Practice Test 48 - Algebra 1

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

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1. You are graphing total cost versus number of tickets. Tickets cost $8 each, and the number of tickets ranges from 0 to 30, so total cost ranges from $0 to $240. What scale is most appropriate for the y-axis (Cost ($))?
2. What is the coefficient of $x$ in the expression $7x^2-4x+1$?
3. Rewrite the radical expression $\sqrt[3]{x^2}$ using rational exponents.
4. A sequence is defined recursively by $a_1=9$ and $a_{n+1}=a_n-2$ for $n=1,2,3,\dots$. What are the first four terms $a_1,a_2,a_3,a_4$?
5. A hiker estimates distance on a map and gets 12.38 km. The map scale and measuring method are only reliable to about the nearest 0.1 km. Round the distance appropriately for this context.
6. A lab models the temperature of a cooling sample by adding a constant room temperature to an exponential cooling term. Let $R(t)=72$ (room temperature in °F) and $C(t)=18(0.85)^t$. Write the combined temperature function $T(t)=(R+C)(t)$.
7. A deposit grows by 10% per year, modeled by $(1.10)^t$ for $t$ years. Which expression is equivalent and shows the growth in days (365 days per year)?​​
8. Solve for $y$ in the literal equation $ax + by = c$ (assume $b \ne 0$). Use the same steps you would use to solve a numeric equation for $y$.
9. What is the starting point of the square root function $f(x)=\sqrt{x+3}$?​
10. Solve $2x^2 + 12x + 10 = 0$ by completing the square (divide first if needed).
11. What is the coefficient of $x$ in the expression $x + 5$?
12. A population model is written as $P(t)=P_0(1.10)^t$ where $t$ is in years. Which expression is equivalent and highlights the approximate monthly growth factor? (Use $1.10^{1/12}\approx 1.0080$.)
13. Function $p$ is given by $p(x)=x^2-6x+8$. Function $q$ is described verbally as: "A parabola that opens upward with vertex at $(1,-3)$." Which function has the smaller minimum value?
14. An environmental toxin concentration follows $T(t) = T_0(0.75)^{t/10}$ where $t$ is in days. To reduce the toxin to 10% of its original level, approximately how long will it take, and what is the daily reduction rate?
15. Subtract: $\left(4x^2 + x - 6\right) - \left(2x^2 - 3x + 5\right)$
16. Solve the system algebraically (substitution). The solutions are the intersection point(s) of the line and the circle: $\begin{cases} x^2 + y^2 = 10 \\ y = x \end{cases}$ What are all solutions $(x,y)$?
17. What is the constant term in the expression $9m-10$?
18. Let $f(x) = 2x - 1$ and $g(x) = x^2 + 3$. If $f(a) = 9$ and $g(b) = 12$, what is the value of $f(b) + g(a)$?
19. A model compares two quantities by division. Let $f(x)=x+2$ (linear) and $g(x)=x-3$ (linear). Find the domain of $(f/g)(x)=\dfrac{f(x)}{g(x)}$.​
20. A gym charges a $25 sign-up fee plus $15 per month. Let $m$ be the number of months and let $C(m)$ be the total cost. Write the function that models this situation.

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