Practice Test 35 - Algebra 1

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

Start practice test

1. Calculate the sum of the geometric series $2+6+18+54$. (This is a geometric series, meaning a sum; the corresponding sequence is $2,6,18,54$.) Use $a=2$, $r=3$, $n=4$ and $S_n=\frac{a(1-r^n)}{1-r}$.
2. Graph the cube root function $f(x)=\sqrt[3]{x+8}$. What point is guaranteed to be on the graph?​
3. Find both intercepts of the linear function $y = 2x - 4$. Give your answer as points.
4. Use exponent properties to rewrite $8^t$ in terms of a power of 2.
5. For the function $f(x) = 2(x + 1)^2$, what is $f(-1)$?
6. A parabola has equation $y = 2x^2 - 12x + 10$. After completing the square to analyze the graph, which statement about the range is correct?
7. What is the explicit formula for the arithmetic sequence with $a_1=10$ and common difference $d=-3$?
8. Use polynomial division to rewrite the rational expression $\frac{2x^3+3x^2-5x+1}{x-2}$ in the form $q(x)+\frac{r(x)}{x-2}$, where $\deg(r)<\deg(x-2)$.
9. Find $(2x^2 + x - 8) - (x^2 - 3x + 5)$.
10. Complete the square to solve $x^2-6x+13=0$ for complex solutions. Use $i^2=-1$ and write answers in $a \pm bi$ form.
11. What is $x$ in the equation $5x - 8 = 2x + 10?$
12. Two students are rewriting $\frac{2x^3 - x^2 + 3x - 7}{x^2 + 2}$. Student A gets $2x - 1 + \frac{-x - 5}{x^2 + 2}$ and Student B gets $2x - 1 + \frac{x + 5}{x^2 + 2}$. Which statement is correct?
13. If $f(x)=x^2$ and $g(x)=x-1$, which expression represents $f(g(x))$?
14. Compare $g(x)=x^2$ (quadratic) and $h(x)=3^x$ (exponential). Which statement is true?
15. A quadratic equation is given as $x^2 - 6x + 2 = 0$. When completing the square to transform this equation into the form $(x - p)^2 = q$, what is the value of $q$?
16. A student starts a savings challenge with $25 on day 1 and adds $4 each new day. Write a recursive definition for the amount saved $a_n$ (in dollars) on day $n$.
17. A streaming service charges $9 per month plus $1.50 per movie rental. When graphing the relationship between number of rentals $r$ and total monthly cost $C$ (in dollars), what should the axes be labeled?​
18. Simple interest is modeled by $I = Prt$ (where $I$ is interest, $P$ is principal, $r$ is annual rate, and $t$ is time). Rearrange to solve for $r$.
19. A town's population is modeled by $P(t)=24000(1.02)^t$, where $t$ is the number of years since 2026. What does the 24000 represent in this context?
20. The graphs of the lines $y=x+2$ and $y=-x+4$ intersect at one point. What is the intersection point (the solution to the system)?​

Practice tests