SAT Math Past Questions

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The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female under age 40…

The graph above shows Marilyn’s distance from her campsite during a 3‑hour hike. She stopped for 30 minutes during her hike to have lunch. Based on the graph, which of the following is closest to the time she finished…

At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

Two isosceles triangles are shown above. If 180 − z = 2y and y = 75, what is the value of x ?

If $\frac{7}{9}x$ - $\frac{4}{9}x$ = $\frac{1}{4}$ + $\frac{5}{12}$, what is the value of $x$ ?

x$^3$(x$^2$ - 5) = -4xIf x > 0, what is one possible solution to the equation above?

C = $\frac{5}{9}$(F − 32)The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true…

What are the solutions to $3x^2 + 12x + 6 = 0$?

The equation $\frac{24x^2 + 25x - 47}{ax -2} = -8x -3 - \frac{53}{ax - 2}$ is true for all values of $x \neq \frac{2}{a}$, where $a$ is a constant. What is the value of $a$ ?

y = a(x− 2)(x+ 4)In the quadratic equation above, $a$ is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). Which of the following is equal to d ?

In the xy-plane, the parabola with equation $y = (x - 11)^2$ intersects the line with equation $y = 25$ at two points, A and B. What is the length of $\overline{\rm AB}$ ?

The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ?

2x − 3y = −14 3x − 2y = −6If (x,y) is a solution to the system of equations above, what is the value of x − y ?

If $\frac{5}{x}$ = $\frac{15}{x + 20}$, what is the value of $\frac{x}{5}$ ?

Which of the following is equal to $a^{\frac{2}{3}}$, for all values of $a$

A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painter’s fee can be calculated by the expression nKlh, where n is the number of walls, K is a constant with un…

A total of two questions refer to the following information.Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)$^t$ to find…

A total of two questions refer to the following information.Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)$^t$ to find…

$h(x) = \frac{1}{(x - 5)^2 + 4(x - 5) + 4}$For what value of x is the function h above undefined?

A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?

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SAT Math Past Questions

The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female under age 40…

The graph above shows Marilyn’s distance from her campsite during a 3‑hour hike. She stopped for 30 minutes during her hike to have lunch. Based on the graph, which of the following is closest to the time she finished…

At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

Two isosceles triangles are shown above. If 180 − z = 2y and y = 75, what is the value of x ?

If \(\frac{7}{9}x\) - \(\frac{4}{9}x\) = \(\frac{1}{4}\) + \(\frac{5}{12}\), what is the value of \(x\) ?

x\(^3\)(x\(^2\) - 5) = -4xIf x > 0, what is one possible solution to the equation above?

C = \(\frac{5}{9}\)(F − 32)The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true…

What are the solutions to \(3x^2 + 12x + 6 = 0\)?

The equation \(\frac{24x^2 + 25x - 47}{ax -2} = -8x -3 - \frac{53}{ax - 2}\) is true for all values of \(x \neq \frac{2}{a}\), where \(a\) is a constant. What is the value of \(a\) ?

y = a(x− 2)(x+ 4)In the quadratic equation above, \(a\) is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). Which of the following is equal to d ?

In the xy-plane, the parabola with equation \(y = (x - 11)^2\) intersects the line with equation \(y = 25\) at two points, A and B. What is the length of \(\overline{\rm AB}\) ?

The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ?

2x − 3y = −14 3x − 2y = −6If (x,y) is a solution to the system of equations above, what is the value of x − y ?

If \(\frac{5}{x}\) = \(\frac{15}{x + 20}\), what is the value of \(\frac{x}{5}\) ?

Which of the following is equal to \(a^{\frac{2}{3}}\), for all values of \(a\)

A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painter’s fee can be calculated by the expression nKlh, where n is the number of walls, K is a constant with un…

A total of two questions refer to the following information.Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)\(^t\) to find…

A total of two questions refer to the following information.Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)\(^t\) to find…

\(h(x) = \frac{1}{(x - 5)^2 + 4(x - 5) + 4}\)For what value of x is the function h above undefined?

A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?