SAT Practice Questions

\(y = x + 9\) \(y = x^{2} + 16 x + 63\) A solution to the given system of equations is \((x, y)\). What is the greatest possible value of \…

\(\sqrt{(x - 2)^{2}} = \sqrt{3 x + 34}\) What is the smallest solution to the given equation?

\(2 x^{2} - 8 x - 7 = 0\) One solution to the given equation can be written as \(\frac{8 - \sqrt{k}}{4}\), where \(k\) is a constant. What …

\(\frac{20}{p} = \frac{20}{q} - \frac{20}{r} - \frac{20}{s}\) The given equation relates the positive variables \(p\), \(q\), \(r\), and \(…

\(y = 18\) \(y = - 3 (x - 18)^{2} + 15\) If the given equations are graphed in the xy -plane, at how many points do the graphs of the equat…

\(\frac{14 x}{7 y} = 2 \sqrt{w + 19}\) The given equation relates the distinct positive real numbers \(w\), \(x\), and \(y\). Which equatio…

\(y = 2 x^{2} - 21 x + 64\) \(y = 3 x + a\) In the given system of equations, \(a\) is a constant. The graphs of the equations in the given…

\(x (x + 1) - 56 = 4 x (x - 7)\) What is the sum of the solutions to the given equation?

\(8 x + y = - 11\) \(2 x^{2} = y + 341\) The graphs of the equations in the given system of equations intersect at the point \((x, y)\) in …

Which quadratic equation has no real solutions?

\(x (k x - 56) = - 16\) In the given equation, \(k\) is an integer constant. If the equation has no real solution, what is the least possib…

\(x^{2} + y + 7 = 7\) \(20 x + 100 - y = 0\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

\(\frac{12}{n} - \frac{2}{t} = - \frac{2}{w}\) The given equation relates the variables \(n\), \(t\), and \(w\), where \(n > 0\), \(t > 0\)…

The solutions to \(x^{2} + 6 x + 7 = 0\) are \(r\) and \(s\), where \(r < s\). The solutions to \(x^{2} + 8 x + 8 = 0\) are \(t\) and \(u\)…

Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up sharply to the point (0 comma…

The function \(f\) is defined by \(f (x) = x^{3} + 15\). What is the value of \(f (2)\)?

The parabola opens upward. The vertex is at point (4 comma 0). The parabola passes through the following points: (3 comma 5) (4 comma 0) (5…

The function \(g\) is defined by \(g (x) = x^{2} + 9\). For which value of \(x\) is \(g (x) = 25\)?

The graph shows the predicted value \(y\), in dollars, of a certain sport utility vehicle \(x\) years after it is first purchased. The curv…

The function \(f\) is defined by \(f (x) = 6 + \sqrt{x}\). What is the value of \(f (36)\)?

The \(y\)-intercept of the graph of \(y = x^{2} + 31\) in the xy -plane is \((0, y)\). What is the value of \(y\)?

A ball is dropped from an initial height of \(22\) feet and bounces off the ground repeatedly. The function \(h\) estimates that the maximu…

The function \(h\) is defined by \(h (x) = \frac{8}{5 x + 6}\). What is the value of \(h (2)\)?

There are \(240\) players in a tennis competition that includes \(4\) rounds of matches. Each player in the competition will play a match a…

For the first curve: Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up graduall…

The function \(k\) is defined by \(k (x) = x^{3} + 110\). What is the value of \(k (x)\) when \(x = 2\)?

The function \(f\) is defined by \(f (x) = x^{2} + x + 71\). What is the value of \(f (2)\)?

Moving from left to right: The curve passes from quadrant 2 to quadrant 1 to quadrant 4. In quadrant 2, the curve trends down gradually to …

In quadrant 2, the curve falls to its minimum at the point (0 comma 4). In quadrant 1, the curve then rises. The graph of the polynomial fu…

The function \(f\) is defined by \(f (x) = 10 x^{2} - 32 x - 152\). What is the value of \(f (0)\)?

The function \(g\) is defined by \(g (x) = \sqrt{x} + 300\). What is the value of \(g (x)\) when \(x = 81\)?

The parabola opens upward. The vertex is at the point (4 comma 2). The parabola passes through the following points: (0 comma 8) (4 comma 2…

The curve is in quadrant 1. The curve trends gradually up from left to right. The curve begins at the point (0 comma 20,000). The curve pas…

The function \(f\) is defined by \(f (x) = 5 x^{2}\). What is the value of \(f (8)\)?

