December 2023 – 2nd Year High School

What is the value of ?

What is the slope of the tangent line to the curve at the point ?

When the four numbers , , , form an arithmetic sequence in that order, what is the value of ?

The graph of function is shown in the figure.What is the value of ?

In the interval , what is the number of intersection points between the graph of the function and the line ?

When the function is differentiable on the set of all real numbers, what is the value of ? (where and are constants)

For a function where and , what is the minimum value of the function ?

What is the minimum value of the natural number such that the curve intersects with the curve in the first quadrant?

When , what is the value of ?

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

Two sequences , satisfy for all natural numbers . When , what is the value of ?

For a natural number , let be the number of real -th roots of . Find the sum of all natural numbers that satisfy .

Let be the sum of the first terms of the sequence . The two sequences , and constant satisfy the following condition. For all natural numbers , . When , what is the value of ?

For a real number where , let be the distance between the two points where the graph of the function and the line intersect. Find the value of .

Three positive numbers , , (not equal to ) satisfy What is the sum of all natural number values of such that the value of is a natural number not exceeding ?

In triangle where , let be the midpoint of segment and be the point that divides segment AC in the ratio . Given that and the area of the circumcircle of triangle is , find the area of triangle .

Find the value of .

For the function , find the value of .

Find the product of all real values of that satisfy the equation .

Two points P and Q move on a number line. At time , their positions are given by respectively. When both points P and Q change their direction of motion simultaneously at time , find the value of . (Here, and are constants.)

For two constants , (), the function on the closed interval has a maximum value of and a minimum value of . When , find the value of . (Here, and are relatively prime natural numbers.)