Practice Test 25 - Algebra 2

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

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1. A rectangular parking lot is being designed where the length is 20 feet less than three times the width. If the perimeter must be at least 400 feet but no more than 600 feet, which inequality represents the constraint on the width $w$?
2. A car rental company charges a flat fee plus a rate per mile. After driving 120 miles, the total cost is $68. After driving 200 miles, the total cost is $92. Which function represents the total cost $C(m)$ for driving $m$ miles?
3. Rewrite the general-form circle equation $x^2+y^2+10x-2y+17=0$ in standard form $(x-h)^2+(y-k)^2=r^2$.
4. A bacteria culture starts with 80 bacteria and increases by 10% each hour. Let $a_n$ be the number of bacteria after $n$ hours, where $n$ is a nonnegative integer and $a_0$ is the initial amount. Which choice gives both a recursive and an explicit model?
5. Consider the system of constraints $\begin{cases}2x+y \le 12 \\ x+2y \le 14 \\ x \ge 0 \\ y \ge 0 \end{cases}$ Which point is nonviable (infeasible) for this system?
6. A medication dose starts at 200 mg. Each hour, 15% of the medication is eliminated (so 85% remains). Model the amount remaining after $t$ hours with an exponential equation and solve for when 50 mg remains. Let $t$ = time in hours.
7. Apply the sum of cubes identity to factor the polynomial $x^3+8$ completely over the integers.
8. Graph $f(x)=\frac{(x-2)(x+4)}{x(x-3)}$ identifying zeros, vertical asymptotes, and the horizontal asymptote.
9. A bike rental shop charges a flat fee of $12 plus $4 per hour. Write an equation for the total cost $C$ (dollars) in terms of hours rented $h$ (hours), and choose appropriate axes labels and a reasonable scale to graph the relationship for $0\le h\le 8$.
10. A lab sample contains 1500 bacteria. After 4 hours, it contains 2400 bacteria. Assume the bacteria grow exponentially at a constant percent rate per hour. Create an exponential model $P(t)=P_0\,b^t$ (with $t$ in hours), then use it to predict when the population will reach 5000 bacteria. Round to the nearest tenth of an hour and interpret your result in context.
11. A radioactive sample has a half-life of 6 years and starts with 80 grams. Create a model for the amount remaining after $t$ years and determine how many years it will take until only 10 grams remain. Round to the nearest tenth of a year.
12. Recognize structure to factor completely: $x^6-64$.
13. Which restriction makes $f(x)=(x-4)^2-7$ invertible by ensuring it passes the horizontal line test?
14. The quadratic $h(x) = x^2 + px + q$ satisfies $h(2+i) = 0$. If $p$ and $q$ are real numbers, which equation must also be satisfied?
15. For the polynomial function $g(x)=x^3-x^2-6x,$ identify the zeros and describe the end behavior (based on the leading term).
16. Factor $s(x)=x^2-7x+10$ and use the zeros to determine the x-intercepts of the parabola.
17. Examine the graph showing temperature changes throughout the day. During which time interval does the temperature change at a constant rate?
18. Function $k$ has an inverse, and the following values are known: $k(1) = 3$, $k(4) = -2$, and $k(7) = 0$. What is $k^{-1}(-2) + k^{-1}(0)$?
19. A toy car's position relative to a starting line is modeled by $s(x)=x^4-3x^2$, where $x$ is time in seconds. Does $s(x)$ have symmetry? What type?
20. In geometry, the volume of a cone is $V = \dfrac{1}{3}\pi r^2 h$, where $r$ is radius and $h$ is height. Solve $V = \dfrac{1}{3}\pi r^2 h$ for $r$.

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