Praxis Algebra i 5162 Practice Test

If \( x \) and \( y \) are inversely proportional, and \( x = 4 \) when \( y = 3 \), what is the value of \( y \) when \( x = 12 \)?

What are the solutions of the equation \( x^2 - 5x + 6 = 0 \)?

If \( 3^{2x+1} = 81 \), what is the value of \( x \)?

Find the value of \( k \) for which the equation \( x^2 + kx + 9 = 0 \) has one real solution.

What is the standard form of the equation of the circle with a radius of 5 units and center at (3, -4)?

What is the slope of the line given by the equation \( 2x - 3y = 6 \)?

What is the inverse function of \( f(x) = 3x - 4 \)?

Given \( f(x) = 2x^3 - x^2 + 4x - 7 \), what is the value of \( f(-2) \)?

Given \( g(x) = \frac{1}{x-2} \), for which values of \( x \) is \( g(x) \) undefined?

If \( \frac{x}{5} = \frac{y}{3} \) and \( x = 10 \), what is the value of \( y \)?

Which of the following represents the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots \)?

If \( a \) and \( b \) are integers such that \( a > b \) and \( ab = -24 \), which of the following could be the value of \( a - b \)?

What is the simplified form of the expression \( \frac{x^2 - 16}{x^2 - 5x + 4} \)?

What is the product of the roots of the equation \( x^2 - 7x + 12 = 0 \)?

If \( 3x - 2y = 12 \) and \( 5x + 3y = -9 \), what is the value of \( x \)?

If \( f(x) = 2x^2 - 5x + 3 \), what is the value of \( f(-2) \)?

For what value of \( k \) will the system of equations \( 2x + 3y = 6 \) and \( kx - 5y = 10 \) have no solution?

What is the solution set for the inequality \( 2(x - 3) < 4x - 6 \)?

If \( g(x) = \frac{2x}{x - 1} \), for what value(s) of \( x \) is \( g(x) \) undefined?

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

What are the solutions to the equation \( x^2 - 6x + 9 = 0 \)?

Which of the following represents the vertex form of the quadratic equation \( y = x^2 - 4x + 1 \)?

If \( 3x - 2y = 12 \) and \( 5x + 3y = -9 \), what is the value of \( x \)?

Which of the following represents the inverse function of \( f(x) = \frac{2x}{x - 1} \)?

If \( f(x) = 3x^2 - 2x + 1 \), what is \( f(-1) \)?

If the function \( f(x) = 2x^3 - 5x^2 + x - 1 \) has a root at \( x = 1 \), what is \( f(1) \)?

If \( f(x) = |x - 3| \), what is the minimum value of \( f(x) \)?

For the function \( h(x) = \frac{1}{x^2 - 4} \), what are the asymptotes?

What is the domain of the function \( f(x) = \log_3(x + 2) \)?

What is the range of the function \( h(x) = \sqrt{x - 2} \)?

Given \( g(x) = x^2 - 4x + 4 \), for what values of \( x \) is \( g(x) \leq 0 \)?

What is the domain of the function \( f(x) = \sqrt{9 - x^2} \)?

Given the piecewise function \( f(x) = \begin{cases

If \( h(x) = 3^{x+1} \), what is \( h^{-1}(27) \)?

Which of the following is the graph of the function \( f(x) = -|x| + 3 \)?

What is the end behavior of the function \( f(x) = x^3 - 2x^2 + x \)?

Which of the following is not a possible output for the function \( f(x) = \frac{x^2 - 4}{x - 2} \)?

Which of the following is the equation of a function whose graph is symmetric about the y-axis?

What is the vertex of the parabola defined by the function \( g(x) = -2(x - 1)^2 + 3 \)?

For the function \( g(x) = \frac{1}{x - 1} - \frac{2}{x + 1} \), what is \( g(0) \)?

The function \( f(x) = \frac{2x - 1}{x + 2} \) has what kind of discontinuity at \( x = -2 \)?

What is the probability of drawing a red card or a queen from a standard deck of 52 playing cards?

If the interquartile range of a data set is 12, and the first quartile is 8, what is the third quartile?

Find the standard deviation of the data set: 3, 7, 7, 9, 11.

If \( x \) is inversely proportional to \( y \), and \( y = 2 \) when \( x = 3 \), what is the value of \( y \) when \( x = 6 \)?

If \( f(x) = 2x^2 + 3x - 5 \), find \( f(-3) \).

What is the coefficient of variation for a data set with a mean of 20 and a standard deviation of 5?

What is the 20th term of the arithmetic sequence where \( a_1 = 3 \) and \( a_2 = 7 \)?

A bag contains 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue or green marble?

If the odds in favor of an event are 4 to 1, what is the probability of the event occurring?

The function \( f(x) = \frac{1}{x-2} \) is undefined for what value of \( x \)?

If \( a \) and \( b \) are the roots of the equation \( x^2 - 5x + 6 = 0 \), what is \( a^2 + b^2 \)?

What is the equation of the line that passes through the points \( (2, 3) \) and \( (4, -1) \)?

A box contains 6 red, 4 blue, and 5 green balls. What is the probability of randomly selecting a red or a green ball?

If \( f(x) = x^3 - 2x + 1 \), find the value of \( f(-2) \).

What is the 15th term of the arithmetic sequence 5, 9, 13, ...?

What is the equation of the parabola with focus \( (4, 3) \) and directrix \( y = 1 \)?

A die is rolled twice. What is the probability of getting a 4 on the first roll and a 6 on the second roll?

If the range of a set of data is 20 and the lowest value is 15, what is the highest value in the set?

What is the equation of the circle with center at \( (3, -2) \) and radius 4?