SAT Practice Questions

The function \(f (x) = 206 (1.034)^{x}\) models the value, in dollars, of a certain bank account by the end of each year from \(1957\) thro…

The function \(f (w) = 6 w^{2}\) gives the area of a rectangle, \(\text{in }\text{ft}^{2}\), if its width is \(w\text{ ft}\) and its length…

A physics class is planning an experiment about a toy rocket. The equation \(y = - 16 (x - 5.6)^{2} + 502\) gives the estimated height \(y\…

A rectangle has a length of \(x\) units and a width of \((x - 15)\) units. If the rectangle has an area of \(76\) square units, what is the…

The product of two positive integers is \(546\). If the first integer is \(11\) greater than twice the second integer, what is the smaller …

A rectangle has a length that is \(15\) times its width. The function \(y = (15 w) (w)\) represents this situation, where \(y\) is the area…

The table shows the exponential relationship between the number of years, \(x\), since Hana started training in pole vault, and the estimat…

The function \(f\) is defined by \(f (x) = \left|x - 4 x\right|\). What value of \(a\) satisfies \(f (5) - f (a) = - 15\)?

The area of a triangle is \(270\) square centimeters. The length of the base of the triangle is \(12\) centimeters greater than the height …

Moving from left to right: The curve is in quadrant 1. From point (0 comma 9), the curve trends down sharply. From point (5 comma 1), the c…

\(f (x) = \frac{a - 19}{x} + 5\) In the given function \(f\), \(a\) is a constant. The graph of function \(f\) in the xy -plane, where \(y …

Moving from left to right: The curve is shown in quadrant 1. The curve trends down sharply to x equals 3. The curve then trends down gradua…

Bacteria are growing in a liquid growth medium. There were \(300,000\) cells per milliliter during an initial observation. The number of ce…

The function \(f\) is defined by \(f (x) = 8 x^{3} + 4\). What is the value of \(f (2)\)?

A company opens an account with an initial balance of \(\$ 36,100.00\). The account earns interest, and no additional deposits or withdrawa…

\(f (t) = 500 (0.5)^{\frac{t}{12}}\) The function \(f\) models the intensity of an X-ray beam, in number of particles in the X-ray beam, \(…

A sample of a certain isotope takes \(29\) years to decay to half its original mass. The function \(s (t) = 184 (0.5)^{\frac{t}{29}}\) give…

For the polynomial function \(f\), the graph of \(y = f (x)\) in the xy -plane passes through the points \((- 5, 0)\), \((1, 0)\), and \((4…

\(q (x) = 32 (2^{x})\) Which table gives three values of \(x\) and their corresponding values of \(q (x)\) for function \(q\)?

The parabola opens downward. The parabola passes through the following approximate points: (50 comma negative 33.83) (149.02 comma 186.05) …

The equation \(E (t) = 5 (1.8)^{t}\) gives the estimated number of employees at a restaurant, where \(t\) is the number of years since the …

A function \(p\) estimates that there were \(2,000\) animals in a population in \(1998\). Each year from \(1998\) to \(2010\), the function…

\(p (x) + 57 = x^{2}\) The given equation relates the value of \(x\) and its corresponding value of \(p (x)\) for the function \(p\). What …

\(y = 0.25 x^{2} - 7.5 x + 90.25\) The equation gives the estimated stock price \(y\), in dollars, for a certain company \(x\) days after a…

The population of the town of Smithville doubled every \(75\) years from \(1659\) to \(1959\). The population of this town was \(240,000\) …

On April \(1\), there were \(233\) views of an advertisement posted on a website. Every \(2\) days after April \(1\), the number of views o…

The parabola opens downward. The vertex is at the approximate point (0.2 comma 10.2). The parabola passes through the following points: (0 …

An egg is thrown from a rooftop. The equation \(h = - 4.9 t^{2} + 9 t + 18\) represents this situation, where \(h\) is the height of the eg…

The area \(A\), in square centimeters, of a rectangular cutting board can be represented by the expression \(w (w + 9)\), where \(w\) is th…

The table shows three values of \(x\) and their corresponding values of \(y\) for the equation \(y = 4 (2)^{x} + 3\). In the table, \(a\) i…

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

An object is kicked from a platform. The equation \(h = - 4.9 t^{2} + 7 t + 9\) represents this situation, where \(h\) is the height of the…

\(g (x) = x^{2} + 55\) What is the minimum value of the given function?

