SAT Math Past Questions

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If a$^2$ + b$^2$ = z and ab = y, which of the following is equivalent to 4z + 8y ?

\[ y=x^2 \] \[ 2y+6=2(x+3) \] If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy?

In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T) = 0.6T + 331.4.Which of the following statements is the best interpretation of t…

Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per wee…

Which of the following is equivalent to the sum of the expressions a$^2$ - 1 and a + 1 ?

$\sqrt{k + 2} - x = 0$ In the equation above, k is a constant. If x = 9, what is the value of k ?

Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?

What are the solutions of the quadratic equation 4x$^2$ - 8x - 12 = 0?

The circle above with center O has a circumference of 36. What is the length of minor arc $\widehat{AC}$ ?

Which of the following is an equation of line l in the xy-plane above?

In a circle with center O, central angle AOB has a measure of $\frac{5\pi}{4}$ radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?

In triangle ABC, the measure of ∠B is 90°, BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is \(\f…

In the figure above, lines k, l, and m intersect at a point. If x + y = u + w, which of the following must be true?I. x = z II. y = w III. z = t

kx - 3y = 4 4x - 5y = 7In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?

The line y = kx + 4, where k is a constant, is graphed in the xy-plane. If the line contains the point (c,d), where c ≠ 0 and d ≠ 0, what is the slope of the line in terms of c and d ?

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined be…

If 3r = 18 , what is the value of 6r + 3 ?

A total of 2 questions refer to the following information.Ms. Simon drives her car from her home to her workplace every workday morning. The table above shows the distance, in miles, and her average driving speed, in mil…

A total of 2 questions refer to the following information.Ms. Simon drives her car from her home to her workplace every workday morning. The table above shows the distance, in miles, and her average driving speed, in mil…

Point P is the center of the circle in the figure above. What is the value of x ?

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SAT Math Past Questions

If a\(^2\) + b\(^2\) = z and ab = y, which of the following is equivalent to 4z + 8y ?

\[ y=x^2 \] \[ 2y+6=2(x+3) \] If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy?

In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T) = 0.6T + 331.4.Which of the following statements is the best interpretation of t…

Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per wee…

Which of the following is equivalent to the sum of the expressions a\(^2\) - 1 and a + 1 ?

\(\sqrt{k + 2} - x = 0\) In the equation above, k is a constant. If x = 9, what is the value of k ?

Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?

What are the solutions of the quadratic equation 4x\(^2\) - 8x - 12 = 0?

The circle above with center O has a circumference of 36. What is the length of minor arc \(\widehat{AC}\) ?

Which of the following is an equation of line l in the xy-plane above?

In a circle with center O, central angle AOB has a measure of \(\frac{5\pi}{4}\) radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?

In triangle ABC, the measure of ∠B is 90°, BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is \(\f…

In the figure above, lines k, l, and m intersect at a point. If x + y = u + w, which of the following must be true?I. x = z II. y = w III. z = t

kx - 3y = 4 4x - 5y = 7In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?

The line y = kx + 4, where k is a constant, is graphed in the xy-plane. If the line contains the point (c,d), where c ≠ 0 and d ≠ 0, what is the slope of the line in terms of c and d ?

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined be…

If 3r = 18 , what is the value of 6r + 3 ?

A total of 2 questions refer to the following information.Ms. Simon drives her car from her home to her workplace every workday morning. The table above shows the distance, in miles, and her average driving speed, in mil…

A total of 2 questions refer to the following information.Ms. Simon drives her car from her home to her workplace every workday morning. The table above shows the distance, in miles, and her average driving speed, in mil…

Point P is the center of the circle in the figure above. What is the value of x ?