Practice Test 37 - Algebra 1

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

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1. Solve the system. The solutions are where the line intersects the circle: $\begin{cases} x^2 + y^2 = 25 \\ y = 4 \end{cases}$ What are all intersection points $(x,y)$?
2. In the distance formula $d = rt$ (where $d$ is distance, $r$ is rate, and $t$ is time), solve for $t$ in terms of $d$ and $r$.
3. The height of a projectile is modeled by $h(t) = -4t^2 + 16t + 12$, where $t$ is time in seconds. At what time does the projectile reach its maximum height?
4. If $s(x)=x^2+2$, what is $s(-4)$?​
5. You time a short sprint using a stopwatch that displays tenths of a second. The recorded time is 12.7 s. In a report, what is an appropriate way to record this time?
6. The function $f(x) = x^2 - 6x + 5$ represents the height (in feet) of a ball $x$ seconds after it is thrown. After factoring to find when the ball hits the ground, what is the axis of symmetry of this parabola?
7. A polynomial is given by $P(x)=(x-3)(x+3)(x-1)^2.$ Use zeros, multiplicities, and degree to sketch a rough graph. Which statement is correct?
8. Is the expression $\left(\frac{3}{4}\right)\times\pi$ rational or irrational? Choose the option with correct reasoning.​
9. A bathroom scale measures to the nearest 0.1 lb. It reads 156.4 lb. Which reporting shows appropriate precision?
10. A student writes $S_n=a+ar+ar^2+\cdots+ar^{n-1}$ and multiplies by $r$ to get $rS_n=ar+ar^2+\cdots+ar^n$. When subtracting to make the middle terms cancel, which equation is correct? (Assume $r\ne 1$.)
11. For the floor (greatest integer) function $f(x)=\lfloor x\rfloor$, what is $f(2.7)$?
12. An investment account is modeled by $A(t)=1000(1.05)^t$, where $t$ is the number of years. What is the annual percent growth rate?
13. A ball's height (in feet) is modeled by $h(t) = -16t^2 + 32t$. When does it hit the ground (solve $h(t)=0$)?
14. Solve the system algebraically. (The solution(s) are the intersection point(s) of the line and the circle.) $\begin{cases} x^2 + y^2 = 25 \\ y = 4 \end{cases}$
15. What is the completed square form of $x^2+4x-5=0$ written as $(x-p)^2=q$?
16. Factor $x^2-49$ by recognizing it as a difference of squares.​
17. Which equation correctly demonstrates why we define $27^{1/3}$ to equal 3?
18. Prove or disprove the claim: "If $r$ is a nonzero rational number and $i$ is an irrational number, then $r\times i$ is irrational." Which reasoning is correct?
19. If $r$ represents regular meals and $p$ represents premium meals, which system correctly models all constraints for viable daily operation?
20. View the expression $\frac{x+6}{x-2}$ by identifying what's being done to what. Which statement best describes its structure?

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