Practice Test 13 - Algebra 1

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

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1. A roller coaster's height (in meters) above the ground is modeled by $H(x)=-(x-2)^2+9$, where $x$ is the horizontal distance (in meters) from the start of a section of track. What is the maximum of $H(x)$?
2. A coffee shop sells two types of drinks. Let $x$ represent the number of lattes sold and $y$ represent the number of cappuccinos sold. If the shop sold twice as many lattes as cappuccinos, and the total number of drinks sold was 36, which system of equations represents this situation?
3. A student incorrectly concludes that $\sqrt{2} + \sqrt{8}$ is irrational because "the sum of two irrational numbers is always irrational." What is wrong with this reasoning?
4. The kinetic energy formula is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity. If a physics student wants to find the velocity required to achieve a specific kinetic energy for an object of known mass, which rearranged formula should they use?
5. Solve by factoring: $x^2 + 9x + 20 = 0$
6. A bacteria culture starts with 50 bacteria. Every 3 hours, the population triples. After observing this pattern, a researcher needs to predict the population after 15 hours. Which function correctly models the bacteria population $P(t)$ after $t$ hours?
7. The function $k$ is defined by $k(x)=\sqrt{9-x}$. What is the domain of $k$? (Give your answer in interval notation.)
8. A city employee is making a descriptive model of traffic at one intersection during the 7–9 AM rush hour. Which set of quantities is most relevant for describing what is happening?
9. Two pumps fill a tank together in 6 hours. Pump A alone can fill the tank in 10 hours. How long would it take Pump B alone to fill the tank? Let $x$ = Pump B's time in hours.
10. A function $f$ is defined on the integers $n=1,2,3,\dots$ by $f(1)=2$ and $f(n+1)=3\,f(n)$ for $n\ge 1$. What is $f(4)$?
11. The compound interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal, $r$ is the interest rate, and $t$ is time. A financial advisor needs to determine what interest rate is required to reach a target amount in a given time. Which equation correctly solves for $r$?
12. Solve graphically and algebraically (substitution is fine). The solutions are the intersection point(s) of the line and the parabola: $\begin{cases} y = 2x - 1 \\ y = x^2 - 4 \end{cases}$
13. In the model $y=800\cdot(1.03)^x$, what does the base $1.03$ represent?
14. What are the factors of the expression $-4x(x+1)$?
15. A charity's monthly donations follow this pattern: Month 1: $1000, Month 2: $1100, Month 3: $1200, Month 4: $1300. Is this exponential growth, exponential decay, or neither?
16. A student deposits $500 into an account that grows at 8% per year. Which exponential function models the balance after $t$ years?
17. Temperature can be converted using $C = \dfrac{5}{9}(F - 32)$, where $C$ is degrees Celsius and $F$ is degrees Fahrenheit. Solve the formula for $F$ in terms of $C$.
18. For the linear function $y = \tfrac{1}{2}x - 4$, what is the slope?
19. The height of a ball thrown upward can be modeled by $h(t) = -16t^2 + 48t + 6$, where $h$ is the height in feet and $t$ is the time in seconds. Which equation would you solve to find when the ball reaches a height of 54 feet?
20. If $f$ is linear, $f(0)=8$, and $f(4)=20$, what is $f(x)$? Write in the form $f(x)=mx+b$.

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