Practice Test 90 - Algebra 2

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

What is the remainder when dividing $p(x)=2x^4-x^2+5$ by $(x+1)$ ? Use the Remainder Theorem (remainder $=p(a)$ for divisor $(x-a)$ ).
Given the recursive formula $a_1 = 7$ and $a_n = 2a_{n-1} - 3$ for $n \geq 2$ , what type of sequence is this, and what is the explicit formula?
For the geometric series $5+15+45+135+405,$ identify $a$ , $r$ , and $n$ , then find the sum $S_n$ .
A geometric series has first term $a=12$ , common ratio $r=\frac{1}{3}$ , and $n=8$ terms. What is $S_8$ ? (Use $S_n=\dfrac{a(1-r^n)}{1-r}$ for $r\ne 1$ .)
The function $f(x)=x^2$ has domain all real numbers, but it fails the horizontal line test (for example, $f(2)=f(-2)=4$ ), so it is not one-to-one. What domain restriction makes $f$ invertible?
A streaming service charges a one-time sign-up fee and then a monthly fee. The total cost after $m$ months is $T = 9.99m + 19.99$ , where $T$ is in dollars. What does the parameter $9.99$ represent in this context?
Which situation shows constant percent change (exponential) rather than constant additive change (linear)?
For $p(x)=x^4-16,$ which of the following are factors? Use the Remainder Theorem by checking whether $p(a)=0$ . I. $(x-2)$ II. $(x+2)$ III. $(x-4)$
What is the y-intercept of the exponential function $f(x)=7\cdot 3^x$ ? (Connect to the parent $y=3^x$ and evaluate at $x=0$ .)
Simplify using the conjugate multiplication property $(a+bi)(a-bi)=a^2+b^2$ : $(6- i)(6+i).$
Convert $4\left(\cos 150^\circ + i \sin 150^\circ\right)$ to rectangular form $a + bi$ . Use $a = r \cos \theta$ and $b = r \sin \theta$ .
A rectangular garden has a length that is 8 feet more than twice its width. If the area of the garden is 96 square feet, which equation could be used to find the width $w$ of the garden?
A complex number in polar form is given as $z = 6\left(\cos\frac{11\pi}{6} + i\sin\frac{11\pi}{6}\right)$ . When $z$ is written in rectangular form $a + bi$ and then converted back to polar form using the principal argument in $(-\pi, \pi]$ , what is the new polar representation?
Divide $P(x)=x^3+x^2-5x+2$ by $(x-1)$ using synthetic division (more efficient than long division for $(x-c)$ ). Use $c=1$ and coefficients $1,1,-5,2$ . Read the quotient coefficients from the bottom row and the remainder from the last entry (which equals $P(1)$ ). What is the quotient and remainder?
Find the inverse function $f^{-1}(x)$ for $f(x)=\dfrac{x-4}{2}$ .
Use the Rational Zeros Theorem to help factor the polynomial completely over the integers: $P(x)=x^3-7x-6.$
Write the exponential function in the form $f(x)=a\cdot b^x$ that passes through $(0,6)$ and $(2,24)$ . Which formula is correct?
An investment account starts with $1000 and grows by $4\%$ per year, compounded annually. (1) Create an exponential model for the balance after $t$ years. (2) Use your model to determine when the account balance will double. Round to the nearest tenth of a year and interpret your result in context.
In the expression $5(x-1)^2 + 2x(x+3) - 4$ , identify all the terms (additive parts separated by $+$ or $-$ ).
What function undoes $f(x)=\dfrac{x-4}{3}$ ? (That is, find $f^{-1}(x)$ .)

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