SAT Pastpaper with Solutions

The given equation relates the distinct positive numbers v, w, and x, Which equation correctly expresses w in terms of v and x?

In the given equation, r is a constant. The equation has no solution. What is the value of r?
-3x +6rx =54

A real estate company offers a series of three webinars. 3,750 people attended the first webinar. 54%of the people who attended the first webinar attended the second webinar, and 36%of the people who attended the first and second webinars attended the third webinar How many people attended all three webinars?

The graph of y =f(x) is shown. What is the y-intercept of the graph of y =f(r)+11?

The function f is defined by f(x)=|x-6x|. What value of a satisfies f(2)-f(a)=-30?

If -7(13-5x)+3=-8(13-5x)+25, what is the value of 13-5x?

The minimum value of x is 4 less than 8 times another number n. Which inequality shows the possible values of x?

The shaded region shown represents the solutions to the inequality -19y<c, where c is a constant. What is the value of c?

At a constant temperature, a scuba diver combines two different concentrations of nitrox mix (oxygen-nitrogen gas mixture)to fill a tank to a total pressure of 90 atmospheres (atm), of which 37%is contributed by oxygen. Nitrox mix A contributes x atm of pressure to the tank,of which 22% is contributed by oxygen. Nitrox mix B contributes y atm of pressure to the tank, of which 49% is contributed by oxygen. Which system of equations represents this situation?

The graph of the equation y=2^x+k is shown, where k is a constant. What is the value of k?

A certain town has an area of 3.51 square miles. What is the area, in square yards, of this town? (1 mile =1,760 yards)

The function f gives the product of a number, x, and a number that is 7 more than x. Which equation defines f?

The function gives a toy car's height above the ground f(x), in inches,z seconds after it started moving on an elevated track, where 0≤x≤10. Which of the following is the best interpretation of the vertex of the graph of y =f(x)in the xy-plane?

One of the factors of 5x³+105x²+540x is z+b, where b is a positive constant. What is the smallest possible value of b?

Kenny engages in up to 3 types of exercise each week for a total of 6 hours while training for a triathlon. Kenny swims for the same number of minutes each week. The equation y=360-x-170 represents the situation where Kenny bikes for x minutes during a week and runs for any remaining training time y, in minutes. If this equation is graphed in the xy-plane, which statement is the best interpretation of the x-intercept of the graph?

Two lines intersect at exactly one point, forming two acute angles and two obtuse angles. The measure of one of these angles is (9x-110)°. Which of the following could NOT be the sum of the measures of any two of these angles?

In the given equation,   is a positive constant. The product of the solutions to the equation is 64. What is the value of  ?

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 table shows the volume of two similar solids. right circular cylinder A and right circular cylinder B. The radius of right circular cylinder A is 3 units.The surface area of right circular cylinder A is k square units, and the surface area of right circular cylinder B is n square units, where k and n are constants. What is the value of n-k? (The surface area of a right circular cylinder with radius r and height h is 2r²+2rh)

Function f is a quadratic function. The graph of y=f(x)in the xy-plane has a vertex at(-5, -8), and passes through the point (-6,-10), and has a y-intercept at (0, a). The graph of y=6·f(x)has a y-intercept at (0, b). What is the positive difference between a and b?