SAT Pastpaper with Solutions

To purchase a used car at a total price of 14,000 dollars, a onetime down payment is required, and then fixed monthly payments are made for the remaining amount owed for the car. The equation 14,000 = 2,800 + 200t represents this situation, where t is the number of fixed monthly payments that are made. Which of the following is the best interpretation of 200 in this context?

A model predicts that the population of a certain town was 3,000 in 2007, the model also predicts that each year for the next 5 years, the population p increased by 8% of the previous year's population. Which equation best represents this model, where x is the number of years after 2007, for x ≤ 5?

A park rents beach umbrellas to visitors. The park earns revenue of  $16 for each beach umbrella they rent for the day. On Wednesday, the park earned  $400 in profit from renting beach umbrellas after paying daily expenses of  $144, how many beach umbrellas did the park rent on Wednesday? (profit = total revenue - total expenses)

One solution to the given equation can be written as   , where k is a constant. What is the value of k?
x² - 2x - 18 = 0

The given equation relates the real numbers r and w, where . Which equation correctly expresses w in terms of r?

A hemisphere is half of a sphere. If a hemisphere has a radius of 70 inches, which of the following is closest to the volume, in cubic inches, of this hemisphere?

For a certain type of rope, the equation y = 900ax², where a is a constant, gives the estimated breaking strength y, in pounds, of a rope with a circumference of x inches. Based on this equation, if a rope of this type has a circumference of 2.75 inches, it has an estimated breaking strength of 9,528.75 pounds. What is the estimated breaking strength, in pounds, of a rope of this type that has a circumference of 7.50 inches?

The function h is defined by h(x) = (x+p)(x-2)(2x-12), where p is a constant. In the xy-plane, the graph of y = h(x) passes through the point (-3,0). What is the value of h(0)?

If x ≥ -6 represents all solutions to the inequality ax - 27 ≤ 15, where a is a constant, what is the greatest possible value of a?

The solution to the given system of equations is (x,y). What is the value of 8x+6y?

5(8x) + 4(6y) = 12 
-5(8x) + 4(6y) = 12 

For the positive quantities h, j and k, 27% of h is equivalent to 24% of j, and j is equivalent to 45% of k. What percentage of k is h? (Disregard the % sign when entering your answer. For example, if your answer is  39%, enter 39 )

The function f is defined by f(x) = 30x. For what value of x is f(x) = 180?

In the given equation, r is a constant. The equation has exactly one real solution. What is the value of r?
4x² + 21 = 48x + r

For the function f, for every increase of 2 in the value of x, the value of f(x) increases by a factor of c, where c is a constant. Which of the following equivalent forms of function f displays the value of c as the base or the coefficient?

In the figure shown,   units, AC = 8 units, and CE = 24 units. What is the area, in square units, of triangle ADE?

The graph of line g is shown in the xy-plane. Line k is defined by 165x + py = w, where p and w are constants. If line k is graphed in this xy-plane, resulting in the graph of a system of two linear equations, the system of two linear equations will have infinitely many solutions. What is the value of p+w?

Each of the following frequency tables represents a data set. Which of these frequency tables represents the data set with the smallest standard deviation?

The given equation is one equation in a system of two linear equations. If the system of equations has at least one solution, which of the following equations could be the other equation in the system?

I.9x + 4.5y = 7.5

II. 9x - 4.5y = 7.5

The function f is defined by f(x) = ax² + bx + c, where a, b, and c are constants. The graph of y = f(x) in the xy-plane passes through the points (10,0) and (-5,0). If a  is an integer greater than 1, which of the following could be the value of a+b?

An object's speed is increasing at a rate of 1.1 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth? (Use 1 mile = 1,609 meters.)