2025 Academic Year College Scholastic Ability Test – Calculus

What is the value of ?

For the function , what is the value of ?

For a geometric sequence where both the first term and common ratio are positive , if it satisfies what is the value of ?

When the function is continuous on the set of all real numbers, what is the value of the constant ?

For the function , what is the value of ?

When , what is the value of ?

When a polynomial function satisfies for all real numbers , what is the value of ?

For two real numbers , , what is the value of ?

For the function , when , what is the value of the positive number ?

For the function defined on the closed interval , find the minimum value of for ordered pairs of natural numbers such that the function has a maximum value of at .

A point P moves along a number line starting at time . The position of point P at time is given by What is the acceleration of point P at the time when the direction of motion changes after starting?

Given a sequence with and an arithmetic sequence with that satisfy for all natural numbers , find the value of .

A cubic function with leading coefficient satisfies For the origin and point , let be the point where line segment intersects the curve , other than point . Let be the area enclosed by the curve , the -axis, and line segment , and let be the area enclosed by the curve and line segment . Find the value of .

As shown in the figure, in triangle ABC, point D is taken on segment AB such that , and let O be the circle centered at point A and passing through point D, and let E be the point where circle O intersects segment AC. Given that , and the ratio of the areas of triangle ADE and triangle ABC is . When the radius of the circumcircle of triangle ABC is , what is the maximum value of the area of triangle PBC for a point P on circle O? (Note: )

For a constant and a quadratic function with a negative leading coefficient, the function satisfies the following conditions. (a) The function is differentiable on the entire set of real numbers. (b) The number of distinct real roots of the equation with respect to is . What is the value of ?

Find the value of the real number that satisfies the equation

Given that the sequence satisfies for all natural numbers , find the value of .

Let be the -coordinate of the intersection point of the curve and the line . A function defined on the set of all real numbers satisfies the following conditions. For all real numbers such that , and . Find the value of .

For all sequences where all terms are integers and satisfy the following conditions, find the sum of all possible values of . (a) For all natural numbers , (b) The minimum value of the natural number such that is .

What is the value of ?

What is the value of ?

For the sequence , given that , find the value of .

As shown in the figure, there is a solid figure with a base formed by the region enclosed by the curve , the -axis, and the two lines and . When this solid figure is cut by planes perpendicular to the -axis, all cross-sections are squares. What is the volume of this solid figure?

The derivative of a function that is differentiable on the set of all real numbers is given by For a positive number , let be the area of the region enclosed by the tangent line to the curve at the point , the curve , and the -axis. What is the value of ?

For two constants , , the function satisfies the following conditions. (가) (나) The minimum positive value of such that is . Let be the set of all values of in the open interval where the function has a local maximum at . If is the number of elements in set and is the smallest value among the elements of set , then . Find the value of . (Here, and are coprime natural numbers.)