Practice Test 1 - College Algebra

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

Which expression represents $\frac{x^2+5x+6}{x^2-x-2} \div \frac{x^2+4x+3}{x^2-4}$ in lowest terms?
If $x$ and $y$ are nonzero real numbers, and $\frac{1}{x} + \frac{1}{y} = \frac{1}{2}$ , which property justifies the step $\frac{y + x}{xy} = \frac{1}{2}$ ?
A bacteria culture follows $P(t)=1000e^{0.22t}$ (t in hours); when does it reach $3000$ ?
Which expression is equivalent to $x^4 - 13x^2 + 36$ after complete factorization?
Which option correctly simplifies $\log_b\!\left(\frac{x}{x^2}\right)$ using the quotient rule?
Which option correctly applies the quotient rule to $\log_b\!\left(\frac{x}{7}\right)$ ?
For the piecewise function $h(x) = \begin{cases} x^2-4 & \text{if } x < 2 \\ \sqrt{x-1} & \text{if } x \geq 2 \end{cases}$ , what is the range?
For what value of $k$ does the equation $\log_k(27) = \frac{3}{2}$ hold true?
Simplify the expression using exponent rules: $(2x^2)(3x^4)$ .
The graph of $y = f(x)$ passes through the point $(2, 5)$ and has a horizontal asymptote at $y = 3$ . After applying the transformations to create $y = 4f(\frac{1}{2}x - 1) - 2$ , what is the equation of the new horizontal asymptote?
The quadratic $2x^2 + px + 8 = 0$ has discriminant $\Delta = p^2 - 64$ . For what value of $p$ will the equation have a repeated root, and what will that root be?
A cubic polynomial has zeros at $x = -2, 1,$ and $4$ . If the coefficient of $x^3$ is $\frac{1}{2}$ , and the graph passes through the point $(0, k)$ , what is the value of $k$ and what does it represent graphically?
A sequence is defined recursively as $a_1 = -3$ and $a_n = a_{n-1} + 4$ for $n \geq 2$ . Which explicit formula correctly represents the 12th term of this sequence?
Mixing: solve $\frac{x}{6}+\frac{1}{2}=\frac{5}{6}$ for $x$ mL.
An arithmetic sequence has its 4th term equal to 22 and its 10th term equal to 46. What is the explicit formula for the $n$ th term of this sequence?
If $\log_3(a) - \log_3(b) = 2$ and $\log_3(ab) = 6$ , what is the value of $\log_3(a^2b)$ ?
Select the expression that represents $\log_b(x^3)$ using the power rule.
Which of the following functions represents a horizontal stretch of $f(x) = (x-1)^2 + 2$ by a factor of 3?
Consider $m(x) = \ln(x - 2) + 4$ . Which expression correctly represents $m^{-1}(x)$ , and what is its domain?
If $4^{x-1} = 16$ and $\log_2(y) = x$ , then what is the value of $y$ ?

Practice tests