Practice Test 10 - Algebra 1

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

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1. If $f(x)=4-x$ and $g(x)=x^2$, what is $g(f(x))$?
2. A student tries to find distance using $d=vt$ but writes: $d=(60\ \text{mi/hr})+(2\ \text{hr})=62\ \text{mi}.$ Identify the unit error in the calculation.
3. What is the boundary line for the inequality $3x - y \le 6$?​​
4. A line is modeled by $y=\frac{1}{2}x-4$. At what point does the graph cross the $y$-axis?
5. The cost in dollars to rent a bike for $x$ hours is $C(x)=8x+12$. What is $C(3)$?
6. A garden has perimeter 40 feet. Let $l$ be the length (feet) and $w$ be the width (feet). Create an equation relating $l$ and $w$ that represents this relationship for graphing.
7. A school cafeteria wants a descriptive model of how much food is thrown away during lunch each day (what is happening now, not what will happen next month). Define 3–5 appropriate quantities (variables) to track, with clear units and time granularity.
8. Multiply: $\left(2x - 1\right)\left(x + 4\right)$
9. A geometric sequence has first term $a_1=6$ and common ratio $r=\tfrac{1}{2}$. Write the recursive formula.
10. Solve using the quadratic formula: $x^2+2x+2=0$. Write solutions in $a+bi$ form (use $i^2=-1$).
11. Which expression has correct units for a distance $d$ if speed $v$ is in meters/sec and time $t$ is in seconds?
12. A student council is describing attendance at after-school club meetings this semester. Compare these quantity definitions: which is better for modeling attendance in a measurable, specific way?
13. Multiply: $(2x - 5)(x + 4)$
14. Is the expression $\frac{1}{2}+\frac{1}{3}$ rational or irrational? Choose the option that correctly explains why.
15. Express $\sqrt{x}\,\sqrt[3]{x}$ using a single rational exponent.​
16. An investment account grows according to the formula $A = 2500(1.06)^t$, where $A$ is the account value and $t$ is time in years. At the same time, the investor makes annual withdrawals of $200. Which equation represents the net account balance when accounting for both growth and withdrawals over $t$ years?
17. Solve the quadratic equation $x^2 + 8x + 7 = 0$ by completing the square. Give both solutions.
18. A school is selling tickets for a play. The function $R(n)=8n$ gives the revenue (in dollars) from selling $n$ tickets, where $n$ is the number of tickets sold. What is an appropriate realistic domain for $R$?
19. If $f$ is linear and $f(0) = 7$ and $f(3) = 19$, what is $f(x)$ in the form $f(x) = mx + b$?​​​
20. Use the factored form $P(x)=2(x+4)(x-2)^2$ to identify the zeros and sketch a rough graph. Which description matches the correct x-intercepts and behavior at each?

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