انطلق مجانا 🚀 | الحصة الثانية من دورة تقييم المكتسبات في الرياضيات | بكالوريا 2026

Introduction

This tutorial provides step-by-step instructions for effectively preparing for the Bacalaureate 2026 in mathematics. Based on a comprehensive video lesson, you'll learn various techniques for solving equations, inequalities, and polynomial analysis. This guide is tailored for students aiming to build a solid mathematical foundation and achieve excellent results.

Step 1: Solving Equations Using Factorization

• Begin by identifying the type of equation you are dealing with (linear, quadratic, etc.).
• Rearrange the equation to set it equal to zero if necessary.
• Factor the equation:
  • Look for common factors.
  • Apply the difference of squares, perfect square trinomials, or other factoring techniques as applicable.
• Set each factor to zero and solve for the variable.

Practical Tips

• Always check your solutions by substituting them back into the original equation.
• Familiarize yourself with common factoring patterns to save time.

Step 2: Utilizing the Discriminant

• Understand the discriminant formula (D = b^2 - 4ac) for quadratic equations (ax^2 + bx + c = 0).
• Calculate the discriminant to determine the nature of the roots:
  • If (D > 0): Two distinct real roots.
  • If (D = 0): One real double root.
  • If (D < 0): No real roots (two complex roots).
• Solve the equation using the quadratic formula (x = \frac{-b \pm \sqrt{D}}{2a}).

Common Pitfalls

• Ensure that you simplify the discriminant correctly.
• Double-check calculations with the quadratic formula.

Step 3: Analyzing Polynomials

• Identify the degree of the polynomial to determine its behavior.
• Use synthetic division or polynomial long division for simplification.
• Factor the polynomial, if possible, to find its roots.

Practical Tips

• Graphing the polynomial can provide insights into its roots and behavior.
• Use the Rational Root Theorem to test possible rational roots.

Step 4: Solving Inequalities

• Rewrite the inequality in a standard form.
• Determine critical points by solving the corresponding equation.
• Test intervals between critical points to find where the inequality holds true.

Key Considerations

• Remember to flip the inequality sign when multiplying or dividing by a negative number.
• Always express the solution in interval notation.

Step 5: Solving Systems of Equations

• Choose a method (substitution, elimination, or graphical) based on the problem.
• For substitution:
  • Solve one equation for one variable and substitute it into the other.
• For elimination:
  • Align equations and add or subtract to eliminate a variable.
• Solve the resulting equation for the remaining variable.

Practical Tips

• Verify the solution by substituting back into both original equations.
• Use graphing for visual confirmation of intersection points.

Conclusion

This tutorial has outlined essential steps for mastering key mathematical concepts relevant to the Bacalaureate 2026. By practicing these techniques for solving equations, analyzing polynomials, and working with inequalities and systems of equations, you can build a strong mathematical foundation.

To enhance your learning, consider downloading the provided PDF resource and keep practicing with various problems. Stay engaged with the course materials and reach out for help when needed. Good luck with your studies!