Practice Test 6 - Algebra 1

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

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1. A company's profit is modeled by $P(x)=(x-1)(x-5)(x+2)$, where zeros represent break-even points. Which set lists all break-even x-values (zeros) and the corresponding x-intercepts?
2. A student claims that $(2x + 3)(x^2 - x + 1) = 2x^3 + x^2 - 2x + 3$. To verify this claim, which of the following approaches would be most efficient?
3. Why must $16^{1/4}$ equal 2 if we want exponent properties to hold (working with positive real numbers)? Choose the reasoning that correctly uses $(b^a)^c=b^{ac}$.
4. Multiply: $(x + 4)(x - 3)$
5. A line is graphed on a coordinate plane and crosses the $y$-axis at $-7$. The line is described by the equation $y = 4x - 7$. At what point does the graph cross the $y$-axis?
6. A savings account earns compound interest where the balance triples every 5 years. If the account starts with $200, what function represents the balance $B(t)$ after $t$ years, and what will be the balance after 15 years?
7. If $f(x)=4-2x$, what does $f(5)$ equal?
8. Why is the condition "nonzero" necessary in the statement: "rational × irrational is irrational"? Choose the option that correctly addresses the exception.​​​
9. The figure shows the graph of $y = f(x)$. Which statement about the intervals where $f(x)$ is positive and the intervals where $f(x)$ is increasing is most accurate?
10. Which expression is equivalent to $\left(3^{2}\right)^{5t}$? Give your answer in simplest form.
11. A digital scale reads to the nearest 0.1 g. You measure a sample as 42.7 g. How should the mass be reported given the scale's measurement limitation?
12. Does the table show a constant rate of change between $t$ (time in hours) and $d$ (distance in miles)? If so, what is the constant rate $\Delta d/\Delta t$? Table (equal $t$-intervals of 2 hours): - $t$: 0, 2, 4, 6 - $d$: 0, 120, 240, 360
13. A geometric sequence has the explicit formula $g_n = 5 \cdot 3^{n-1}$. If this sequence were written recursively, what would be the correct recursive definition?
14. How many terms are in the expression $5y-3$?
15. What values of $x$ make $x^2 + 2x - 8 = 0$? (Factor first, then use the Zero Product Property.)
16. Solve $x^2+8x+20=0$ and write solutions in the form $a\pm bi$. Use $i^2=-1$ when simplifying $\sqrt{-n}$.​
17. For the geometric series $2 + 6 + 18 + 54$, identify $a$, $r$, and $n$, then find the sum using $S_n = \frac{a(1-r^n)}{1-r}$.
18. A plant grows at a steady rate. Its height (in centimeters) after $t$ weeks is $H(t) = 3t + 10$. What is $H(4)$?
19. Use polynomial division to express $\frac{x^3-2x^2+5x+1}{x-1}$ as $q(x)+\frac{r(x)}{x-1}$, where $\deg(r)<1$.​
20. A sequence is defined as a function $f$ on the integers $n = 1, 2, 3, \dots$ by $f(1)=4$ and $f(n+1)=f(n)+3$. What is $f(5)$?

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