Practice Test 24 - Algebra 1

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

Start practice test

1. Express $\frac{4x^2+9x-1}{2x-1}$ in the form $q(x)+\frac{r(x)}{2x-1}$ using polynomial division, where $\deg(r)<1$.
2. A square has side length $\sqrt{5}$ meters (an irrational number). Is the perimeter rational or irrational? Choose the option with correct reasoning.
3. A town's population is modeled by $P(t) = 18{,}000(1.02)^t$, where $t$ is the number of years since 2026. In the function $P(t)$, what is the meaning of the parameter $18{,}000$?
4. A gym charges a one-time sign-up fee of $25 and then $15 per month. Let $m$ be the number of months and let $C$ be the total cost (in dollars). Which equation models the total cost?
5. Which value of $x$ satisfies $\frac{x - 2}{5} = \frac{3}{2}$?
6. What does the transformation $(1.15)^t = \left(1.15^{1/12}\right)^{12t}$ reveal about the growth factor $1.15^{1/12}$?
7. An exponential function passes through the points $(0, 2)$ and $(3, 54)$. What is the function in the form $y = a \cdot b^x$?​​​
8. A savings account is modeled by $A(t)=1000(1.01)^{12t}$, where $t$ is measured in years. What is the monthly interest rate?
9. Let $f(x)=\dfrac{1}{x}$ and $g(x)=x^2+1$. Find the domain of $(f+g)(x)$.
10. What does the transformation $(1.15)^t = \left(1.15^{1/12}\right)^{12t}$ reveal about the growth factor $1.15^{1/12}$?​​
11. Tickets to a school play cost $9 each, and there is a one-time online fee of $4 per order. Jordan has at most $40 to spend. Write an inequality representing the number of tickets Jordan can buy. Let $t$ = the number of tickets.
12. What is the value of $16^{3/4}$?
13. Function $f$ is defined by the equation $f(x) = -2x^2 + 8x - 3$. Function $g$ is represented by the table shown. Which statement correctly compares the y-intercepts of these functions?
14. Solve $x^2 - 6x + 10 = 0$. Express solutions in $a + bi$ form, using $i^2 = -1$.
15. A company's profit $P$ (in thousands) is modeled by $P = -2x^2 + 16x - 24$, where $x$ is the number of products sold (in hundreds). The company needs a profit of at least $8,000. Which represents this constraint and identifies whether $x = 2$ is a viable option?
16. What is the minimum value of $f(x)=x^2+6x+2$? (You may use completing the square.)
17. For $P(x)=-(x+1)(x-2)(x-4)$, which description correctly matches the zeros and end behavior of the graph of $y=P(x)$?
18. A function $f$ is defined on the positive integers (so the domain is $n = 1,2,3,\dots$) by $f(1)=2$ and $f(n+1)=2f(n)$ for $n\ge 1$. What is $f(5)$?
19. Explain the relationship between the equation $y = 2x + 1$ and its graph.
20. Solve graphically and algebraically (substitution is recommended). The solutions are the intersection point(s) of the line and the parabola: $\begin{cases} y = x^2 - 4 \\ y = 2x - 4 \end{cases}$​

Practice tests