Digital SAT Practice Questions

Which of the following is equivalent to the expression \( x^{\frac{5}{3}} \) for \( x > 0 \)?...

>32° >10 >B >C >A >? >E >F >D Note: Figure not drawn to scale. In right triangle \( ABC \), angle \( C \) is a right angle. Triangle \( DEF \) is similar to tri...

A local theater sells tickets for an upcoming play. Adult tickets cost \( \$15 \) and child tickets cost \( \$9 \). The theater sold a total of \( 150 \) ticket...

If \( \frac{x^{a^2}}{x^{b^2}} = x^{16} \), where \( x > 1 \), and \( a + b = 2 \), what is the value of \( a - b \)?...

The equation \( y = -2x^2 + 12x - 10 \) is graphed in the \( xy \)-plane. What is the \( y \)-coordinate of the vertex of the parabola?...

In right triangle \( ABC \), the measure of angle \( C \) is \( 90^\circ \). If \( \sin(A) = \frac{3}{5} \), what is the value of \( \cos(B) \)?...

A list of 5 numbers has a mean (average) of 12. If a 6th number, \( n \), is added to the list, the new mean of the 6 numbers becomes 15. What is the value of \...

A system of two linear equations is given below: \[ 3x + 4y = 18 \] \[ 2x - y = 1 \] If the ordered pair \( (x, y) \) is the solution to the system of equations...

The quadratic equation \( 2x^2 - 4x + c = 0 \) has exactly one real solution. What is the value of the constant \( c \)?...

A boutique clothing store increases the price of a winter coat by \( 20\% \) at the start of the season. At the end of the season, the store decreases the new p...

If \( 8^x = 2^{y+1} \), which of the following expressions correctly represents \( y \) in terms of \( x \)?...

The equation of a circle in the \( xy \)-plane is given by \( x^2 + 6x + y^2 - 8y = 11 \). What is the radius of the circle?...

\[ \frac{1}{2}x - \frac{3}{4}y = 5 \] \[ cx - 3y = 20 \] In the given system of linear equations, \( c \) is a constant. For what value of \( c \) does the syst...

A toy rocket is launched from a raised platform. Its height \( h(t) \), in feet, after \( t \) seconds is given by the function \[ h(t) = -16t^2 + 64t + 80 \] W...

If \( x > 0 \), which of the following expressions is equivalent to \[ \sqrt{x^5} \cdot \sqrt[3]{x^2} \] ?...

A culture of bacteria initially contains 500 bacteria. The population increases by 15% every 4 hours. Which of the following functions \( P(t) \) models the num...

The equation of a circle in the \( xy \)-plane is given by \[ x^2 + 8x + y^2 - 10y = 8 \] What is the radius of the circle?...

Consider the following system of linear equations: \[ 3x - 4y = 12 \] \[ 6x + ky = 10 \] In the system of equations above, \( k \) is a constant. If the system ...

The function \( f \) is defined by \( f(x) = -2x^2 + 16x - 24 \). Which of the following equivalent forms of the function \( f \) displays the maximum value of ...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 10x + 6y + 9 = 0 \] If this circle is translated 2 units to the right and 3 units dow...

A conservationist is tracking a population of a specific rare beetle in a protected forest. The population is observed to increase by \( 12\% \) every year. If ...

Consider the rational equation below: \[ \frac{x^2 + 5x + 6}{x + 3} = x^2 + 2x - 4 \] What is the sum of all valid solutions \( x \) to the given equation?...

A system of linear equations is shown below, where \( a \) and \( b \) are constants. \[ \frac{1}{2}x - \frac{3}{4}y = 5 \] \[ ax - by = 20 \] If the system has...

The height \( h(t) \), in feet, of a small rocket \( t \) seconds after it is launched from a platform is modeled by the function: \[ h(t) = -16t^2 + 64t + 80 \...