March 2023 National Unified Academic Achievement Test (Grade 11)

Given two polynomials , what is the simplified form of ?

What is the truth set for the condition on real number : " is a non-negative real number."

For two points A(-5) and B(1) on a number line, what is the coordinate of the point that externally divides line segment AB in the ratio 3:1?

When and , what is the value of ?

When the equation of the tangent line at point on the circle is , what is the value of ? (where is a positive number, and are constants.)

There are 2 first-year students and 4 second-year students. Find the number of ways to seat all 6 students in 6 chairs arranged in a row such that the following conditions are satisfied: (a) First-year students are not adjacent to each other. (b) Both chairs at the ends are occupied by second-year students.

Find the value of integer such that the number of integers satisfying the system of inequalities is .

For the set , the function from to is a bijection. Find the value of . (Here, and are constants.)

For two integers such that there exists an imaginary number satisfying the following conditions, what is the minimum value of ? (Here, is the complex conjugate of .) (a) (b)

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

The figure represents a function .Find the value of .

When polynomial is divided by , the quotient is and the remainder is . Find the remainder when is divided by .

There are 2 dolls of each of 4 different types. Find the number of ways to select 5 dolls from these 8 dolls. (Note: Dolls of the same type are indistinguishable from each other.)

For a natural number , let the -coordinates of the two points where the line intersects the graph of the quadratic function be and respectively. Find the number of natural numbers not exceeding such that the value of is a natural number.