Digital SAT Practice Questions

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-4, 2) \) and \( B(6, 8) \). The perpendicular bisector of segment \( AB \) can be written in the for...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-2, -3) \) and \( B(4, 9) \). The perpendicular bisector of segment \( AB \) can be written in the fo...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-6, 4) \) and \( B(2, -2) \). The perpendicular bisector of segment \( AB \) can be written in the fo...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-4, 0) \) and \( B(4, 6) \). The perpendicular bisector of segment \( AB \) can be written in the for...

The rational function \( f \) is defined by: \[ f(x) = \frac{2x^2 + ax - 12}{x^2 - 9} \] where the coefficient in the numerator is a constant. If \( f \) has a ...

The rational function \( f \) is defined by: \[ f(x) = \frac{3x^2 + bx - 10}{x^2 - 4} \] where the coefficient in the numerator is a constant. If \( f \) has a ...

The rational function \( f \) is defined by: \[ f(x) = \frac{x^2 + cx - 20}{x^2 - 16} \] where the coefficient in the numerator is a constant. If \( f \) has a ...

The rational function \( f \) is defined by: \[ f(x) = \frac{2x^2 + kx - 15}{x^2 - 25} \] where the coefficient in the numerator is a constant. If \( f \) has a...

The polynomial function \( P \) is defined by: \[ P(x) = 2x^3 - kx^2 + 4x - 8 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \( ...

The polynomial function \( P \) is defined by: \[ P(x) = x^3 + px^2 - 10x + 15 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \(...

The polynomial function \( P \) is defined by: \[ P(x) = 3x^3 - 4x^2 + cx - 18 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \(...

The polynomial function \( P \) is defined by: \[ P(x) = 4x^3 + mx^2 - 2x + 7 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \( ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 2x^2 + (-8)x + 5 \] \[ y = 4x - k \] where \( k \) is a ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 3x^2 + (-6)x + 2 \] \[ y = 6x - k \] where \( k \) is a ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 1x^2 + (-10)x + 15 \] \[ y = 2x - k \] where \( k \) is ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 4x^2 + (-16)x + 7 \] \[ y = 8x - k \] where \( k \) is a...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 2x^2 + (-4)x + 9 \] \[ y = 8x - k \] where \( k \) is a ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 1x^2 + (-6)x + 12 \] \[ y = 4x - k \] where \( k \) is a...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 2x^2 + (-10)x + 3 \] \[ y = 2x - k \] where \( k \) is a...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 3x^2 + (-12)x + 4 \] \[ y = 6x - k \] where \( k \) is a...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 8x + 6y - 11 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(4, 3)...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 10x + 4y - 20 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(5, 5...

The graph of the quadratic function \( f(x) = ax^2 + bx + c \) in the \( xy \)-plane passes through the point \( (0, 18) \) and has a vertex at \( (3, 0) \). If...

A circle in the \( xy \)-plane is defined by the equation \( x^2 + y^2 - 8x + 14y - 35 = 0 \). A line passing through the center of this circle has an equation ...