Practice Test 4 - Algebra 1

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

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1. What property allows you to go from $\dfrac{x}{5}=7$ to $x=35$? Step shown: $\dfrac{x}{5}=7 \;\rightarrow\; x=35$
2. Which direction should be shaded for the inequality $x < 3$?
3. Graph the inequality $y > 2x - 1$. Which description is correct for the boundary line and the shaded half-plane (solution region)?
4. Which function best models the number of bacteria $B(t)$ after $t$ hours, and how many complete doubling periods will have occurred after 10 hours?
5. Graph the square root function $f(x)=\sqrt{x-2}+1$. In your graph, show the starting point and indicate the domain.​
6. The value of a laptop after $t$ years is modeled by $V(t)=25000(0.88)^t$. Is this exponential growth, exponential decay, or neither?​
7. Add: $\left(3x^2 - 5x + 7\right) + \left(2x^2 + 4x - 9\right)$. Give your answer in simplest form.
8. A savings account balance $B$ (in dollars) is recorded at the end of each week $w$. Does the table represent a constant rate of change of $B$ with respect to $w$? Choose the best answer.
9. Is the sequence $81,\ 27,\ 9,\ 3,\ \dots$ arithmetic, geometric, or neither?
10. Solve the inequality: $3x - 5 > 16$
11. What is the domain of the function $f(x)=\sqrt{x-5}$? Give your answer in interval notation.
12. Consider $P(x)=x(x-2)^2(x+1)$. Identify the zeros (with multiplicity) and describe whether the graph crosses or touches the x-axis at each x-intercept. Which option is correct for a rough sketch based on zeros and multiplicity?
13. What are the quotient $q(x)$ and remainder $r(x)$ when dividing $x^3+4x^2+x+6$ by $x+3$? Then write $\frac{x^3+4x^2+x+6}{x+3}=q(x)+\frac{r(x)}{x+3}$ with $\deg(r)<1$.​
14. The line equation $ax + by = c$ has constants $a$, $b$, and $c$. Solve for $y$ in terms of $x$, $a$, $b$, and $c$.
15. Which describes the structure of $4\left(1-\frac{x}{3}\right)^5?$ (Treat $\left(1-\frac{x}{3}\right)$ as one chunk.)
16. $\frac{3}{x-1} - \frac{1}{x+1}$
17. Solve by taking square roots: $(x - 4)^2 = 25$. Find all solutions.
18. A phone plan costs $25 each month plus $0.05 per text message sent. What function models the monthly cost $C(t)$ (in dollars) in terms of the number of texts $t$?
19. For the floor (greatest integer) function $f(x)=\lfloor x\rfloor$, what is $f(2.7)$?​
20. Does the table show a constant rate of change between $x$ and $y$? If so, what is the constant rate $\Delta y/\Delta x$? Table (equal $x$-intervals of 1): - $x$: 0, 1, 2, 3, 4 - $y$: 5, 8, 11, 14, 17

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