March 2024 National Unified Academic Achievement Test (Grade 10)

What is the value of ?

What is the solution to the linear equation ?

When the graph of the linear function is translated by units in the direction of the -axis and passes through the point , what is the value of the constant ?

In a right triangle ABC where ∠B = 90°, AB = 3, and BC = 2 as shown in the figure, what is the area of a square that has side AC?

When the expanded form of the polynomial is , what is the value of ? (where and are constants)

When the coordinates of the intersection point of the graphs of the two linear equations are , what is the value of ?

When throwing two different dice simultaneously, what is the probability that the difference between the numbers shown on each die is 2 or 4?

As shown in the figure, for three points A, B, C on a circle and a point P outside the circle, line PA and line PB are tangent to the circle, and ∠ACB = 65°. What is the measure of angle BPA?

The following is a frequency distribution table showing the reading time over one month for 45 students at a school. In this frequency distribution table, when the relative frequency of the class with reading time of 10 hours or more and less than 15 hours is a non-zero finite decimal, what is the value of ?

There is a trapezoid ABCD with two bases AD and BC having lengths and respectively, and height . When the midpoint of segment CD is E, what is the area of quadrilateral ABED?

As shown in the figure, for a positive number , let the graphs of the two inverse proportional relationships intersect the line at points and respectively, and let the two line segments and intersect the line at points and respectively. When the area of quadrilateral is , what is the value of ? (Note: is the origin.)

As shown in the figure, there is a graph of a quadratic function that passes through the origin and has vertex in the fourth quadrant. For two points and , line segment and line segment meet at point . Given that the area of triangle is , and the areas of triangle and triangle are equal, find the value of . (Note that point is not point .)

In the isosceles triangle ABC where and , let D be the foot of the perpendicular from point C to line AB. Let I be the incenter of triangle ABC and J be the incenter of triangle DBC. What is the length of segment IJ?

When the coordinates of the vertex of the graph of the quadratic function are , find the value of .

In right triangle ABC where , , and , find the length of segment AC.

For a two-digit natural number and a three-digit natural number such that , find the value of .

As shown in the figure, let O be the circumcenter of isosceles triangle ABC where and . Let D be the foot of the perpendicular from point O to segment AB, and let E be the intersection of line AO and segment BC. Given that and the area of triangle ADO is 6, find the area of triangle ABC.

Among the four numbers , , , , when the largest possible value obtained by multiplying two different numbers is and the smallest possible value is , find the value of .

As shown in the figure, let G be the centroid of triangle ABC where , , . Let D be the point where line AG intersects segment BC. The area of triangle ADC is 4. When , find the value of . (where and are relatively prime natural numbers.)

As shown in the figure, there is a parallelogram ABCD with , , , and area . On segment AD, take point E such that , and on the extension of segment CB, take point F such that . Let G be the point where the line passing through point E and parallel to line AB intersects segment DF. Given that , find the value of . (Here, and are relatively prime natural numbers.)