🎓 مراجعة شاملة في الرياضيات مجانا | الحصة الأولى من دورة تقييم المكتسبات | بكالوريا 2026

Introduction

Welcome to the comprehensive review of mathematics aimed at students preparing for the 2026 Baccalaureate exam. This tutorial breaks down key mathematical concepts through a series of exercises with detailed solutions. The goal is to reinforce foundational knowledge and equip students for success.

Step 1: Operations with Fractions

• Understand the basic operations involving fractions, including addition, subtraction, multiplication, and division.
• Follow these steps:
  1. Finding a Common Denominator: When adding or subtracting fractions, find the least common denominator (LCD).
  2. Performing the Operation: Adjust the fractions to have the same denominator, then add or subtract the numerators.
  3. Simplifying: After performing the operation, simplify the resulting fraction if possible.

Step 2: Operations with Powers

• Review the rules of exponents which include:
  • Product of Powers: ( a^m \times a^n = a^{m+n} )
  • Quotient of Powers: ( \frac{a^m}{a^n} = a^{m-n} )
  • Power of a Power: ( (a^m)^n = a^{m \times n} )
• Steps to solve problems:
  1. Identify the base and exponents from the expressions.
  2. Apply the rules accordingly to simplify the expression.
  3. Check for any final simplifications before arriving at the answer.

Step 3: Operations with Roots

• Focus on simplifying roots and performing operations involving them.
• Key steps include:
  1. Identifying Perfect Squares: Recognize which numbers have whole number roots.
  2. Adding and Subtracting Roots: Only combine like terms (e.g., ( \sqrt{2} + \sqrt{2} = 2\sqrt{2} )).
  3. Multiplying and Dividing Roots: Use the property ( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} ).

Step 4: Expansion and Simplification

• Learn how to expand and simplify algebraic expressions.
• Steps include:
  1. Using the Distributive Property: Apply ( a(b + c) = ab + ac ) to expand expressions.
  2. Combining Like Terms: Group similar terms together to simplify.
  3. Final Review: Ensure the expression is in its simplest form.

Step 5: Factorization

• Understand the different methods of factorization including:
  • Factoring out the greatest common factor (GCF).
  • Using the difference of squares: ( a^2 - b^2 = (a - b)(a + b) ).
• Steps to factor:
  1. Identify the GCF of the terms in the expression.
  2. Apply appropriate factorization techniques based on the type of polynomial.
  3. Check your work by expanding the factors to ensure they match the original expression.

Step 6: Inequalities

• Review how to solve and graph inequalities.
• Key points:
  1. Understanding the Inequality Symbols:
     • ( <, >, \leq, \geq ) indicate the relationship between numbers.
  2. Solving the Inequality: Treat it like an equation, but remember to flip the inequality sign when multiplying or dividing by a negative number.
  3. Graphing the Solution: Use a number line to represent the solution set.

Conclusion

This tutorial covered essential mathematics concepts through structured exercises, aimed at preparing students for the Baccalaureate exam. Each step provides foundational knowledge critical for tackling more complex problems. For further practice, consider downloading the provided PDF and working through additional exercises. Engage with your peers or instructor for clarification and support as you prepare for your exam. Good luck!