March 2024 National Unified Academic Achievement Test (Grade 11)

The diagram shows a function . What is the value of ?

When the polynomial in is divided by , the remainder is . What is the value of the constant ?

How many integers satisfy the system of inequalities ?

When the graph of the function passes through the point and one asymptote has the equation , what is the value of ? (where and are constants)

What is the -intercept of the line that passes through the intersection point of the two lines and and is parallel to the line ?

The universal set has two subsets that satisfy the following conditions. (a) (b) What is the sum of all elements in set ?

For two positive numbers and , when two points and on the graph of the function satisfy the following conditions, what is the value of ? (a) The slope of line is . (b) When points and are the points obtained by reflecting points and with respect to the origin, respectively, the area of quadrilateral is .

As shown in the figure, let A be the center of a circle that is tangent to both lines Let P be the point of tangency between line and the circle, Q be the point of tangency between line and the circle, and R be the point where line PQ intersects the x-axis. The three points P, Q, and R satisfy the following conditions: (a) (b) The area of triangle OPQ is 24. When B is the intersection point of line and line AQ, what is the length of segment BQ? (Note: The center A of the circle is in the first quadrant, and O is the origin.)

For the two sets find the sum of all elements in the set .

Find the minimum value of the natural number such that the line intersects the graph of the quadratic function .

For the set , find the number of functions that satisfy the following conditions. (a) For any , , if , then . (b) The function does not have an inverse function.

For two constants and , let the function . The function and two real numbers , satisfy the following conditions. (A) For a real number , let be the number of intersection points between the graph of the function and the line . Then . (B) The minimum value of the real number that satisfies the equation is , and the maximum value is . Find the value of .