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Maths Luxembourg: End of Study Exam Preparation (1st year) | Method & Rigor | MEN Program Expert
From 30.18 £ /h
Hello! I help Luxembourgish high school students succeed in the crucial mathematics exam. My approach focuses on past exam papers and official marking criteria.
1. Analysis & Differential Calculus (The core of the exam) Complex functions: Complete study of logarithmic and exponential functions. Limits and Continuity: Resolving indeterminates and using L'Hôpital's rule. Integral Calculus: Antiderivatives, integration by parts, and calculating areas/volumes.
2. Linear Algebra & Geometry (Luxembourg Specific) - Complex Numbers: Algebraic and trigonometric forms and solving equations in C. Analytical geometry of space: Vectors, planes, lines and intersections. Systems of equations: Gaussian elimination and geometric interpretation.
3. Probability & Combinatorics - Counting (arrangements, combinations). Probability laws (Binomial, Normal).
My Online Tutoring Method - "Prep" Exam Correction: Specific work on in-class assignments (tests) to aim for the highest grade. Past Exams: Step-by-step solutions to final exams from the last 5 years.
Interactive screen: Use of digital tools where I write the solutions to exercises and explanations of the lesson.
1. Analysis & Differential Calculus (The core of the exam) Complex functions: Complete study of logarithmic and exponential functions. Limits and Continuity: Resolving indeterminates and using L'Hôpital's rule. Integral Calculus: Antiderivatives, integration by parts, and calculating areas/volumes.
2. Linear Algebra & Geometry (Luxembourg Specific) - Complex Numbers: Algebraic and trigonometric forms and solving equations in C. Analytical geometry of space: Vectors, planes, lines and intersections. Systems of equations: Gaussian elimination and geometric interpretation.
3. Probability & Combinatorics - Counting (arrangements, combinations). Probability laws (Binomial, Normal).
My Online Tutoring Method - "Prep" Exam Correction: Specific work on in-class assignments (tests) to aim for the highest grade. Past Exams: Step-by-step solutions to final exams from the last 5 years.
Interactive screen: Use of digital tools where I write the solutions to exercises and explanations of the lesson.
Location
Online from Luxembourg
About Me
Hello, I am Dr. Raouf Laroussi, holder of a PhD in Mathematics with extensive experience in higher education and personalized academic support. I guide students in Luxembourgish high schools (both classical and general) as well as university students towards excellence.
My teaching method is based on simplifying abstract concepts and mastering the problem-solving methods required by the Luxembourg Ministry of National Education ESC (Classical) and ESG (General).
1. Secondary Education (Sections B, C, D, G)**
* **Analysis:** In-depth study of functions (logarithms, exponentials), limits, derivatives and integral calculus.
* **Linear Algebra:** Analytic geometry in space, vectors, and systems of equations (Gaussian method).
* **Complex Numbers:** Algebraic and trigonometric forms and solutions in .
* **Preparation for the Final Examination:** Intensive work on past exam papers (Past Papers).
2. Higher Education (University of Luxembourg / CPGE)
Calculus & Real Analysis: Sequences, series, generalized integrals.
Matrix algebra: Vector spaces, diagonalization, eigenvalues.
My Online Methodology
Digital tools: Use of an interactive whiteboard and a graphics tablet for clear and shared writing in real time.
Strict adaptation to the marking schemes and writing criteria of the Luxembourg baccalaureate.
Personalized follow-up: Sending a summary of the lesson and application exercises after each session.
My teaching method is based on simplifying abstract concepts and mastering the problem-solving methods required by the Luxembourg Ministry of National Education ESC (Classical) and ESG (General).
1. Secondary Education (Sections B, C, D, G)**
* **Analysis:** In-depth study of functions (logarithms, exponentials), limits, derivatives and integral calculus.
* **Linear Algebra:** Analytic geometry in space, vectors, and systems of equations (Gaussian method).
* **Complex Numbers:** Algebraic and trigonometric forms and solutions in .
* **Preparation for the Final Examination:** Intensive work on past exam papers (Past Papers).
2. Higher Education (University of Luxembourg / CPGE)
Calculus & Real Analysis: Sequences, series, generalized integrals.
