Đề thi thử Toán vào năm 2023 2024 trường THCS Ba Đình Hà Nội

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Đề thi thử Toán vào năm học 2023 - 2024 trường THCS Ba Đình Hà Nội

Ladies and gentlemen, Sytu is pleased to present the practice test for the Mathematics entrance exam to grade 10 at THPT Ba Đình High School for the academic year 2023 - 2024. The exam will take place on May 29, 2023, with answer keys and scoring guidelines provided.

Quoted from the Mathematics practice test for grade 10 at THCS Ba Đình in Hanoi:

Question 1: Solve the following problem by setting up equations or a system of equations: A workshop is assigned to produce 400 shirts within a specified period of time. Due to increased labor productivity, the workshop can now make an additional 20 shirts per day, thus completing the task 1 day earlier than planned. How many shirts should the workshop make each day according to the schedule?

Question 2: A bottle contains 1.5 liters of soft drink. How much soft drink is needed to fill 5 cylindrical glass cups, each with a base radius of 3 cm and a height of 12 cm? (Take π ~ 3.14 and ignore the thickness of the glass cup).

Question 3: Consider a semicircle (O; R) with diameter AB and chord EF (E is on arc AF and AE < BF). The lines AE and BF intersect at M; AF intersects BE at H. 1) Prove that MEHF is a cyclic quadrilateral. 2) Prove that BF.BM = BH.BE. 3) Let I be the midpoint of MH. Prove that IO is perpendicular to EF and OF is tangent to the circumcircle of triangle MEF.