\(f (x) = (x + 6) (x - 4)\) If the given function \(f\) is graphed in the xy -plane, where \(y = f (x)\), what is the x -coordinate of an x…

The parabola opens downward. The vertex is at point (4 comma 9). The parabola passes through the following points: (0 comma 5) (2 comma 8) …

A model predicts that the population of Bergen was \(15,000\) in \(2005\). The model also predicts that each year for the next \(5\) years,…

For the exponential function \(f\), the value of \(f (0)\) is \(c\), where \(c\) is a constant. Of the following equations that define the …

A machine launches a softball from ground level. The softball reaches a maximum height of \(51.84\) meters above the ground at \(1.8\) seco…

For the exponential function \(f\), the value of \(f (1)\) is \(k\), where \(k\) is a constant. Which of the following equivalent forms of …

\(f (x) = - 6 x^{2} + 60 x - 126\) The function \(f\) is defined by the given equation. Which of the following equivalent forms of the equa…

Function \(f\) is defined by \(f (x) = (x + 6) (x + 5) (x + 1)\). Function \(g\) is defined by \(g (x) = f (x - 1)\). The graph of \(y = g …

Moving from left to right, the curve passes from quadrant 3 to quadrant 4. As x decreases, the curve approaches line y equals negative 7. T…

The table shows three values of \(x\) and their corresponding values of \(g (x)\), where \(g (x) = \frac{f (x)}{x + 3}\) and \(f\) is a lin…

\(y = x^{2} - 14 x + 22\) The given equation relates the variables \(x\) and \(y\). For what value of \(x\) does the value of \(y\) reach i…

The area of a triangle is equal to \(x^{2}\) square centimeters. The length of the base of the triangle is \(2 x + 22\) centimeters, and th…

The function \(g\) is defined by \(g (x) = \frac{\left|x\right|}{a} - 14\), where \(a < 0\). What is the product of \(g (15 a)\) and \(g (7…

The function \(f\) is defined by \(f (x) = a^{x} + b\), where \(a\) and \(b\) are constants. In the \(x y\)-plane, the graph of \(y = f (x)…

\(f (x) = x^{2} - 48 x + 2,304\) What is the minimum value of the given function?

The area of a rectangular banner is \(2,661\) square inches. The banner's length \(x\), in inches, is \(24\) inches longer than its width, …

The first term of a sequence is \(9\). Each term after the first is \(4\) times the preceding term. If \(w\) represents the \(n\)th term of…

\(f (t) = 55 t - 2 t^{2}\) The function \(f\) is defined by the given equation. The function \(g\) is defined by \(g (t) = f (t) + 3\). Whi…

\(f (x) = 9 (4)^{x}\) The function \(f\) is defined by the given equation. If \(g (x) = f (x + 2)\), which of the following equations defin…

The product of two positive integers is \(462\). If the first integer is \(5\) greater than twice the second integer, what is the smaller o…

A rectangle has an area of \(155\) square inches. The length of the rectangle is \(4\) inches less than \(7\) times the width of the rectan…

The function \(f\) is defined by \(f (x) = (x - 6) (x - 2) (x + 6)\). In the xy -plane, the graph of \(y = g (x)\) is the result of transla…

\(f (x) = 9,000 (0.66)^{x}\) The given function \(f\) models the number of advertisements a company sent to its clients each year, where \(…

\(y = 576^{(2 x + 2)}\) The graph of the given equation in the xy -plane has a y -intercept of \((r, s)\). Which of the following equivalen…

The function \(f\) gives the product of a number, \(x\), and a number that is \(91\) more than \(x\). Which equation defines \(f\)?

At the time that an article was first featured on the home page of a news website, there were \(40\) comments on the article. An exponentia…

\(f (x) = (1.84)^{\frac{x}{4}}\) The function \(f\) is defined by the given equation. The equation can be rewritten as \(f (x) = (1 + \frac…

The quadratic function \(g\) models the depth, in meters, below the surface of the water of a seal \(t\) minutes after the seal entered the…

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launch…

For the function \(f\), \(f (0) = 86\), and for each increase in \(x\) by \(1\), the value of \(f (x)\) decreases by \(80 \%\). What is the…

The parabola opens upward. The vertex is at point (negative 1 comma negative 8). The parabola passes through the following points: (negativ…

Function \(f\) is defined by \(f (x) = - a^{x} + b\), where \(a\) and \(b\) are constants. In the xy -plane, the graph of \(y = f (x) - 12\…

The functions \(f\) and \(g\) are defined by the given equations, where \(x \ge 0\). Which of the following equations displays, as a consta…

\(f (x) = a x^{2} + 4 x + c\) In the given quadratic function, \(a\) and \(c\) are constants. The graph of \(y = f (x)\) in the xy -plane i…

Function \(f\) is a quadratic function where \(f (- 20) = 0\) and \(f (- 4) = 0\). The graph of \(y = f (x)\) in the xy -plane has a vertex…

The function \(f\) is defined by \(f (x) = (- 8) (2)^{x} + 22\). What is the y -intercept of the graph of \(y = f (x)\) in the xy -plane?

