Math Problem Statement
ĐỀ GIAO LƯU CLB TOÁN HỌC 9- THÁNG 2-.pdf
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The file you uploaded contains a set of math problems in Vietnamese. Here’s a summary of the questions in the document:
Part I: Multiple Choice and Calculations
- Solve the equation:
- Find the domain of the expression .
- Find the square root of 196.
- In a right triangle ABC with a right angle at A, , and cm. Find the length of side AC.
- Simplify the expression: , for .
- Calculate the volume of a cylinder with a given radius and height.
- Calculate the proportion of students with a height between 158 cm and 161 cm based on frequency distribution data.
- Determine the probability that the sum of two dice equals 9.
- Calculate the lateral surface area of a cone with a base radius of 6 cm and a slant height of 10 cm.
- Evaluate the expression .
Part II: Problem Solving
- Simplify and evaluate the given algebraic expression.
- Solve a work problem about the production rate of workers.
- Calculate the remaining volume of a cylindrical metal object after drilling a hole through both ends.
- Prove geometric properties involving a cyclic quadrilateral and various triangle-related theorems.
- Optimize the dimensions of a rectangular box to minimize the material used while maintaining a fixed volume.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Probability
Statistics
Trigonometry
Volume
Formulas
Quadratic formula: ax^2 + bx + c = 0
Volume of a cylinder: V = πr^2h
Surface area of a cone: A = πr * l
Probability: P = favorable outcomes / total outcomes
Theorems
Pythagorean Theorem
The Law of Sines
Cyclic Quadrilateral Theorem
Optimization in Geometry
Suitable Grade Level
Grade 9
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