September 2023 National Unified Academic Achievement Test (Grade 11)

What is the value of ?

What is the value of ?

What is the value of ?

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

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

For the sequence , given that find the value of .

For two positive numbers such that what is the value of ?

Let be a geometric sequence with first term and common ratio greater than . Let be the sum of the first terms from the first term to the -th term. When what is the value of ?

A sequence with first term satisfies the following for all natural numbers : Find the value of .

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

For a natural number , let be the -coordinate of the point where the circle meets the line in the first quadrant. What is the value of ?

When three positive numbers satisfy what is the value of ?

For all sequences with all positive terms satisfying the following conditions, what is the minimum value of ? (a) For all natural numbers , . (b)

As shown in the figure, two curves meet at point . Let be the points where the two curves meet the -axis, respectively, and let be the points where they meet the line , respectively. When , what is the value of ? (where )

Find the radius of a sector whose arc length is and area is .

For the function defined on the set , let be the maximum value and be the minimum value. Find the value of .

Let and be the two distinct real roots of the equation . Find the value of .

Two quadratic functions satisfy Find the value of .

For a natural number , there is a function defined on the set . Let be the sum of all distinct real roots of the equation . Find the value of .