The parabola opens upward. The parabola passes through the following points: (negative 1 comma 5) (0 comma 2) (1 comma 5) The graph of the …

Moving from left to right: The curve passes from quadrant 3 to quadrant 4. In quadrant 3, the curve trends up sharply to point (0 comma neg…

Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up gradually to point (0 comma 8…

Moving from left to right: The curve is in quadrant 1. The curve trends down gradually. The curve passes through the following approximate …

\(P (t) = 1,800 (1.02)^{t}\) The function \(P\) gives the estimated number of marine mammals in a certain area, where \(t\) is the number o…

\(y = - \frac{1}{4} x^{2} + 2 x + 29\) The given equation models a company’s scheduled deliveries over \(8\) months, where \(y\) is the est…

During the first part of an experiment, a ball was launched from a \(7\)-foot-tall platform. The graph shows the height \(y\), in feet, of …

\(P (t) = 24.8 (1.036)^{t}\) The function \(P\) gives the predicted population, in millions, of a certain country for the period from \(198…

All values are approximate. The parabola opens downward. The vertex of the parabola is at (0.6 comma 5.5). The parabola passes through the …

The function \(f\) is defined by \(f (x) = 4 + \sqrt{x}\). What is the value of \(f (144)\)?

The function \(f\) is defined by \(f (x) = 8 \sqrt{x}\). For what value of \(x\) does \(f (x) = 48\)?

The function \(f\) is defined by \(f (x) = \frac{16}{x}\). What is the value of \(f (x)\) when \(x = 17\)?

The function \(f\) is defined by \(f (x) = \frac{1}{6 x}\). What is the value of \(f (x)\) when \(x = 3\)?

At the time of posting a video, a social media channel had \(53\) subscribers. Each day for five days after the video was posted, the numbe…

The kinetic energy, in joules, of an object with mass \(9\) kilograms traveling at a speed of \(v\) meters per second is given by the funct…

Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up gradually to point (0 comma 2…

The function \(f (x) = 240,000 (1.22)^{x}\) gives a company’s predicted annual revenue, in dollars, \(x\) years after the company started s…

Moving from left to right, the curve passes from quadrant 2 to quadrant 1. The curve has 1 relative maximum and 1 relative minimum. The cur…

The function \(g\) is defined by \(g (x) = \sqrt{8 x + 1}\). What is the value of \(g (3)\)?

For the first curve: Moving from left to right, the curve is in quadrant 3. As x decreases, the curve approaches the line y equals negative…

The parabola opens upward. The vertex is at the point (0 comma 7). The parabola passes through the following points: (negative 1 comma Star…

Moving from left to right: The curve passes from quadrant 3 to quadrant 4 to quadrant 1. In quadrant 3, the curve trends up gradually to th…

For the first curve: Moving from left to right: The curve is in quadrant 3. As x decreases, the curve approaches the line y equals 0. As x …

The parabola opens upward. The parabola passes through the following points: (0 comma 0) (3 comma negative 12) (6 comma 0) Scientists recor…

In quadrant 3, the curve rises to its maximum at point (0 comma negative 3). In quadrant 4, the curve then falls. The graph of the polynomi…

The function \(f (x) = 200,000 (1.21)^{x}\) gives a company’s predicted annual revenue, in dollars, \(x\) years after the company started s…

An investment account was opened with an initial value of \(\$ 890\). The value of the account doubled every \(10\) years. Which equation r…

The function \(g\) is defined by \(g (x) = \left|x + 18\right|\). What is the value of \(g (4)\)?

The parabola opens upward. The vertex is at the point (2 comma negative 2). The parabola passes through the following points: (1 comma nega…

The parabola opens upward. The vertex is at point (7 comma 0). The parabola passes through the following points: (6 comma 3) (7 comma 0) (8…

\(h (x) = x^{2} - 3\) Which table gives three values of \(x\) and their corresponding values of \(h (x)\) for the given function \(h\)?

Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends down sharply to the point (0 com…

The function \(f\) is defined by \(f (x) = x^{3} + 9\). What is the value of \(f (2)\)?

Moving from left to right: The curve passes from quadrant 3 to quadrant 4. In quadrant 3, the curve trends up sharply to point (0 comma neg…

\(f (x) = (x + 6) (x + 5) (x - 4)\) The function \(f\) is given. Which table of values represents \(y = f (x) - 3\)?

