Shakeel ur Rahman (O/A levels, IGCSE, IB, SAT) Math & Physics expert
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I hold a Master’s degree in Physics from NUST University, Islamabad — one of Pakistan’s premier institutions. With over eight years of teaching experience, including the last five years teaching online, I have had the privilege of working with students from the USA, UK, Canada, Oman, and Saudi Arabia.

I specialize in a wide range of curricula, including O Levels, A Levels, IB, IGCSE, Matric, FSc, SAT, SHSAT, KS3, KS4, and middle school science subjects. I am also an experienced tutor for Cadet, Military, and PAF College entrance exam preparation, and have proudly guided many students into top-tier institutes.

As a passionate science educator, I strive to ignite curiosity, encourage critical thinking, and make learning an engaging experience. I maintain a student-friendly, interactive classroom environment, where questions are always welcome and learning is tailored to individual needs.

To enhance the online experience, I use a graphic tablet for real-time problem-solving and well-equipped digital platforms that replicate the effectiveness of in-person teaching. I also provide access to high-quality worksheets and practice materials, curated from trusted educational resources, to ensure students are fully prepared for their exams.

My teaching philosophy is rooted in clarity, engagement, and adaptability. Every student is different, and I design custom lesson plans and activities to match their pace and style of learning. The goal is not just to improve grades — but to develop a deeper understanding and love for science.

Outside of teaching, I enjoy reading about philosophy and history, exploring nature, and listening to music.

If you're looking for a committed, experienced, and engaging science tutor — whether for academic support or exam preparation — feel free to reach out. I look forward to helping you achieve your goals.

▌║█║▌│║▌│║▌║▌█║𝐂𝐨𝐦𝐩𝐫𝐞𝐡𝐞𝐧𝐬𝐢𝐯𝐞 𝐒𝐮𝐛𝐣𝐞𝐜𝐭 𝐋𝐢𝐬𝐭𝐢𝐧𝐠𝐬 ▌│║▌║▌│║║▌█║▌║█

✩░▒▓▆▅▃▂▁ 𝐌𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐬 ▁▂▃▅▆▓▒░✩

🔹 **𝗧𝗿𝗶𝗴𝗼𝗻𝗼𝗺𝗲𝘁𝗿𝘆 (12 𝗪𝗲𝗲𝗸𝘀)**
1️⃣ Introduction to Trigonometry: Basic concepts, angles, trigonometric ratios
2️⃣ Trigonometric Functions: Properties, graphs, applications
3️⃣ Inverse Trigonometric Functions: Graphs, properties, solving equations
4️⃣ Trigonometric Identities & Equations: Verifications, fundamental identities
5️⃣ Angles & Unit Circle: Reference angles, function evaluation
6️⃣ Laws of Sines & Cosines: Triangle solutions, applications
7️⃣ Applications in Engineering & Physics
8️⃣ Polar Coordinates & Complex Numbers
9️⃣ Vectors in Trigonometry: Magnitude, components, dot & cross product
🔟 Trigonometric Series: Fourier series, physics applications
1️⃣1️⃣ Hyperbolic Functions
1️⃣2️⃣ Advanced Applications

🔹 **𝗔𝗹𝗴𝗲𝗯𝗿𝗮 (12 𝗪𝗲𝗲𝗸𝘀)**
1️⃣ Introduction to Algebra: Operations, properties
2️⃣ Solving Linear Equations: One-step to multi-step
3️⃣ Graphing Linear Equations: Slope, intercepts, equations
4️⃣ Systems of Equations: Graphing, substitution, elimination
5️⃣ Factoring Polynomials: Trinomials, special products
6️⃣ Rational Expressions: Simplifications, equations
7️⃣ Quadratic Equations: Factoring, quadratic formula
8️⃣ Exponential & Logarithmic Functions
9️⃣ Sequences & Series: Arithmetic, geometric, infinite series
🔟 Conic Sections: Parabolas, ellipses, hyperbolas
1️⃣1️⃣ Advanced Algebra Applications
1️⃣2️⃣ Real-World Problem Solving

🔹 **𝗚𝗲𝗼𝗺𝗲𝘁𝗿𝘆 (12 𝗪𝗲𝗲𝗸𝘀)**
1️⃣ Foundations: Points, lines, planes, angles
2️⃣ Congruence & Similarity: Theorems, proofs
3️⃣ Triangle Properties: Types, inequalities, congruence theorems
4️⃣ Polygons & Quadrilaterals: Properties, classifications
5️⃣ Circles: Chords, tangents, arcs
6️⃣ Area & Perimeter: Polygons & circles
7️⃣ 3D Geometry: Prisms, pyramids, cylinders
8️⃣ Transformations: Reflections, rotations, dilations
9️⃣ Coordinate Geometry: Graphs, equations
🔟 Non-Euclidean Geometry: Hyperbolic applications
1️⃣1️⃣ Advanced Theorems
1️⃣2️⃣ Applications in Design & Architecture

