September 2024 National Unified Academic Achievement Test (Grade 11)

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

What is the value of ?

What is the arc length of a sector with a central angle of and an area of ?

When the function defined on the set has a maximum value of , what is the value of the constant ?

For natural numbers where , let be the number of real -th roots of , and let be the number of real -th roots of . What is the sum of all natural numbers that satisfy ?

A sequence satisfies the following conditions. (A) (B) For all natural numbers , When , what is the value of ?

For the functionfind the sum of all real values of such that the difference between the maximum and minimum values of function on the interval equals .

For a constant , let the line intersect the graphs of the two functionsat points and respectively. When , what is the value of ?

Find the value of the real number that satisfies the equation .

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

When , find the sum of all natural number values of that satisfy the inequality