Practice Test 89 - Algebra 2

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

Start practice test

1. Sketch a graph of a function $y=f(x)$ that satisfies all of the following features: - $x$-intercepts at $(-2,0)$ and $(4,0)$ - $y$-intercept at $(0,3)$ - A relative maximum at $(1,5)$ - End behavior: as $x\to\infty$, $f(x)\to-\infty$ and as $x\to-\infty$, $f(x)\to\infty$ Which option shows a sketch that matches these features?
2. The graph of $y = g(x)$ passes through the point $(2, 0)$ and has the property that $g(x) = (x-2)^2 \cdot h(x)$ where $h(x)$ is a polynomial with $h(2) \neq 0$. Based on this information and the factor $(x-2)^2$, what can be concluded about the graph near $x = 2$?
3. In the polynomial $3x^3 - 7x^2 + 2x + 9$, what is the coefficient of $x^2$?
4. Let $f(x)=2x^3$ (polynomial), $g(x)=50x$ (linear), $h(x)=x^2$ (quadratic), and $k(x)=1.3^x$ (exponential). For sufficiently large $x$, which ordering is correct from greatest to least?
5. In physics, the kinematic relation $v^2=u^2+2as$ connects final speed $v$, initial speed $u$, acceleration $a$, and displacement $s$. Solve for $a$ in terms of $v$, $u$, and $s$.
6. A machine part is worth $900 when new and loses $12\%$ of its value each year. Create an exponential decay model for its value $V(t)$ after $t$ years, then solve for when its value will be $500. Round to the nearest tenth of a year and interpret your result.
7. The polynomial $p(x) = x^4 - 16$ can be factored completely over the complex numbers. Which of the following represents the complete factorization?
8. Which situation shows a constant percent rate of change (exponential), rather than a constant additive change (linear)?​​
9. Using inspection or polynomial long division, express $\dfrac{x^2+5x+7}{x+2}$ as $q(x)+\dfrac{r(x)}{x+2}$ with $\deg(r)<\deg(x+2)$.
10. Let the parent function be $f(x)=|x|$. What is the effect on the graph of $g(x)=-f(x)$ compared to $f(x)$?
11. Show by composition whether $f(x)=x^3-5$ and $g(x)=\sqrt[3]{x+5}$ are inverse functions. Compute and simplify $f(g(x))$ and $g(f(x))$.
12. Use the Remainder Theorem to find the remainder when $p(x)=3x^3-x^2-7x+2$ is divided by $(x+2)$.​
13. Polynomials are closed under multiplication, so the product of two polynomials is also a polynomial. Multiply and write the result in standard form: $\,(x^2-3x+2)(x+4)\,$.
14. Viewing complex numbers as points on the complex plane, the midpoint of the segment joining $z_1=a+bi$ and $z_2=c+di$ is $\frac{z_1+z_2}{2}=\frac{a+c}{2}+\frac{b+d}{2}i.$ What is the midpoint of the segment from $z_1=1-5i$ to $z_2=7+1i$?
15. The equation $2x^2 - 8x + m = 0$ has solutions that are complex numbers with imaginary parts of $\pm\frac{\sqrt{6}}{2}$. What is the value of $m$?
16. Condense the expression into a single logarithm (base 10): $2\log(x)+\tfrac{1}{2}\log(y)-\log(z).$
17. Verify that the polynomial identity $a^3+b^3=(a+b)(a^2-ab+b^2)$ is true for all real $a,b$ by expanding the right-hand side.​
18. Solve the system and identify the relationship between the lines: $\begin{cases} 2x + y = 7\\ x + \tfrac{1}{2}y = \tfrac{7}{2} \end{cases}$
19. Using the identity $(a^2 + b^2)^2 = (a^2 - b^2)^2 + (2ab)^2$, which of the following sets of three positive integers could form a Pythagorean triple when $a = 3$ and $b = 2$?
20. Condense to a single logarithm (base 10): $\log(x)-\tfrac{1}{2}\log(y)+\log(z)$​

Practice tests