Practice Test 36 - Algebra 1

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

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1. Examine the solution region of the system shown in the graph. If the system were modified by changing one inequality from $\leq$ to $<$, which statement about the resulting solution region would be true?
2. A tank contains 500 liters of water and is being drained at 18 liters per minute. Write an explicit expression for the remaining volume $V(t)$ (in liters) in terms of time $t$ (in minutes).
3. A function $f$ is defined on $n=0,1,2,\dots$ by $f(0)=1$, $f(1)=1$, and $f(n)=f(n-1)+f(n-2)$ for $n\ge 2$. What is $f(6)$?
4. Which example best illustrates why the definition $a^{m/n} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$ must be consistent with the power property $(a^p)^q = a^{pq}$?
5. Simplify $\frac{\frac{2x-6}{x+1}}{\frac{x-3}{3x+3}}$.
6. A balance grows by 1% per month, so after $12t$ months it is multiplied by $(1.01)^{12t}$. What is the equivalent annual growth factor for $t$ years?​​
7. A student solving $5x - 3 = 2x + 9$ writes the next step as $3x - 3 = 9$. What mathematical reasoning supports this transformation?
8. In physics, $F = ma$ (force equals mass times acceleration). Solve for $a$ in terms of $F$ and $m$.
9. What is the sum of $(3x^3 - 2x^2 + x - 4)$ and $(x^3 + 5x^2 - 3x + 6)$?
10. From the coordinate plane, a line passes through the points $(-1, 4)$ and $(3, -4)$. What is the equation of the line? Write in the form $y=mx+b$.
11. A quadratic function has been written in the form $h(x) = (x - 3)^2 - 16$. Which statement about the zeros and vertex is correct?
12. Based on the graph shown, what are the most appropriate units for the slope of the line?
13. To calculate the final price of an online order, you (1) subtract a $20\%$ discount from the original price $p$, (2) add $6 shipping, and then (3) add $8\%$ sales tax to the discounted-plus-shipping subtotal. How would you calculate the final price in terms of $p$? (Choose the expression that matches the described steps.)
14. Rewrite $\sqrt[3]{x^5}$ using rational exponents.
15. The function $r(x)=(x-1)(x-9)$ is in factored form. What does this form reveal about the graph? Choose the option that correctly gives the zeros and axis of symmetry.
16. Let $k(x)=x^2+2x$. What is $k(a+1)$?
17. A quadratic expression $x^2 + px + q$ has zeros at $x = -3$ and $x = 2$. If this expression is multiplied by 2 to get $2x^2 + 2px + 2q$, what are the zeros of the new expression?
18. How many solutions does the system have? $\begin{cases}2x+4y=10\\x+2y=5\end{cases}$
19. Where is the vertex of the absolute value function $g(x)=|x-4|+2$?​
20. How many terms are in the expression $3(x+2)$?

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