Practice Test 30 - Algebra 1

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

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1. The function $f(x)=3(x+1)(x-5)$ is in factored form. What does this form reveal about the graph's zeros and axis of symmetry?
2. Solve and check for extraneous solutions: $\frac{3}{x-2}=2$
3. Solve using elimination: $\begin{cases} 2x+3y=12 \\ 2x-y=4 \end{cases}$ What is the solution $(x,y)$?​
4. The sequence $a_n$ is defined recursively for $n=1,2,3,\dots$ by $a_1=3$ and $a_{n+1}=3a_n$. What is the next term after $3, 9, 27$?
5. Given $g(x) = x^2 + 2x - 8$, what is $g(0)$?
6. Consider the rational equation $\frac{x+4}{x^2-4} - \frac{2}{x+2} = \frac{1}{x-2}$. Before solving, a student should recognize that this equation is undefined when:
7. Add and simplify (the sum of two rational expressions is a rational expression): $\frac{3}{x}+\frac{2}{x+1}$
8. Compare $f(x)=100x$ (linear) and $h(x)=1.1^x$ (exponential). Which statement is true about their long-term behavior?
9. A theater is choosing how many balcony seats and floor seats to sell. Let $x$ = balcony tickets and $y$ = floor tickets. The theater can sell at most 300 total tickets: $x+y\le 300$. Fire code requires at least 120 floor tickets to be sold for staffing plans: $y\ge 120$. Also, $x\ge 0$ and $y\ge 0$. Which point is nonviable?
10. Let $f(x)=x^2-1$ and $g(x)=x+3$. Compute $f(g(0))$.
11. A ball's height (in feet) after $t$ seconds is $h(t)=-t^2+10t+4$. Use completing the square to find the maximum height and when it occurs.
12. The sequence $2,\ 5,\ 8,\ 11,\ \dots$ is a function with domain $n=1,2,3,\dots$. How is this sequence defined recursively?
13. Rewrite the expression $(2^3)^t$ using the power-of-a-power property $(b^a)^c=b^{ac}$.
14. A population is modeled by $P(t)=12{,}000\cdot(0.98)^t$, where $t$ is in years. Which statement is correct?
15. In the expression $-8n^2+3n+10$, what is the coefficient of $n^2$?
16. Which of the following is equivalent to $\sqrt{x^3} \cdot \sqrt[4]{x}$ when $x \geq 0$?
17. A bus travels at a constant speed of 45 miles per hour. Let $t$ be time in hours and $d$ be distance in miles. If this relationship is graphed, which equation represents it?
18. A student earns $9 per hour babysitting. Let $h$ be hours worked and $E$ be earnings (in dollars). How should the coordinate plane be set up to show this context?
19. Show that the equations $x^2+4x-5=0$ and $(x+2)^2=9$ have the same solutions by solving using the completed-square form.
20. Rewrite $8^t$ in terms of a power of 2 using exponent properties.​​

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