Digital SAT Practice Questions

The value of a rare antique automobile is projected to increase by \( r\% \) every 5 years. If the value of the automobile increases by exactly \( 72.8\% \) eve...

In the \( xy \)-plane, the terminal side of an angle of measure \( \alpha \) in standard position intersects the unit circle at point \( (x, y) \). If \( y = -\...

The system of equations below has no solutions. \[ a x + 3 y = 12 \] \[ -5 x + b y = 8 \] If \( a \) and \( b \) are integers, which of the following is the max...

The equation \( y = cx^2 - 4x + 5 \) represents a parabola in the \( xy \)-plane, where \( c \) is a constant. The line \( y = kx - 3 \) intersects the parabola...

Let \( P(x) = ax^4 + bx^3 + cx^2 + dx + e \), where \( a, b, c, d, \) and \( e \) are constants. When \( P(x) \) is divided by \( (x - 2) \), the remainder is 1...

A circle has radius \( r \) and center \( O \). Point \( P \) lies outside the circle such that the distance from \( P \) to \( O \) is \( d \). Two distinct li...

In a large population of registered voters, 60% are homeowners and 50% are over the age of 50. If the probability of randomly selecting a voter who is both a ho...

A scientist is observing two bacterial cultures. Culture X has an initial population of \( P_0 \) and doubles every \( a \) hours. Culture Y has an initial popu...

The system of equations is given by: \[ y = 2x^2 - 4x + c \] \[ y = kx - 5 \] where \( c \) and \( k \) are constants. The system has exactly one real solution ...

The function \( f \) is defined by \( f(x) = \frac{ax^2 + bx - 120}{2x^2 - 14x + 20} \), where \( a \) and \( b \) are constants. The graph of \( y = f(x) \) in...

In the xy-plane, a circle is defined by the equation \( x^2 + y^2 - 10x + 6y = c \), where \( c \) is a constant. A line with the equation \( y = \frac{4}{3}x -...

The absolute value inequality \( |kx - 12| \le c \) has a solution set of \( -2 \le x \le 8 \), where \( k \) and \( c \) are positive constants. What is the va...

A solid glass right circular cone has a height of \( H \) centimeters. A horizontal cut parallel to the base separates the solid cone into a smaller top cone an...

In the \( xy \)-plane, the system of equations is given by: \[ x^2 + y^2 - 8x + 6y + c = 0 \] \[ 3x - 4y = 12 \] where \( c \) is a constant. For what value of ...

The function \( f \) is defined by \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants. In the \( xy \)-plane, the vertex of the parab...

A right rectangular prism has a total surface area of \( 144 \) and a space diagonal of length \( \sqrt{52} \). What is the sum of the lengths of all 12 edges o...

In a certain animal population, \( 40\% \) of the individuals exhibit Trait A, and \( 30\% \) of the individuals exhibit Trait B. The event of an individual exh...

In the \( xy \)-plane, the terminal side of an angle of measure \( \theta \) radians in standard position intersects the unit circle at point \( P \). The termi...

The polynomial \( P(x) = x^4 + c x^3 + d x^2 + c x + 1 \), where \( c \) and \( d \) are real constants, has \( x = 1 + i \) as a root (where \( i = \sqrt{-1} \...

A circle in the \( xy \)-plane is given by the equation \[ x^2 + y^2 - 14x - 6y + 33 = 0 \] Line \( L \) is tangent to the circle at the point \( (10, 7) \). Li...

A radioactive isotope decays such that its mass decreases by \( p\\% \) every \( h \) hours. If the mass of the isotope decreases by \( q\\% \) every \( 3h \) h...

How many integers \( x \) satisfy the inequality \[ |x^2 - 12x + 20| \le -x^2 + 12x - 20 \]?...

The circle \( C \) in the \( xy \)-plane is given by the equation \[ x^2 + y^2 = 36 \] A triangle is formed by the origin \( O(0,0) \), the point \( A(6, 0) \),...

In the \( xy \)-plane, the graph of the line \( y = 2x + 5 \) intersects the graph of the parabola \( y = x^2 - 4x + c \) at exactly one point. What is the \( y...