meters) after $t$ seconds is modeled by a function $H(t)$, and the model is only intended to be used for $0\le t\le 6$. What is the domain of $H$ in this context? (Use interval notation.)
12. Multiply: $3x(2x^2 - 5x + 1)$
13. Find the exponential function $y=a\cdot b^x$ that passes through the points $(0, 5)$ and $(2, 45)$.
14. Solve by factoring: $x^2 + 5x + 6 = 0$
15. A rental car company charges a flat fee plus a per-mile rate. Two customers provide the following data: Customer A drove 120 miles and paid $89, while Customer B drove 200 miles and paid $129. What is the per-mile rate the company charges?
16. Use the factored form $P(x)=x(x-2)^2(x+1)$ to answer: What are the x-intercepts, and how does the graph behave at each intercept (crosses vs touches)?
17. Complete the square to show that $f(x)=-x^2+14x-30$ has a maximum, and find the maximum value.
18. How many terms are in the expression $2x^3-5x^2+x-9$?
19. Which statement correctly describes $0\times i$ where $i$ is an irrational number?
20. Factor $x^2-10x+25$ by recognizing it as a perfect square trinomial.

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