Practice Test 40 - Algebra 1

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

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1. In the formula $d=rt$, distance equals rate times time. If $r$ is measured in $\text{miles/hour}$ and $t$ is measured in hours, what are the units of $d$ (using unit cancellation)?
2. A video game costs $60 before tax. A store coupon takes 25% off the original price. Write and solve an equation to find the sale price. Let $p$ = the sale price (in dollars).
3. The formula for the period of a pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$, where $T$ is the period, $L$ is the length, and $g$ is gravitational acceleration. A physicist wants to determine the length needed for a pendulum to have a specific period. Which equation correctly isolates $L$?
4. If $\frac{2p - 1}{p + 3} = \frac{3}{4}$ and $p \neq -3$, what is the value of $p$?
5. A gym membership costs $15 to start and then $5 per week. You want to graph total cost $C$ (in dollars) versus weeks $w$ for up to 12 weeks. What is an appropriate scale to use for the axes?
6. In the exponential function $y=200\cdot(1.10)^x$, what does the base $1.10$ represent?
7. A rectangle has perimeter 40 feet. Let $l$ be the length (feet) and $w$ be the width (feet). What equation represents the relationship between $l$ and $w$?
8. In physics, kinetic energy is given by $K = \dfrac{1}{2}mv^2$, where $K$ is kinetic energy, $m$ is mass, and $v$ is speed. Solve for $m$ in terms of $K$ and $v$.
9. A ride at an amusement park moves up and down in a repeating pattern. The height (in meters) above the ground is modeled by $h(t)=12+4\sin\left(\frac{\pi}{3}t\right)$, where $t$ is time in seconds. What is the period of $h(t)$?
10. Solve using elimination: $\begin{cases} 2x+3y=12 \\ 2x-y=4 \end{cases}$ What is the solution $(x,y)$?
11. For the quadratic function $y=(x-1)^2-5$, does the parabola open up or down?
12. A student is assembling care packages with granola bars and juice boxes. Let $x$ = number of granola bars and $y$ = number of juice boxes. Each granola bar has 120 calories and each juice box has 80 calories. The package must have at least 800 calories: $120x+80y\ge 800$. The student can include at most 12 items total: $x+y\le 12$. Also, $x\ge 0$ and $y\ge 0$. Is the point $(4,6)$ a viable solution?
13. Let $f(x)=4x$ and $g(x)=x^2-2$. Find $g(f(x))$.
14. In the rectangle area formula $A = lw$ (where $A$ is area, $l$ is length, and $w$ is width), solve for $w$. Treat the other variables like numbers as you would in a numeric equation.
15. What is $\sqrt[3]{64}$ written in rational exponent form?​
16. Complete the square to solve $x^2 + 2x + 5 = 0$. What are the solutions?
17. In a savings plan, you deposit $100 at the end of each month. The account earns $0.5\%$ interest per month. After 12 months, the value of the deposits is $100\big(1.005^{11}+1.005^{10}+\cdots+1.005^1+1.005^0\big).$ Use $S_n=\dfrac{a(1-r^n)}{1-r}$ to find the total value after 12 months (in dollars, to the nearest cent).
18. For a function $p(x)$, it is known that $p(5) = 8$, $p(8) = 2$, and $p(2) = 5$. What is the value of $p(p(p(5)))$?
19. A water balloon is launched upward from a platform. The height $h(t) = -16t^2 + 64t + 80$ gives the balloon's height in feet after $t$ seconds. Which statement correctly describes a key feature of this function in the context of the problem?
20. What does the vertex form $f(x)=-(x-3)^2+16$ reveal about the graph? Choose the statement that correctly gives the vertex, axis of symmetry, and maximum value.

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