SAT Pastpaper with Solutions

A certain blue whale calf weighed 5,600 pounds when it was born, and its weight increased at an average rate of 250 pounds per day for the first n days after birth, where n is an integer. If the calf's weight was greater than 8,850 pounds but less than 9,850 pounds n days after birth, what is one possible value of n?

The solution to the given system of equations is (x,y). What is the value of 2y?

A hemisphere is half of a sphere. If a hemisphere has a radius of 69 inches, which of the following is closest to the volume, in cubic inches, of this hemisphere?

The given equation defines the function f . For what value of x does f(x) reach its minimum?
f(x) = 18x² - 45x + 13

An exponential function f is defined by f(x) = c^x,where c is a constant greater than 1. If f(7) = 9*f(5), what is the value of c?

A line in the xy-plane passes through the points (7,1), (0,4), and (c,0). What is the value of c?

A group of biology students conducted an experiment to study the relationship between a person's femur length and the person's height. The given equation describes the relationship between the length L, in inches, of a student's femur and the student's estimated height H, in inches, for the students in the group. Which of the following is the best interpretation of 2.403 in this context?
H = 2.403L + 23.31

The histogram summarizes a data set of the weights, in pounds, of 14 salmon. If an additional weight of 85 pounds is added to the original data set to create a new data set of 15 weights of salmon, which of the following measures must be greater for the new data set than for the original data set?

I.The median

II. The mean

In the figure shown, WZ and XY intersect at point Q, YQ = 36, WQ = 90, WX = 70, and XQ = 150. What is the length of YZ?

A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed was 6950% of the number of postdoctoral students surveyed and the number of graduate students surveyed was 35% of the number of undergraduate students surveyed. If there were 4,865 graduate students surveyed, what was the sum of the number of undergraduate students and postdoctoral students surveyed?

The function gives the estimated air temperature T(x), in degrees Celsius (℃), surrounding a hot air balloon at an altitude of x meters. If the estimated air temperature surrounding the hot air balloon is16℃, which of the following is closest to the altitude, in meters, of the hot air balloon?

The function q is defined by , where a and b are constants, and a > b > 87. If q(639) = h and q(-621) = k, where h and k are constants, what is the value of 9(-639)^h-k + 621(9)^k-h?

The graph of the linear function y = f(x) + 13 is shown. If c and d are positive constants, which equation could define f?

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) = 16(1.3)^x+5

II. g(x) = 16(1.09)(1.3)^x+3 

A set designer is hammering nails along the top edge of a wall with a length of 3x feet, where x is an integer, that will be used to hang garland. The designer hammers the first nail at the left edge of the wall. The designer then hammers an additional nail every feet along the entire length of the wall,  starting from the first nail and with the last nail being hammered at the right edge of the wall. Which equation best represents this situation, where y is the number of nails the designer hammers along the entire length of the wall?

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

The table shows three values of x and their corresponding values of g(x) , where  and f is a linear function.
What is the y-intercept of the graph of y = f(x) in the xy-plane?

In the figure shown, points A, B, C, and E lie on the circle, and AB < BC. Segment AC is perpendicular to segment BE at point D, and . The diameter of the circle is 115. If , what is the value of r?