Analysis of the final mathematics test papers for the second semester of the eighth grade in the 2021-2022 school year at the Middle School Affiliated to Xi'an Jiaotong University, Beilin District, Xi'an City, Shaanxi Province.

Analysis of the final mathematics test papers for the second semester of the eighth grade in the 2021-2022 school year at the Middle School Affiliated to Xi'an Jiaotong University, Beilin District, Xi'an City, Shaanxi Province.

Analysis of the final mathematics test papers for the second semester of the eighth grade in the 2021-2022 school year at the Middle School Affiliated to Xi'an Jiaotong University, Beilin District, Xi'an City, Shaanxi Province.This famous school test paper is very unique and is a relatively good review material. It is worthy of reference for eighth grade students.

A. 30°B. 32°C. 34° D. 36°

Answer: A

[Analysis]

First, calculate ∠ABC=70° based on the properties of the isosceles triangle and the sum of the interior angles of the triangle. Then, based on the properties of the vertical bisector of the line segment, we get DA=DB, then ∠DBA=∠A =40°, the answer can be obtained through calculation.

[Detailed explanation]

Solution: In △ABC, AB=AC, ∠A ＝40°,

∴∠ABC＝∠ ACB＝70°,

∵AB AC at the point D,

∴DA＝ DB,

∴∠DBA＝∠A＝40°,

∴∠D BC=30°,

, so choose: A.

[Finding Point]

This question examines the properties of isosceles triangles and perpendicular bisectors, and the sum of interior angles theorem of a triangle; proficiency in the properties of isosceles triangles is the key to solving the problem.

7. As shown in the figure, the straight line y=x+1 and the straight line y=mx+n intersect at the point P (a, 2), then about the inequality The solution set of x+1≥mx+n is ( )

A. x≥-1 B. 0≤x≤1 C． x≥1 D． x≤1

Answer: C

[Analysis]

Use the straight line y=x+1 to find a, and then use the function graph to get the solution set of the inequality.

[Detailed explanation]

solution: ∵ straight line l1: y＝x+1 and straight line l2: y = mx+n intersects at the point P (a, 2),

∴a+1＝2,

solution: a＝1 ,

observe the image to know: Regarding the inequality of x, the solution set of x+1≥mx+n is x≥1,

, so choose: C.

[Finding Point]

This question examines the intersection of two straight lines. Use images to find the solution set of inequalities. Correctly understanding the relationship between images and inequalities is the key to solving the problem.

Interested students can print it out on A4 paper for use.