Practice Test 28 - Algebra 1

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

Start practice test

1. Graph the solution set to the system $\begin{cases} y\ge 2x \\ y\le -x+6 \end{cases}$ Which description is correct?
2. For the series with $a=4$, $r=3$, and $n=5$, find $S_n$. That is, find the sum $4+12+36+108+324$.
3. A ball is thrown upward from the ground. Its height (in feet) after $t$ seconds is given by $h = -16t^2 + 64t$. Solve for the time(s) when the ball is on the ground. Let $t$ = time in seconds, and set $h = 0$.
4. The first four terms of a sequence are 1, 4, 16, 64. A student claims this can be modeled by both $a_n = 4^{n-1}$ and the recursive formula $a_1 = 1$, $a_n = 4a_{n-1}$. Is the student correct, and what is $a_7$?
5. A student is making a descriptive model of how long it takes them to get to school each day. What units should be used for the variable representing travel time?
6. A function $f$ is defined only for integers $n = 1,2,3,\dots$ by $f(1)=2$ and $f(n+1)=2f(n)$. What is $f(4)$?
7. On a coordinate plane, the quadratic function $y = x^2 - 5x + 6$ is graphed. What are the x-intercepts of $y = x^2 - 5x + 6$ (as points)?
8. A rectangular room is 12 ft long and 9 ft wide. Find the area and include correct units. Use the formula $A=\ell\times w$ and check that the units are consistent.
9. To factor $4x^2 - 12xy + 9y^2 - 25$, which approach best uses the expression's structure?
10. Simplify the rational expression (a quotient of polynomials). The simplified form should have no common factors in the numerator and denominator: $\frac{x^2-16}{x+4}$
11. A function $V(r) = \frac{4}{3}\pi r^3$ represents the volume of a sphere with radius $r$. In the context of manufacturing ball bearings where the radius must be between 2 mm and 8 mm inclusive, and considering the precision of the manufacturing equipment, which domain is most appropriate?
12. Rewrite $\frac{x^3+4x^2+x-6}{x+2}$ in the form $q(x)+\frac{r(x)}{x+2}$ using polynomial division, with $\deg(r)<\deg(x+2)$.
13. Two quadratic functions are given: $f(x) = x^2 - 8x + 15$ and $g(x) = x^2 - 8x + 16$. By factoring each function to reveal their zeros, how many zeros do these functions have in common?
14. Order the following functions by growth rate for large $x$ (from slowest to fastest): $L(x)=50x$ (linear), $Q(x)=3x^2$ (quadratic), $P(x)=x^5$ (polynomial), $E(x)=1.2^x$ (exponential).
15. A savings account balance is modeled by $B(t)=100\cdot(1.5)^t$, where $t$ is the number of months. Is the rate of change $\Delta B/\Delta t$ constant? (No calculus.)
16. Factor $x^2-49$ by recognizing it as a difference of squares.
17. What is $x$ in the equation $5x - 8 = 2x + 10$?
18. What are the terms in $4a^2 - a + 7$?
19. See $x^4-16$ as $(x^2)^2-4^2$ and factor completely.
20. A subscription service charges according to $C(n) = 15n + 8$, where $n$ is the number of premium features activated and $C$ is the monthly cost in dollars. The company is considering restructuring to $C(n) = 12n + 20$. Comparing these two models, what does the change in the coefficient of $n$ indicate about the pricing strategy?

Practice tests