Praxis Mathematics 5165 Domain 1: Number and Quantity and Algebra

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 the complex number \( z \) satisfies the equation \( z^2 + 4z + 13 = 0 \), what is the imaginary part of \( z \)?

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