Math Problem Statement

MÃ-121.pdf

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Solution

This document is an entrance exam for 12th-grade math students from the 2024–2025 academic year. It contains three parts: multiple-choice questions, true/false questions, and short-answer questions. Here is a breakdown:

  1. Multiple Choice (Part I):

    • There are 12 questions, each with four options. Topics include trigonometry, functions, limits, series, geometry, probability, and calculus. For example:
      • Solve for all solutions of 2sinx=32\sin x = 3.
      • Maximum value of the function y=3cosx+1y = 3\cos x + 1.
      • A geometric series calculation.
      • Limit calculations and basic probability questions.
  2. True/False (Part II):

    • Contains 4 questions with sub-parts a), b), c), and d), where students decide whether the statements are true or false. Topics range from calculus, geometry, combinatorics, to logarithmic and exponential functions.
  3. Short Answer (Part III):

    • This section requires more detailed solutions, covering problems like:
      • Finding minimum velocity in a motion problem.
      • A question involving exponential growth of a forest area.
      • Geometric problems involving volumes of prisms and pyramids.
      • Probability calculations.

Would you like to solve any specific questions from the exam?

Here are 5 possible directions for exploration:

  1. Solving the trigonometric equation in Question 1.
  2. Calculating the maximum of a trigonometric function in Question 2.
  3. Exploring limits and calculus in Question 4.
  4. Working on the probability of students' selection in Question 12.
  5. Solving the volume problem of pyramids or prisms in geometry.

Tip: For problems involving geometric volumes, always visualize the shape and use the correct formula for each solid.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Functions
Limits
Series
Geometry
Probability
Calculus

Formulas

Sine function solution
Maximum value of trigonometric function
Geometric series formula
Limit calculation formula
Basic probability rules

Theorems

Fundamental theorem of trigonometry
Geometric progression
Probability laws

Suitable Grade Level

Grade 12