Practice Test 96 - Algebra 2

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

Start practice test

1. Consider the functions $f(x)=5x$ (linear), $g(x)=2x^2$ (quadratic), $h(x)=x^4$ (polynomial), and $p(x)=1.5^x$ (exponential). Order these functions by eventual growth rate as $x\to\infty$ (fastest to slowest).
2. Solve the quadratic equation $x^2 + 2x + 10 = 0$ and express the solutions as complex numbers in $a + bi$ form.
3. Use the discriminant to analyze $x^2-4x+5=0$. For a quadratic $ax^2+bx+c=0$, the discriminant $b^2-4ac$ determines the type of solutions, but in the complex numbers there are always exactly 2 solutions counting multiplicity (previewing the Fundamental Theorem of Algebra for degree 2). Which option correctly gives the solutions?
4. Use the Rational Zeros Theorem to find all rational zeros of $P(x)=2x^3+5x^2-x-6.$ Test candidates by substitution or synthetic division, and report the rational zeros you verify.
5. Because polynomials are closed under subtraction, the difference of two polynomials is also a polynomial. Subtract and write the result in standard form: $\,(x^3+5x^2-2x+7)-(2x^3-x^2+4x-1)\,$.
6. A student attempts to complete the square for $4x^2 + 12x - 5 = 0$ and writes $4(x + \frac{3}{2})^2 = 14$. To verify this is correct, which calculation should be performed?
7. A moving company models the cost (in dollars) to rent a truck for $h$ hours by $C(h)=\dfrac{120}{10-h}$. In the real situation, $h$ is the number of hours the truck is rented, and the company allows rentals for up to 9 hours. What is an appropriate realistic domain for $h$?
8. Sketch $f(x)=\frac{x^2-9}{x^2-x-6}$ showing all zeros and vertical asymptotes. (Factor to identify shared factors, if any.)
9. Sketch the polynomial $f(x)=(x-2)(x+1)(x+4)$ identifying all zeros and the end behavior. Which description matches the correct sketch?
10. An exponential function has the form $g(x)=a\cdot b^x$ and passes through $(0,5)$ and $(2,45)$. Which function is correct?
11. Calculate the rate of change over each interval and determine whether it is constant. Table (equal $x$-intervals of 2): $x$: 0, 2, 4, 6 $y$: 1, 5, 13, 25
12. Solve $x^2 - 7x + 10 = 0$ by factoring or by the quadratic formula. Which pair of solutions is correct?
13. Subtract and simplify to lowest terms. Be careful to distribute the subtraction across the entire numerator when using a common denominator. Subtract: $\frac{4}{x+3}-\frac{1}{x-3}$ (Assume $x\neq \pm 3$.)​​
14. A delivery app models the total pay (in dollars) for completing $n$ deliveries as $P(n)=7n+15$. A driver can complete at most 25 deliveries in a shift. What values of $n$ are appropriate for this context?​
15. When $(2 + 3i)^2$ is written in standard form $a + bi$, what is the value of $a - b$?
16. A population is modeled by $P(t)=P_0(1.08)^t$, where $t$ is in years. To express the same growth using quarters, rewrite $(1.08)^t$ as a quarterly factor raised to the number of quarters $4t$. Which rewrite is correct?
17. For $q(x)=-2(x-2)^2(x+4),$ identify the zeros and determine crossing vs. touching at each zero. Also state the end behavior.
18. Solve the system using the elimination method: $\begin{cases} 2x + 3y = 12\\ 4x - 3y = 6 \end{cases}$ What is the solution $(x, y)$?
19. A student saves money by depositing $30$ dollars each week, starting with $30$ dollars in week 1. Let $S(n)$ be the total saved after $n$ weeks (domain: positive integers). Which choice gives both a correct recursive and explicit formula for $S(n)$?
20. Perform the operation and simplify to lowest terms: $\frac{2}{x-3}-\frac{1}{x+3}$ (Assume $x\neq 3,-3$.)

Practice tests