Praxis Mathematics (5165) Practice Test

What are the solutions to the equation \( \frac{1}{x+2} + \frac{1}{x-2} = \frac{1}{x} \)?

If the function \( f(x) = x^2 - 4x + 4 \), what is the vertex of its graph?

If \( \log_2(x) = 4 \), what is the value of \( x \)?

If \( i \) is the imaginary unit, what is \( (2 - 3i)(2 + 3i) \)?

If \( x \) and \( y \) satisfy the system of equations \( 3x - 2y = 7 \) and \( 2x + 3y = -1 \), what is the value of \( x \)?

Find the coefficient of \( x^3 \) in the expansion of \( (2x - 1)^5 \).

What is the sum of the roots of the quadratic equation \( x^2 - 6x + 8 = 0 \)?

What is the inverse function of \( f(x) = 2x + 3 \)?

What is the simplified form of \( \frac{\sqrt{12}}{\sqrt{3}} \)?

If \( \log(x) + \log(5) = 2 \), what is the value of \( x \)?

Which of the following represents the simplified form of \( \frac{2x^2 - 8}{x^2 - 4} \)?

What is the remainder when \( x^3 - 4x^2 + 6x - 8 \) is divided by \( x - 2 \)?

What is the solution set of \( x^2 - x - 6 < 0 \)?

What is the degree of the polynomial \( 4x^5 - 3x^3 + 2x^2 - x + 7 \)?

If \( a, b, \) and \( c \) are in arithmetic progression with \( a < b < c \), and \( b = 5 \), what is \( c \) when \( a = 2 \)?

What are the asymptotes of the function \( f(x) = \frac{2x}{x - 1} \)?

What is the domain of the function \( f(x) = \sqrt{x^2 - 4} \)?

The expression \( \frac{1}{x-1} - \frac{1}{x+1} \) simplifies to which of the following?

What is the product of the roots of the equation \( 2x^2 - 5x + 3 = 0 \)?

If \( f(x) = x^3 - 6x^2 + 11x - 6 \), what are the x-intercepts of its graph?

Calculate the integral \( \int (3x^2 - 2x + 1) \, dx \).

What is the limit of \( \frac{\sin(x)}{x} \) as \( x \) approaches 0?

What is the derivative of the function \( g(x) = \frac{x^2 - 1}{x^2 + 1} \)?

What is the area under the curve of \( f(x) = 4 - x^2 \) from \( x = -2 \) to \( x = 2 \)?

Given the function \( f(x) = x^3 - 6x^2 + 11x - 6 \), for which values of \( x \) does \( f(x) = 0 \)?

What is the convergence interval of the power series \( \sum_{n=1}^{\infty} \frac{(x-1)^n}{n2^n} \)?

Evaluate the limit \( \lim_{x \to \infty} \frac{3x^3 + 2x^2 - x}{4x^3 - x^2 + 5} \).

Find the critical points of the function \( f(x) = x^4 - 4x^2 \).

Find the derivative of the function \( f(x) = x^2e^{3x} \).

Calculate the volume of the solid formed by revolving the area between \( y = x^2 \) and \( y = x \) around the x-axis.

Determine the radius of convergence for the series \( \sum_{n=1}^{\infty} \frac{n!x^n}{n^n} \).

What is the limit as \( x \) approaches infinity of \( \frac{e^x}{x^2} \)?

What is the derivative of \( f(x) = \ln(\sqrt{x^2 + 1}) \)?

If \( f(x) = \tan^{-1}(x) \), what is \( f''(0) \)?

If \( h(x) = e^{2x} \), what is the second derivative of \( h \) at \( x = 0 \)?

Calculate the area between the curves \( y = \sin x \) and \( y = \cos x \) from \( x = 0 \) to \( x = \frac{\pi}{4} \).

Evaluate the integral \( \int_0^1 \ln(1 + x) \, dx \).

Find the Taylor series for \( \cos(x) \) centered at \( \pi \).

If \( f(x) = \int_{0}^{x} t^2 e^{t^3} dt \), what is \( f'(x) \)?

What is the Maclaurin series expansion of \( e^{x^2} \)?

If two circles are tangent internally at point P, and the diameters of the circles are 10 cm and 6 cm, what is the distance from P to the center of the larger circle?

What is the area of a trapezoid with bases of lengths 8 cm and 14 cm and a height of 6 cm?

A regular hexagon is inscribed in a circle. If the radius of the circle is 8 cm, what is the perimeter of the hexagon?

What is the volume of a cylinder with a radius of 3 cm and a height of 10 cm?

A square and a regular hexagon have the same perimeter. If the side of the square is 6 cm, what is the length of each side of the hexagon?

In a triangle, if two angles measure \( 35^\circ \) and \( 55^\circ \), what is the measure of the third angle?

A cone has a height of 9 cm and a base radius of 3 cm. What is its slant height?

A sphere has a volume of \( 288\pi \text{ cm}^3 \). What is its surface area?

What is the length of the diagonal of a square with a side length of \( 5 \) units?

In a 45-45-90 right triangle, if the length of one of the legs is \( \sqrt{2} \) units, what is the length of the hypotenuse?

What is the sum of the interior angles of a polygon with 12 sides?

In a right triangle, if one angle measures \( 30^\circ \), what is the ratio of the length of the side opposite the \( 30^\circ \) angle to the hypotenuse?

In an isosceles triangle, the base angles are each \( 45^\circ \). What is the measure of the vertex angle?

A set of data is normally distributed with a mean of 50 and a standard deviation of 5. What percentage of the data falls between 45 and 55?

If the probability of an event A is 0.2 and the probability of an event B is 0.5, what is the probability of either A or B occurring, assuming the two events are independent?

What is the variance of the data set \( \{4, 8, 12, 16, 20\} \)?

If the correlation coefficient between two variables is 0.8, what is the coefficient of determination?

If a continuous random variable X has a uniform distribution on the interval [0, 4], what is the probability that \( X \leq 2 \)?

In a binomial experiment with 10 trials and a probability of success of 0.6, what is the probability of exactly 6 successes?

A standard normal distribution has a mean of 0 and a standard deviation of 1. What is the z-score for a value of 2.5 in this distribution?

In a probability distribution, the probabilities of 5 mutually exclusive events are 0.1, 0.2, 0.3, 0.2, and 0.2. What is the entropy of this distribution?

In a regression analysis, if the slope of the regression line is negative, what does this indicate about the relationship between the independent and dependent variables?

A test has a reliability coefficient of 0.9. If the true score is 80, what is the expected range of observed scores for this test?

For a set of data, if the quartile deviation is 5, what is the interquartile range?

In a Poisson distribution with a mean of 4, what is the probability of observing exactly 3 events?

Given a dataset with a positively skewed distribution, which of the following is true regarding its mean, median, and mode?