SAT Pastpaper with Solutions

The graph of a system of a linear equation and a quadratic equation is shown. Which of the following is a solution (x , y) to the system?

An object moves at a speed of feet per second. What is this speed, in yards per second? (3 feet = 1 yard )

The function f is defined by . What is the y-intercept of the graph of in the xy-plane?

In right triangle RST, the sum of the measures of angle R and angle S is 90 degrees. The value of is . What is the value of ?

Which inequality represents the x values for all solutions (x,y) that satisfy the given system of inequalities in the xy-plane?

In the xy-plane, an equation of circle A is . Circle B has the same center as circle A but has a radius that is twice the radius of circle A. Which equation represents circle B?

A property owner wants to find the length x, in feet, across a pond as represented in the figure, PR intersects ST at point Q, and ∠PTQ is congruent to ∠RSQ. The lengths represented by PQ, TQ, QS, and RS were determined to be 4,200 feet, 8,400 feet, 1,400 feet, and 1,600 feet, respectively. What is the value of x?

The given equation relates the variables P, N, and C. Which expression represents the value of C for distinct positive values of P and N?
PC = N ( 44 - C )

In the figure shown, the measure of angle X is 52°. The length of XY is 24 units and the length of XZ is 17 units. What is the area, in square units, of triangle XYZ?

A partially filled container containing 24 milliliters of water is placed under a leaky faucet that produces one 0.03-milliliter drop of water every 3 seconds. Until the container is full, which of the following can be used to represent the volume v, in milliliters, of water in the container t seconds after it is placed under the faucet, where t is a multiple of 3?

A research manager selected 2 random samples of ovens of a certain type to estimate the average amount of time this type of oven takes to preheat to 325 degrees Fahrenheit (°F). The research manager recorded the amount of time, in minutes, each oven takes to preheat to. Based on the first sample, the research manager estimated that this type of oven takes an average of 15.2 minutes to preheat to , with an associated margin of error of 1 minute. Based on The second sample, the research manager estimated that this type of oven takes an average of 15.4 minutes to preheat to, with an associated margin of error of 2.2 minutes. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a smaller margin of error than the second sample?

In the given equation, r and s are constants. The equation has no solution. What is the value of r?

One solution to the given equation can be written as , where s and t are positive integers. What is the value of ?
-8x(x+9) = 40

The equation gives the predicted population N(m), in thousands, of a certain bacteria colony m minutes after the initial measurement, where Q is a constant greater than 1. The predicted population increases by  every 120 seconds. What is the value of p in terms of Q?

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. According to the model, the object was launched from a height of 0 feet and reached its maximum height of 1,600 feet 10 seconds after it was launched. Based on the model, what was the height, in feet, of the object 7 seconds after it was launched?

The function p is defined by, where a, b, and c are constants. In the xy-plane, the graph of passes through the points and . What is the value of ?

One of the equations in a system of two linear equations is given, where n is a positive constant. The system has no solution. Which equation could be the second equation in this system?
13(x - n) = 13y + 13n

In the given equation, a and k are constants, where k > 5a. The sum of the solutions to the equation is 3k+32. What is the value of a?