SAT Pastpaper with Solutions

The function g is defined by . For what value of x does ?

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

The population of a certain city doubled every 30 years from 1852 to 1972. The population of this city was 41600 in 1972. What was the population of this city in 1852?

The graph models a magazine's number of subscribers x years after the beginning of 2001 . According to the model, what is the estimated number of magazine subscribers at the beginning of 2002?

If (x + 5)² = 28, what is the value of the x² + 10x?

Between 1985 and 2003, data were collected every three years on the amount of plastic produced annually in the United States, in billions of pounds The graph below shows the data and a line of best fit. The equation of the line of best fit is y = 3.39x + 46.89, where x is the number of years since 1985 and y is the amount of plastic produced annually, in billions of pounds.

Which of the following is the best interpretation of the number 3.39 in the context of the problem?

Line n has the equation . If line m is perpendicular to line n , what is the slope of line m?

The range of the polynomial function f is the set of real numbers less than or equal to 4. If the zeros off are −3 and 1, which of the following could be the graph of y = f (x) in the xy-plane?

The solution to the given system is (x,y). What is the value of 8x? y = 20x - 5 -12x + y = 10

The function g is a quadratic function. In the xy-plane, the graph of y = g(x) has a vertex at (-1, -4) and passes through the points (-2, -43) and (1, -160). What is the value of g(0) - g(2)?

One of the two equations in a system of two linear equations is given. If the system has infinitely many solutions, which of the following could be the second equation in the system?
4x + 3y = 24

The function f is defined as , where a and b are positive integers. If the minimum value of f(x) is 7, which is a possible value of b?

The table summarizes the distribution of heights, in inches (in.), for 300 participants in a study. If a participant that is at most 71 inches tall is chosen at random, what is the probability that the participant was selected from Group 2?

The average annual energy cost for a certain home is . The homeowner plans to spend to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be . Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

The area of the base of a right rectangular prism is 30 square meters, and its perimeter is 26 meters. The height of the prism, which is perpendicular to the base, is 4 meters. What is the surface area of the prism in square meters?

The area of a rectangular region is increasing at a rate of 2700 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter = 3.28 feet.)

For the equation, b and c are constants. For any real number t, the point lies on the graph of the equation in the xy-plane. What is the value of c?
bx + 3y = c

The value of an autographed baseball increased by from the end of 2002 to the end of 2003 and then decreased by from the end of 2003 to the end of 2004. What was the net percentage increase in the value of the autographed baseball from the end of 2002 to the end of 2004?

If a and b are numbers greater than 1 and is equivalent to , for what value of n is equal to b?

A circle in the xy-plane has equation . Line p is tangent to the circle at point , C). where c is a constant. Which of the following could be the slope of line p
I .
II. 
III.