Matrix algebra: Vector spaces, diagonalization, eigenvalues.
My Online Methodology
Digital tools: Use of an interactive whiteboard and a graphics tablet for clear and shared writing in real time.
Strict adaptation to the marking schemes and writing criteria of the Luxembourg baccalaureate.
Personalized follow-up: Sending a summary of the lesson and application exercises after each session.
Education
Master's degree in Mathematics. PhD in Applied Mathematics. Mathematical researcher at the Modeling Laboratory of the National Engineering School of Tunis. My areas of expertise in mathematics range from the foundational concepts acquired during secondary education to advanced mathematics at the Bachelor's and Master's levels, as well as preparatory classes for engineering studies. I am also proficient in the numerical analysis and functional analysis curricula taught in engineering schools.
Experience / Qualifications
A career spanning more than 20 years in an engineering school in Tunisia whose training programs are EUR-ACE accredited.
Age
Teenagers (13-17 years old)
Adults (18-64 years old)
Seniors (65+ years old)
Student level
Intermediate
Advanced
Duration
60 minutes
The class is taught in
French
English
Arabic
Reviews
Availability of a typical week
(GMT -05:00)
New York
Online via webcam
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
My method: Logic before calculation
In the final year of high school, the difficulty is often not the calculation itself, but understanding the problem statement and choosing the correct theorem. My support focuses on three key areas:
Analysis: Perfect mastery of sequences, functions (logarithms, exponentials) and continuity.
Geometry in space: Visualization and vector calculation.
Probability: Understanding the laws and knowing when to apply them.
We will delve particularly into the 4 Pillars of Success in the Baccalaureate (Final Year Program)
For each session, we will work on the priority themes of the French curriculum:
Analysis & Algebra: Mastery of functions (Exponentials, Logarithms), limits, and integral calculus. Particular focus is placed on numerical sequences and proof by induction.
Geometry in Space: Learning to "see" in 3 dimensions and mastering parametric representations and the dot product.
Probability & Statistics: Understanding binomial distributions and density to avoid interpretation errors.
Specialty "Expert Maths" (Optional): For those aiming for preparatory classes, we delve deeper into complex numbers, arithmetic and matrices.
Session content:
Demonstration techniques: Knowing how to write a recurrence or a proof by contradiction without losing points for rigor.
Automation: Calculation of complex derivatives, antiderivatives and limits to gain speed on the day.
Analysis of typical Baccalaureate exam topics: We break down the topics that came up in 2024 and 2025 to anticipate the expectations of examiners in June 2026.
For who ?
First-year students: To consolidate the basics before the decisive year.
Final year students (Maths specialization): Intensive preparation for written exams.
Complementary / Expert Maths: Advanced training for future Parcoursup applications (CPGE, Engineering Schools).
🛠️ Tools for online courses
Shared Word document: You can see me writing the live demonstrations, and you can write in turn.
Paper correction: You send me your homework assignments done in class, we analyze your mistakes together so that you don't repeat them.
In the final year of high school, the difficulty is often not the calculation itself, but understanding the problem statement and choosing the correct theorem. My support focuses on three key areas:
Analysis: Perfect mastery of sequences, functions (logarithms, exponentials) and continuity.
Geometry in space: Visualization and vector calculation.
Probability: Understanding the laws and knowing when to apply them.
We will delve particularly into the 4 Pillars of Success in the Baccalaureate (Final Year Program)
For each session, we will work on the priority themes of the French curriculum:
Analysis & Algebra: Mastery of functions (Exponentials, Logarithms), limits, and integral calculus. Particular focus is placed on numerical sequences and proof by induction.
Geometry in Space: Learning to "see" in 3 dimensions and mastering parametric representations and the dot product.
Probability & Statistics: Understanding binomial distributions and density to avoid interpretation errors.
Specialty "Expert Maths" (Optional): For those aiming for preparatory classes, we delve deeper into complex numbers, arithmetic and matrices.
Session content:
Demonstration techniques: Knowing how to write a recurrence or a proof by contradiction without losing points for rigor.
Automation: Calculation of complex derivatives, antiderivatives and limits to gain speed on the day.
