Practice Test 2 - College Algebra

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

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1. A savings account has $P(t)=1500e^{0.08t}$ (t in years); when does it reach $3000$?
2. Which shows $10x^2+15x$ factored completely by its GCF?
3. A pharmacist needs to prepare 200 mL of a 12% saline solution by mixing a 20% solution with distilled water (0% saline). Due to measurement constraints, the pharmacist can only measure in increments of 5 mL. What is the minimum amount of the 20% solution needed to achieve a concentration as close as possible to 12%?
4. A savings account uses $A(t)=1000(1.04)^t$; which value is the annual interest rate?
5. If $f(x) = \frac{x^2 + 3x - 10}{x^2 - 25}$ and $g(x) = \frac{x + 5}{x - 2}$, what is the domain of $\frac{f(x)}{g(x)}$?
6. Which expression shows $40x^3+20x^2$ factored by its GCF?
7. If $|x - 2|^2 = 9$, then the product of all solutions is:
8. If $2x - 1 > 5$ OR $3x + 4 \leq 1$, which of the following is NOT included in the solution set?
9. A bacteria culture follows $P(t)=900e^{0.10t}$ (t in hours); when does it reach $2700$?
10. Simplify using the distributive property and additive inverses: $7-(3x-5)+2x$.
11. Which expression represents the complete factorization of $24x^3y^2 - 18x^2y^3 + 30xy^4$?
12. A clothing store sells shirts and pants. Last week, $5$ shirts and $3$ pants cost $139, while $2$ shirts and $7$ pants cost $146. Using substitution to solve for the individual prices, if you first solve for the price of a shirt from the first equation, what equation do you get when you substitute into the second equation?
13. Which option correctly simplifies $\log_b(xy)$ using the product rule?
14. Which expression is equivalent to $\frac{(2a^{-3}b^2)^{-2}}{(4a^2b^{-1})^{-1}}$?
15. Identify the error: $8 - 3 - 2 = 8 - (3 - 2) = 7$.
16. How can $\log_b(x^n)$ be rewritten using the power rule?
17. Consider the polynomial $p(x) = -2x^3(x + 4)^2(x - 1)$. Between which consecutive zeros does the function have a local minimum?
18. When factoring $21x^4y^3 + 14x^3y^2 - 35x^2y^4$, a student writes $7x^2y^2(3x^2y + 2x - 5y^2)$. What error, if any, did the student make?
19. Which option correctly simplifies $\log_b(abc)$ using the product rule repeatedly?
20. In solving $3x - 7y = -4$ and $6x + 2y = 16$ by elimination, which approach requires the fewest arithmetic operations?

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