Đề kiểm tra học kì 2 (HK2) lớp 9 môn Toán năm 2019 2020 trường THCS Nguyễn Trung Trực TP HCM

Nội dung Đề kiểm tra học kì 2 (HK2) lớp 9 môn Toán năm 2019 2020 trường THCS Nguyễn Trung Trực TP HCM Bản PDF

Đề kiểm tra học kì 2 (HK2) lớp 9 môn Toán năm 2019-2020 trường THCS Nguyễn Trung Trực TP HCM

Chào quý thầy cô và các em học sinh! Below is the exam for the second semester of the 9th-grade Math subject for the academic year 2019-2020 at Nguyễn Trung Trực Secondary School, District 12, Ho Chi Minh City. The exam includes answer keys, detailed solutions, and grading instructions.

Sample questions:

1. Given the equation: x^2 - (2m - 1)x - 2m = 0 (m is a parameter).

• a) Prove that the equation always has a solution for all values of m.
• b) Calculate the sum and product of the two roots x1, x2 in terms of m.
• c) Find the value of m so that the two roots x1, x2 satisfy: x1^2 + x2^2 = 1 - x1x2.

2. The school organizes a historical site visit for 180 good and excellent 9th-grade students. They plan to use large buses, each seating 15 more students than small buses, to transport all students in one go, which would require fewer buses compared to using two small buses. Calculate the number of large buses needed (if available).

3. Given circle O with perpendicular diameters AB and CD. Take any point M on minor arc CB (M ≠ B, C), draw AM intersecting CD at N.

• a) Find the angle AMB, then prove that the quadrilateral MNOB is cyclic.
• b) Prove that AM * AN = AO * AB.
• c) Segment MD intersects BC at P. Prove that NP is parallel to AB.

Click the link below to download the Word file for the exam.

Đề kiểm tra học kì 2 (HK2) lớp 9 môn Toán năm 2019-2020 trường THCS Nguyễn Trung Trực TP HCM Word File