Practice Test 34 - Algebra 1

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

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1. A sequence is defined recursively by $a_1 = 4$ and $a_{n+1} = a_n + 3$ for $n = 1,2,3,\dots$. What is $a_5$?
2. What is the simplified form of $\frac{x^2 - 4}{x^2 + 4x + 4} \cdot \frac{x + 2}{x - 2}$?
3. Based on the table shown, which statement best describes the long-term behavior of these three functions?
4. A runner moves at a constant speed of 6 miles per hour. Let $d$ be the distance (miles) and $t$ be the time (hours). Which equation models this relationship?
5. Let $f(x)=\sqrt{x}$ (radical) and $g(x)=x+1$ (linear). Evaluate $(f\cdot g)(4)$.​
6. Two friends start a lawn care business. Their weekly revenue $R$ is $R = 25n + 40$, where $n$ is the number of lawns mowed. If they want to graph this relationship and show when they'll earn at least $200 per week, what should they include on their graph?
7. Let $f(x)=|x|$ and $g(x)=x-7$. Simplify $(f-g)(x)$.
8. Use polynomial division to express $\frac{x^3-2x^2+4x-8}{x-2}$ as $q(x)+\frac{r}{x-2}$, where $\deg(r)<1$.
9. A laptop depreciates according to $V(t)=1200(0.90)^t$, where $t$ is in years. What is the annual percent depreciation rate?
10. A ball is thrown upward from the ground. Its height (in feet) after $t$ seconds is given by $h = -16t^2 + 64t$. Solve for the time(s) when the ball is on the ground. Let $t$ = time in seconds.
11. On a coordinate plane, graph the quadratic function $y = x^2 - 5x + 6$. What are the $x$-intercepts (as points)?
12. Given $p(x)=4(x-2)$, what is the value of $p(3)$?​
13. In the expression $7 \big( (x-1)(x+1) \big),$ what is being multiplied by $7$? View the entire product $(x-1)(x+1)$ as a single unit.
14. Show that $x^2 + 4x - 5 = 0$ and $(x+2)^2 = 9$ have the same solutions by solving the completed-square equation and listing the solution set.
15. Use the geometric series sum formula $S_n=\frac{a(1-r^n)}{1-r}$ (for $r\ne 1$) to calculate $3 + 3(1.1) + 3(1.1)^2 + \cdots + 3(1.1)^9.$ (So $a=3$, $r=1.1$, $n=10$.)
16. Express $\sqrt{x}\cdot \sqrt[3]{x}$ using a single rational exponent.
17. What is the structure of the expression $2(x-5)^2-7?$ View $(x-5)$ as a single unit when describing the structure.
18. Solve and check for extraneous solutions: $\frac{x}{x-3}=2$
19. Is the point $(2, 1)$ on the graph of $y = x^2 - 3$? Use substitution to decide.
20. A quantity is modeled by $y=400(1-0.12)^x$. What is the percent rate of change per unit $x$?

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