SAT Pastpaper with Solutions

The graph of the polynomial function f in the xy-plane, where y = f(x), passes through the point . What is the value of ?

A circle has a circumference of centimeters. What is the diameter, in centimeters, of the circle?

For an object with a mass of 49 kilograms, the given equation relates the kinetic energy K, in joules, of the object to the object's speed v, in meters per second, where K and v are positive. Which equation correctly expresses this object's speed, in meters per second, in terms of the object's kinetic energy, in joules?

The function f is defined by . What is the value of?

If the given function g is graphed in the xy-plane, where , what is the y-intercept of the graph?

The relationship between the variables x and y is defined by an exponential equation. When x = 0, the value of y is 58, and for every increase in the value of x by 1, the corresponding value of y decreases by of its previous value. Which equation represents this relationship?

The population of a certain city doubled every 75 years from 1652 to 1952. The population of this city was 160,000 in 1952. What was the population of this city in 1652?

In right triangle JKL, the tangent of  is . What is the length of JK?

In the figure, line m is parallel to line n, and both lines are intersected by line l. If x = z + 18, what is the value of z?

In the given equation, a is a constant. The equation has infinitely many solutions. What are all possible values of a?
a(7x - 14) + 5a = 7(ax - 2a) - 35

If x > 0 and x is of y, which expression represents y in terms of x?

In the given expression, m is a constant and x > 1. The expression can be rewritten as . What is the value of m?

A book-of-the-month club charges for the first book purchased during the month and an additional for each book after the first. Which equation describes this situation, where y is the total cost, in dollars, for books purchased during a month, x is the number of books purchased during the month, and x > 0?

The function z is defined by the equation shown. The value of z(w) decreases by for each increase by 1 in the value of w. Which of the following is closest to the value of p?

The graph of the linear function is shown. If c and d are positive constants, which equation could define f?

In the given equation, r and s are positive constants. The product of the solutions to the given equation is , where k is a constant. What is the value of k?

The speeds of particles A, B, and C are a meters per second, b meters per second, and c meters per second, respectively. If the speed of particle A is of the speed of particle C and the speed of particle C is of the speed of particle B, which expression represents the value of a+b in terms of c?

The given expression can be rewritten as, where a , b , and c are constants. What is the value of ?

In the given function, b is a positive constant. For every increase in the value of x by 1, the value of  increases by , where  . Which expression gives the value of c in terms of b?

On average, a certain tree grows 87 centimeters every m months. At this rate, which expression represents the number of centimeters, on average, the tree grows every k years?

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 175. If, what is the value of r?