Praxis Middle School Mathematics 5164 Practice Test

What is the least common multiple of 6, 8, and 12?

If \( a \) and \( b \) are integers such that \( 2^a \cdot 2^b = 2^{10} \), and \( a > b \), what is the value of \( a \)?

What is the value of \( 8^{2/3} \)?

What is the result of \( \left(\frac{2}{3}\right)^{-2} \)?

Evaluate: \( \frac{6!}{4! \cdot 2!} \).

Simplify: \( \sqrt[3]{-125} \).

If \( \frac{5}{x} = \frac{x}{20} \), what is the value of \( x \)?

What is the simplified form of the expression \(\frac{5^{x+1} \cdot 5^{x-1}}{5^{2x}}\)?

What is the greatest common divisor (GCD) of 54 and 81?

If \( \frac{2}{3} \) of a number is 60, what is 150% of that number?

What is the decimal equivalent of \( \frac{1}{8} + \frac{1}{4} \)?

What is the product of the prime factors of 210?

If \( 16^{3x} = 64^x \), what is the value of \( x \)?

If \( \frac{7}{x} = \frac{14}{28} \), what is the value of \( x \)?

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

Solve for \( y \) in the equation \( \frac{1}{y} + \frac{1}{y+1} = \frac{1}{2} \).

What is the inverse of the function \( f(x) = \frac{1}{x - 3} \)?

If \( f(x) = x^2 - 4x + 3 \) and \( g(x) = 2x - 1 \), what is the value of \( f(g(2)) \)?

If \( 2^x = 8^2 \), what is the value of \( x \)?

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

What is the coefficient of \( x \) in the expansion of \( (3x - 2)^2 \)?

What is the solution to the system of equations \( y = 2x + 3 \) and \( y = -x + 5 \)?

Which of the following is equivalent to \( \frac{x^2 - 4}{x^2 - 2x - 8} \)?

If \( g(x) = 2x^3 - 3x^2 + x - 5 \), what is \( g(-1) \)?

What are the roots of the quadratic equation \( 3x^2 - 12x + 9 = 0 \)?

Find the inverse function of \( f(x) = \frac{3x - 4}{2} \).

Which of the following is the factored form of \( x^2 - 5x - 6 \)?

What is the value of \( x \) in the inequality \( 3(x - 2) > 2x + 1 \)?

The function \( f(x) = 4x - 7 \) is applied to a number, and the result is 9. What was the original number?

Solve for \( x \) in the equation \( \frac{1}{x} + \frac{1}{x+2} = \frac{1}{2} \).

Find the inverse function of \( f(x) = \frac{3x - 4}{2} \).

Which expression is equivalent to \( \frac{5}{x - 2} - \frac{3}{x + 2} \)?

What is the vertex of the parabola represented by the equation \( y = 2x^2 - 4x + 1 \)?

Given \( f(x) = x^2 - 4x + 3 \), find the value of \( f(2a) \).

What is the solution to the inequality \( 3(2x - 1) > 4x + 5 \)?

If \( g(x) = 2x^3 - 3x^2 + x - 5 \), what is \( g(-1) \)?

What are the roots of the quadratic equation \( 3x^2 - 12x + 9 = 0 \)?

If \( h(x) = 2|x - 3| \), what is the value of \( h(0) \)?

Which of the following is the factored form of \( x^2 - 5x - 6 \)?

If \( x \) and \( y \) satisfy the system of equations \( 2x + 3y = 10 \) and \( x - 4y = -3 \), what is the value of \( x \)?

What is the coefficient of \( x \) in the expansion of \( (3x - 2)^2 \)?

Which expression is equivalent to \( \frac{5}{x - 2} - \frac{3}{x + 2} \)?

What is the volume of a cube with a surface area of \( 150 \text{ cm}^2 \)?

If a regular hexagon has a side length of 8 cm, what is its perimeter?

What is the area of a rhombus with diagonals of length 10 cm and 24 cm?

A regular hexagon has a perimeter of 48 cm. What is the area of the hexagon?

What is the area of an equilateral triangle with side length 10 cm?

If a right triangle has one angle measuring 30 degrees, what is the length of the hypotenuse if the opposite side is 6 cm?

A sphere has a diameter of 10 cm. What is its surface area?

What is the sum of the interior angles of a pentagon?

If the base of a right pyramid is a square with side length 6 cm and the height of the pyramid is 9 cm, what is the volume?

A rectangular prism has dimensions of 4 cm by 6 cm by 8 cm. What is the length of the diagonal of this prism?

A right circular cone has a base radius of 6 cm and a height of 8 cm. What is the volume of the cone?

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

A cone has a radius of 4 cm and a slant height of 5 cm. What is the surface area of the cone?

In a class of 30 students, 18 are wearing glasses. If three students are chosen at random, what is the probability that exactly two of them are wearing glasses?

A set of data is normally distributed with a mean of 50 and a standard deviation of 5. What is the probability that a randomly selected data point is less than 45?

What is the range of the data set \( \{3, 7, 7, 10, 15, 18\} \)?

In a survey, 70\% of respondents chose chocolate as their favorite flavor. If 5 people are surveyed, what is the probability that at least 3 will choose chocolate?

A standard six-sided die is rolled twice. What is the probability of rolling a sum of 8?

A bag contains 5 black and 3 white marbles. Two marbles are drawn sequentially with replacement. What is the probability that at least one marble is black?

If the interquartile range of a data set is 12, and the first quartile is 15, what is the third quartile?

A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads?

A box contains 5 red, 4 blue, and 3 green balls. If two balls are picked at random without replacement, what is the probability that both are green?

A set of data has a mean of 10 and a median of 12. Which of the following statements is true about the data set?

If the mean of a data set is 20 and the standard deviation is 4, what percentage of the data is expected to lie between 16 and 24?