SAT Pastpaper with Solutions

The table gives the number of hours, h, of labor and a plumber's total charge f(h), in dollars, for two different jobs.

There is a linear relationship between h and f(h). Which equation represents this relationship?

Exactly how many x-intercepts does the graph of f(x) = x(x-10)²(x-11)³ have in the xy-plane, where y = f(x)?

The given equation, where t is a positive constant, defines a circle in the xy-plane. The radius of this circle is . What is the value of t?
2x² + 2y² + tx + ty - 78 = 0

In triangle RST , the measure of angle R is 29 degrees. Which statement provides sufficient information to prove that triangle RST is isosceles?

If a = 6k + 5r and b = 9k - 12r + 3, which expression is equivalent to a-b?

For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

A polygonal chain is a connected series of line segments whose length is defined as the sum of the lengths of the line segments it is made of. A polygonal chain with a length of 33 centimeters (cm) is extended by adding line segments that each have a length of 8 - r cm.

Which function f represents the total length, in cm, of the extended polygonal chain after x line segments are added?

If , what is the value of x-5?

A chemist combines 30 grams of compound A, 45 grams of compound B, and x grams of compound C. The resulting mixture has a mass of 135 grams. What is the value of x?

Line k is shown in the xy-plane. Line j (not shown) is perpendicular to line k and passes through the point (19,23). What is the y-coordinate of the y-intercept of line j?

For a study, a group of chipmunks will be selected from a habitat consisting of 220 chipmunks, and a group of prairie dogs will be selected from a habitat consisting of 190 prairie dogs. Some of the chipmunks and prairie dogs will be in a treatment group, and some of the chipmunks and prairie dogs will be in a control group. Which of the following is necessary for this study to attempt to establish a cause-and-effect relationship between two variables?

A certain investment account offers a special interest rate for the first 4 months the account is open followed by a lower interest rate for the remainder of the time the account is open. Akeyla opened one of these accounts with an original account balance of $ 700.00 and did not make any other deposits or withdrawals. 4 months after Akeyla opened the account, the balance had increased by 0.6% of the original balance. 6 months after Akeyla opened the account, the balance had increased by an additional 0.1% of the balance at the end of the first 4 months. Every 2 months after the first 6 months, the balance had increased by an additional 0.1% of the balance 2 months before. Which of the following equations could represent the account balance B(x), in dollars, x months after the account was opened, where x ≥ 4?

As the size of a firework's shell increases, the height above the ground when the firework bursts increases. For a firework to burst 1,075 feet above the ground, a firework's shell in the shape of a sphere with a volume of 542.68 cubic inches could be used. To the nearest whole number, what is the volume of this firework's shell in cubic centimeters? (1 inch = 2.54 centimeters)

What is the least value of x that is a solution to the given equation?

The 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) passes through the points (c,7) and (2c,117), where c is a constant. Which of the following could be the value of b?

In the given system of equations, g, h, and k are constants. The system has infinitely many solutions. What is the value of g/k?

In the given expression, b is a positive integer. If qz⁹ + r is a factor of the expression, where q and r are positive integers, what is the greatest possible value of b?
34z¹⁸ + bz⁹ + 30

A right rectangular prism has a base area of 16t square centimeters (cm²). The length of the base of the rectangular prism is 8/3 cm, and the height of the rectangular prism is 9 cm. Which expression represents the surface area, in cm², of the right rectangular prism?

The mass of object A is 498% of the mass of object B, and the mass of object A is 0.830% of the mass of object C. If the mass of object C is p% of the mass of object B, what is the value of p?