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

  1. Solve the equation: 2x2+x1=02x^2 + x - 1 = 0
  2. Find the domain of the expression 3x+1\frac{3}{x+1}.
  3. Find the square root of 196.
  4. In a right triangle ABC with a right angle at A, ABC=30\angle ABC = 30^\circ, and AB=5AB = 5 cm. Find the length of side AC.
  5. Simplify the expression: 2x+1x+1\frac{2x+1}{x} + 1, for x0x \geq 0.
  6. Calculate the volume of a cylinder with a given radius and height.
  7. Calculate the proportion of students with a height between 158 cm and 161 cm based on frequency distribution data.
  8. Determine the probability that the sum of two dice equals 9.
  9. Calculate the lateral surface area of a cone with a base radius of 6 cm and a slant height of 10 cm.
  10. Evaluate the expression 3+2+32\sqrt{3 + \sqrt{2}} + \sqrt{3 - \sqrt{2}}.

Part II: Problem Solving

  1. Simplify and evaluate the given algebraic expression.
  2. Solve a work problem about the production rate of workers.
  3. Calculate the remaining volume of a cylindrical metal object after drilling a hole through both ends.
  4. Prove geometric properties involving a cyclic quadrilateral and various triangle-related theorems.
  5. 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