The number of bacteria in a liquid medium doubles every day. There are \(44,000\) bacteria in the liquid medium at the start of an observat…

Rosa opened a savings account at a bank. The table shows the exponential relationship between the time \(t\), in years, since Rosa opened t…

\(f (x) = 3,000 (0.75)^{x}\) A conservation scientist implemented a program to reduce the population of a certain species in an area. The g…

Immanuel purchased a certain rare coin on January 1. The function \(f (x) = 65 (1.03)^{x}\), where \(0 \le x \le 10\), gives the predicted …

In quadrant 2 the curve falls sharply to cross the x axis at point (negative 1 comma 0). In quadrant 3 the curve falls sharply to cross the…

The function \(p\) is defined by \(p (n) = 7 n^{3}\). What is the value of \(n\) when \(p (n)\) is equal to \(56\)?

\(g (x) = 11 (\frac{1}{12})^{x}\) If the given function \(g\) is graphed in the xy -plane, where \(y = g (x)\), what is the y -intercept of…

The product of a positive number \(x\) and the number that is \(8\) more than \(x\) is \(180\). What is the value of \(x\)?

The exponential function \(g\) is defined by \(g (x) = 19 \cdot a^{x}\), where \(a\) is a positive constant. If \(g (3) = 2,375\), what is …

The parabola opens downward. The vertex is at point (2 comma 28). The parabola passes through the following points: (0 comma 8.4) (2 comma …

For the quadratic function \(f\), the table shows three values of \(x\) and their corresponding values of \(f (x)\). Which equation defines…

A company has a newsletter. In January \(2018\), there were \(1,300\) customers subscribed to the newsletter. For the next \(24\) months af…

For the exponential function \(g\), the table shows four values of \(x\) and their corresponding values of \(g (x)\). Which equation define…

A scientist initially measures \(12,000\) bacteria in a growth medium. \(4\) hours later, the scientist measures \(24,000\) bacteria. Assum…

\(f (x) = x^{5} + 9 x + 17\) For the given function \(f\), the graph of \(y = f (x)\) in the xy -plane passes through the point \((0, b)\),…

Moving from left to right: The curve passes through quadrant 1. The curve trends up sharply. The curve passes through the following points:…

For the quadratic function \(f\), the table shows three values of \(x\) and their corresponding values of \(f (x)\). Which equation defines…

The function \(f (t) = 60,000 (2)^{\frac{t}{410}}\) gives the number of bacteria in a population \(t\) minutes after an initial observation…

The area A , in square centimeters, of a rectangular painting can be represented by the expression \(w (w + 29)\), where \(w\) is the width…

The function \(f\) is defined by \(f (x) = 7 x^{3}\). In the xy -plane, the graph of \(y = g (x)\) is the result of shifting the graph of \…

In quadrant 3: The curve rises sharply to touch the x axis at point (negative 5 comma 0). The curve falls gradually to a relative minimum a…

\(h (t) = - 16 t^{2} + b\) The function \(h\) estimates an object’s height, in feet, above the ground \(t\) seconds after the object is dro…

\(f (x) = 4,000 (0.75)^{x}\) An entomologist recommended a program to reduce a certain invasive beetle population in an area. The given fun…

What is an x -coordinate of an x -intercept of the graph of \(y = 3 (x - 14) (x + 5) (x + 4)\) in the xy -plane?

The function f is defined by \(f (x) = 5 (\frac{1}{4} - x)^{2} + \frac{11}{4}\). What is the value of \(f (\frac{1}{4})\)?

\(m (t) = - 0.0274 (\frac{t}{7})^{2} + 7.3873 (\frac{t}{7}) + 75.032\) The function \(m\) gives the predicted body mass \(m (t)\), in \(\te…

The function \(f (t) = 40,000 (2)^{\frac{t}{790}}\) gives the number of bacteria in a population \(t\) minutes after an initial observation…

The function \(f\) is defined by \(f (x) = 270 (0.1)^{x}\). What is the value of \(f (0)\)?

\(f (x) = x^{2} - 18 x - 360\) If the given function \(f\) is graphed in the xy -plane, where \(y = f (x)\), what is an x -intercept of the…

The function \(f\) is defined by \(f (x) = 4 x^{- 1}\). What is the value of \(f (21)\)?

\(y = 3,600 (a)^{x}\) The given equation, where \(a\) is a positive constant, gives the predicted number of bacteria, \(y\), in a growth me…