SAT Pastpaper with Solutions

The roofs on the buildings of a public garden are designed to allow water to drain into the garden. The table shows the relationship between the area x, in square feet, of a roof and the amount of water f(x), in gallons, drained from the roof into the garden over a certain period of time. Which equation could define f?

In 2010, a skating team had a total of 35 skaters, each classified as either advanced or intermediate. From 2010 to 2020, the number of advanced skaters on the team increased by approximately 53%, and the number of intermediate skaters on the team increased by approximately 44%. The total number of skaters on the team increased by approximately  49%. Which equation best represents this situation, where a represents the number of advanced skaters on the team in 2010 and b represents the number of intermediate skaters on the team in 2010?

The given equation relates the positive numbers b, x, and y. Which equation correctly expresses x in terms of b and y?

One of the two equations in a system of linear equations is given. The system has infinitely many solutions. If the second equation in the system is y = mx + b, where m and b are constants, what is the value of b?

What is the solution (x, y) to the given system of equations?

y = 6x + 16
-7x - y = 36

The histograms summarize the distributions of scores for team A and team B. Which statement best compares the standard deviations of scores for these teams?

The graph of y = f(x) is shown, where f(x) = ab^x + c, and a, b, and c are constants. For how many values of x does f(x) = 0?

To study fluctuations in leaf water potential, samples of wood were taken from 22 trees and cut in the shape of a cube. The length of the edge of one of these cubes is 3.000 centimeters. This cube has a density of 0.250 grams per cubic centimeter. What is the mass of this cube, in grams?

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 at (r, -64). What is the value of r?

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

In the given equation, c  is a constant. The equation has exactly one solution. What is the value of c?
-2x² + 20x + c = 0

In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point, (x,y), in the xy-plane. What is the value of x?
y = 2x² - 15x + 23
y = x + a

The positive number a is  2352% of the sum of the positive numbers b and c, and b is  84% of c. What percent of b is a?

The functions f and g are defined by the given equations below, where x ≥ 0. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where x ≥ 0?

I. f(x) = 18(1.4)^x+5

II. g(x) = 18(1.16)(1.4)^x+3

In the given equation, s and r are constants, and s > 0. If the equation has infinitely many solutions, what is the value of s?

The perimeter of an isosceles right triangle is   inches. What is the length, in inches, of the hypotenuse of this triangle?

A right triangular pyramid has exactly six edges. Each of these edges is 96 centimeters long. If the surface area of the pyramid is  square centimeters, what is the value of  ?

The cost of renting a piece of construction equipment for up to 5 days is $ 270 for the first day and $ 135 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the equipment for x days, where x is a positive integer and x ≤ 5?

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of these eight angles is  (7x- 250)°. The sum of the measures of four of the eight angles is k°. Which of the following could NOT be equivalent to k, for all values of x?

For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?
7x + 4y = 3
35x + 20y = 15