Digital SAT Practice Questions

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 ...

For a certain exponential growth model \( P(t) = C \cdot (1.25)^{\frac{t}{6}} \), where \( t \) represents the number of hours elapsed, by what percent does \( ...

Recent archaeobotanical excavations at Tell Abu Hureyra reveal that early Neolithic communities actively cultivated rye millennia before widespread agricultural...

In materials science, metamaterials with negative Poisson's ratios—termed auxetic materials—expand laterally when stretched longitudinally, defying conventional...

>P >Q >R >S >12 >x >x+7 Note: Figure not drawn to scale. In the right triangle \( riangle PQR\), shown above, \(\angle PQR\) is a right angle. Altitude \(QS\) i...

>A >B >C >D >BD=x >DC=15 Note: Figure not drawn to scale. In right triangle ABC, with the right angle at vertex A, an altitude is drawn from A to hypotenuse BC,...