Analysis of typical Baccalaureate exam topics: We break down the topics that came up in 2024 and 2025 to anticipate the expectations of examiners in June 2026.
For who ?
First-year students: To consolidate the basics before the decisive year.
Final year students (Maths specialization): Intensive preparation for written exams.
Complementary / Expert Maths: Advanced training for future Parcoursup applications (CPGE, Engineering Schools).
🛠️ Tools for online courses
Shared Word document: You can see me writing the live demonstrations, and you can write in turn.
Paper correction: You send me your homework assignments done in class, we analyze your mistakes together so that you don't repeat them.
Objective: To understand AI without fear, to use it to simplify one's life and to know how to identify digital traps.
1: Demystifying AI (What exactly is it?)
AI is not a movie robot: Difference between fiction and reality.
How it works (simply): The image of the "giant library": AI has read billions of books and uses them to predict the continuation of a sentence or create an image.
Where is it already present? Spell checkers, Netflix/YouTube suggestions, GPS, and voice assistants (Siri/Alexa).
2: Using AI to make life easier
Conversing with AI (ChatGPT, Claude, Gemini):
Ask him to write an administrative email or a complex letter.
Summarize a long newspaper article or document.
Plan a travel itinerary or find recipe ideas with what's left in the fridge.
AI for creativity and memory:
Generate images to illustrate a birthday card (Midjourney, DALL-E).
Using AI to restore or colorize old family photos.
3: Learning to "talk" to AI (The Art of the Prompt)
The context method: Why "Give me a cake recipe" is less effective than "I am allergic to gluten and I am hosting 4 people, give me a simple chocolate cake recipe".
The expert's role: Learning to tell AI "Act like a travel guide" or "Act like an expert gardener".
4: Precautions and Critical Thinking (The Survival Guide)
"Hallucinations": Understand that AI can make false claims with complete certainty (never take medical or legal advice from AI without verification).
Privacy protection:
Never give sensitive data (social security number, passwords, bank details) to an AI.
Knowing that everything we write to the AI is potentially used to train it.
Spotting "Deepfakes":
How to recognize a doctored image or video (details on the hands, strange reflections, slightly metallic voice).
Verify the information: the golden rule of cross-referencing sources.
5: Ethics and Impacts (To go further)
Copyright: Who owns an image created by AI?
The environmental impact: The water and energy consumption of AI servers.
The future: Will AI replace us or assist us?
1: Demystifying AI (What exactly is it?)
AI is not a movie robot: Difference between fiction and reality.
How it works (simply): The image of the "giant library": AI has read billions of books and uses them to predict the continuation of a sentence or create an image.
Where is it already present? Spell checkers, Netflix/YouTube suggestions, GPS, and voice assistants (Siri/Alexa).
2: Using AI to make life easier
Conversing with AI (ChatGPT, Claude, Gemini):
Ask him to write an administrative email or a complex letter.
Summarize a long newspaper article or document.
Plan a travel itinerary or find recipe ideas with what's left in the fridge.
AI for creativity and memory:
Generate images to illustrate a birthday card (Midjourney, DALL-E).
Using AI to restore or colorize old family photos.
3: Learning to "talk" to AI (The Art of the Prompt)
The context method: Why "Give me a cake recipe" is less effective than "I am allergic to gluten and I am hosting 4 people, give me a simple chocolate cake recipe".
The expert's role: Learning to tell AI "Act like a travel guide" or "Act like an expert gardener".
4: Precautions and Critical Thinking (The Survival Guide)
"Hallucinations": Understand that AI can make false claims with complete certainty (never take medical or legal advice from AI without verification).
Privacy protection:
Never give sensitive data (social security number, passwords, bank details) to an AI.
Knowing that everything we write to the AI is potentially used to train it.
Spotting "Deepfakes":
How to recognize a doctored image or video (details on the hands, strange reflections, slightly metallic voice).
Verify the information: the golden rule of cross-referencing sources.
5: Ethics and Impacts (To go further)
Copyright: Who owns an image created by AI?
The environmental impact: The water and energy consumption of AI servers.
The future: Will AI replace us or assist us?
Show more
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