When the quadratic function \(f\) is graphed in the xy -plane, where \(y = f (x)\), its vertex is \((- 3, 6)\). One of the x -intercepts of…

For the function \(q\), the value of \(q (x)\) decreases by \(45 \%\) for every increase in the value of \(x\) by \(1\). If \(q (0) = 14\),…

The functions \(f\) and \(g\) are defined by the given equations, where \(x \ge 0\). Which of the following equations displays, as a consta…

Moving from left to right, the curve passes from quadrant 3 to quadrant 2 to quadrant 1. The curve has 2 relative maximums and 2 relative m…

The function \(g\) is defined by \(g (x) = (x + 14) (t - x)\), where \(t\) is a constant. In the xy -plane, the graph of \(y = g (x)\) pass…

The function \(f\) is defined by \(f (x) = a^{x} + b\), where \(a\) and \(b\) are constants and \(a > 0\). In the xy -plane, the graph of \…

\(f (x) = (x - 10) (x + 13)\) The function \(f\) is defined by the given equation. For what value of \(x\) does \(f (x)\) reach its minimum?

\(f (x) = (x + 7)^{2} + 4\) The function \(f\) is defined by the given equation. For what value of \(x\) does \(f (x)\) reach its minimum?

A right rectangular prism has a height of \(9\) inches. The length of the prism's base is \(x\) inches, which is \(7\) inches more than the…

Two variables, \(x\) and \(y\), are related such that for each increase of \(1\) in the value of \(x\), the value of \(y\) increases by a f…

The functions \(f\) and \(g\) are defined by the given equations. \(f (x) = 3 + \left|- 2 x - x^{2}\right|\) \(g (w) = \left|\frac{- w}{w -…

The function \(f\) is defined by \(f (x) = a (2.2^{x} + 2.2^{b})\), where \(a\) and \(b\) are integer constants and \(0 y -coordinate of th…

\(f (t) = 8,000 (0.65)^{t}\) The given function \(f\) models the number of coupons a company sent to their customers at the end of each yea…

Moving from left to right: The curve is in quadrant 3. The curve trends down sharply. As x increases, the curve approaches the line x equal…

Square P has a side length of \(x\) inches. Square Q has a perimeter that is \(176\) inches greater than the perimeter of square P. The fun…

\(f (x) = (x - 1) (x + 3) (x - 2)\) In the xy -plane, when the graph of the function \(f\), where \(y = f (x)\), is shifted up \(6\) units,…

\(f (x) = \left|59 - 2 x\right|\) The function \(f\) is defined by the given equation. For which of the following values of \(k\) does \(f …

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The…

\(P (t) = 290 (1.04)^{(\frac{4}{6}) t}\) The function \(P\) models the population, in thousands, of a certain city \(t\) years after \(2005…

\(f (x) = 5,470 (0.64)^{\frac{x}{12}}\) The function \(f\) gives the value, in dollars, of a certain piece of equipment after \(x\) months …

\(f (x) = (x - 14) (x + 19)\) The function \(f\) is defined by the given equation. For what value of \(x\) does \(f (x)\) reach its minimum?

An auditorium has seats for \(1,800\) people. Tickets to attend a show at the auditorium currently cost \(\$ 4.00\). For each \(\$ 1.00\) i…

The function \(h\) is defined by \(h(x)=a^x+b\), where \(a\) and \(b\) are positive constants. The graph of \(y=h(x)\) in the \(xy\)-plane …

A model estimates that at the end of each year from \(2015\) to \(2020\), the number of squirrels in a population was \(150 \%\) more than …

A submersible device is used for ocean research. The function \(g (x) = - \frac{1}{55} (x + 19) (x - 35)\) gives the depth below the surfac…

\(P (t) = 260 (1.04)^{(\frac{6}{4}) t}\) The function \(P\) models the population, in thousands, of a certain city \(t\) years after \(2003…

\(f (x) = (x - 2) (x + 15)\) The function \(f\) is defined by the given equation. For what value of \(x\) does \(f (x)\) reach its minimum?

\(f (x) = 4 x^{2} - 50 x + 126\) The given equation defines the function \(f\). For what value of \(x\) does \(f (x)\) reach its minimum?

The functions \(g\) and \(h\) are defined by the given equations, where \(x \ge 0\). Which of the following equations displays, as a consta…

The function \(f (x) = \frac{1}{9} (x - 7)^{2} + 3\) gives a metal ball's height above the ground \(f (x)\), in inches, \(x\) seconds after…

A park ranger hung squirrel houses each in the shape of a right rectangular prism for fox squirrels. Each house has a height of \(11\) inch…