SAT Pastpaper with Solutions

A shopper goes to a pet store to buy dog food and treats. The shopper has $20. Each can of food costs  $1.87, and each bag of treats costs  $2.37. Which inequality represents the relationship between the number of cans of food, c, and the number of bags of treats,  t, the shopper can buy? 

In the given equation,   and   are positive constants. A solution to the equation is  . What is the value of  ?

In the figure, line   is parallel to line  , and both lines are intersected by line  .

If    , what is the value of   ?

If   and  , what is the value of   ?

The solution to the given system of equations is  . What is the value of  ?

To study fluctuations in leaf water potential, samples of wood were taken from 27 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 0.170 grams per cubic centimeter. What is the mass of this cube, in grams?

A plumbing company charges its customers   for the first hour of a plumbing service call and   for each additional hour, plus the cost of plumbing parts. Which equation represents the total cost , in dollars, for an  -hour plumbing service call where the cost of parts was   and   ?

Ari will add a 135 -year-old stamp to her original collection,creating a new collection of 52 stamps. Which statement correctly compares the mean ages and median ages of Ari's original and new collections?

A certain open star cluster contains M-type stars and K-type stars. The estimated total mass of M-type and K-type stars in this open star cluster is 129,492 quettagrams. The graph shown models the possible combinations of the number of M-type stars, , and K-type stars, , that could be in this open star cluster if all the M-type stars have the same estimated mass and all the K-type stars have the same estimated mass. Based on the graph, which of the following is closest to the estimated mass, in quettagrams, of each M-type star in this cluster?

The positive number    is    of the number  , and   is    of the number   . If  , where    is a constant, what is the value of   ?

An object is launched into the air from ground level. According to a quadratic model, 2.1 seconds after the object is launched, it reaches its maximum height of 70.56 feet above ground level. Which equation represents this model, where   is the object's height, in feet, above ground level    seconds after it was launched?

The volume of a right rectangular prism with a square base is 539 cubic centimeters. If the area of each of the four lateral faces is 77 square centimeters, what is the height, in centimeters, of the prism?

A science class studied the feeding behavior of the birds that visited a bird feeder each school day for a period of time. The table summarizes the number of birds the class observed visiting the bird feeder each school day during this period of time. What is the median number of birds the class observed visiting the bird feeder each school day during this period of time?

The graph of   is shown. Which equation defines function  ?

The function g is defined by g(x) = f(x+8). What is the minimum value of g(x)?f(x) = 5x² + 60x + 181

In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer is represented by x. The product of 28 and the third odd integer in the set is at most the value of 50 less than the sum of the first and fourth odd integers in the set. What is the greatest possible value of x?

In the given equation , b is a positive integer. The equation has no real solution. What is the largest possible value of b?

-2x² + bx - 32 = 0

The functions f and g are defined by the equations shown, where a and b are  integer constants, a < b and b < 0. If y = f(x) and y = g(x) are graphed in the  xy-plane, which of the following equations displays, as a constant or coefficient,the y-coordinate of the y intercept of the graph of the corresponding function?

I.f(x) = a(3.3)^x+b

II. g(x) = a(3.3)^x+b

In the given equation,c is a constant. If the equation has exactly one solution, what is the value of c?