🔹 **𝗣𝗿𝗲-𝗖𝗮𝗹𝗰𝘂𝗹𝘂𝘀 (12 𝗪𝗲𝗲𝗸𝘀)**
1️⃣ Functions & Graphs
2️⃣ Exponents & Logarithms
3️⃣ Polynomial & Rational Functions
4️⃣ Trigonometric Functions & Equations
5️⃣ Conic Sections & Coordinate Systems
6️⃣ Sequences, Series & Mathematical Induction
7️⃣ Vectors & Matrices
8️⃣ Limits & Continuity
9️⃣ Introduction to Calculus Concepts

🔹 **𝗖𝗮𝗹𝗰𝘂𝗹𝘂𝘀 (12 𝗪𝗲𝗲𝗸𝘀)**
1️⃣ Limits & Continuity
2️⃣ Differentiation: Rules, applications
3️⃣ Applications of Derivatives: Optimization, motion analysis
4️⃣ Integration: Techniques & applications
5️⃣ Definite & Indefinite Integrals
6️⃣ Differential Equations
7️⃣ Multivariable Calculus: Partial derivatives, gradients
8️⃣ Infinite Series & Convergence
9️⃣ Advanced Calculus Topics
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░▒▓▆▅▃▂▁𝟏𝟐-𝐖𝐞𝐞𝐤 𝐒𝐀𝐓 𝐌𝐚𝐭𝐡 𝐏𝐫𝐞𝐩 𝐏𝐥𝐚𝐧 – 𝐌𝐚𝐬𝐭𝐞𝐫 𝐄𝐯𝐞𝐫𝐲 𝐓𝐨𝐩𝐢𝐜!▁▂▃▅▆▓▒░

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**Week 1: SAT Math Overview & Strategy 🎯**

* Format of SAT Math (Calculator & No-Calculator)
* Key math question types and timing strategy
* Diagnostic test – find your baseline and weak areas

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**Week 2: Algebra Foundations & Linear Equations ➕➖**

* Solving linear equations & inequalities
* Systems of equations – elimination & substitution
* Word problems – translating English into algebra

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**Week 3: Functions & Graph Interpretation 📈**

* Understanding function notation
* Interpreting and manipulating graphs
* Linear, quadratic & exponential functions

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**Week 4: Quadratics, Polynomials & Factoring 🧩**

* Factoring techniques
* Solving quadratic equations (by factoring, completing the square, quadratic formula)
* Analyzing graphs of quadratic functions

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**Week 5: Advanced Algebra & Rational Expressions 🔄**

* Rational expressions & equations
* Radical expressions & exponents
* Absolute value equations and inequalities

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**Week 6: Problem Solving & Data Analysis 📊**

* Ratios, proportions, and percentages
* Unit conversions & rates
* Interpreting tables, charts, and scatterplots

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**Week 7: Geometry Essentials 📐**

* Angles, triangles, and polygons
* Perimeter, area, and volume
* Coordinate geometry basics

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**Week 8: Circles & Trigonometry 🔵📏**

* Circle equations, angles & arcs
* Trigonometric ratios – SOHCAHTOA
* Special right triangles and radians basics

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**Week 9: No-Calculator Section – Mental Math Mastery 🧠**

* Efficient techniques for mental math
* Simplifying algebraic expressions
* Practice with typical No-Calc traps & shortcuts

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**Week 10: Calculator Section – Speed & Accuracy 🖩**

* When & how to use the calculator effectively
* Avoiding over-dependence on the calculator
* Targeting typical graphing calculator problems

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**Week 11: Practice Test – Math Section Only 🏁**

* Take full math section under timed conditions
* Review incorrect answers and weak areas
* Strategy adjustment and pacing drills

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**Week 12: Final Review & Math Mastery 🏆**

* High-frequency topics and formulas to memorize
* Review of common traps & how to avoid them
* Confidence-building strategies & mindset tips

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✩░▒▓▆▅▃▂▁𝟏𝟐-𝐖𝐞𝐞𝐤 𝐇𝐢𝐠𝐡 𝐒𝐜𝐡𝐨𝐨𝐥 𝐏𝐡𝐲𝐬𝐢𝐜𝐬 𝐂𝐨𝐮𝐫𝐬𝐞 – 𝐔𝐧𝐥𝐨𝐜𝐤 𝐭𝐡𝐞 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐞! ▁▂▃▅▆▓▒░✩

**Week 1: Physics—The Language of the Universe!**
- What is physics, and why does it rule everything? 🌎
- The metric system, units, and dimensions 📏
- Precision, accuracy, and the magic of significant figures 🎯

**Week 2: The Secrets of Motion – Kinematics!**
- Speed, velocity, and acceleration—what’s the difference? ⚡
- Equations of motion that even astronauts use! 🚀
- The wild world of free fall & projectile motion 🎯

**Week 3: Newton’s Laws—The Rules of Reality!**
- Who was Newton, and why do his laws still shape the world? 🍏
- Forces, inertia, and the secret to pushing objects effortlessly! 💨
- Real-life applications—from cars to rocket launches 🚗🚀

**Week 4: Work, Energy & Power—The Science of Getting Things Done!**
- What really happens when you push something? 🤔
- Kinetic & potential energy—the key to roller coasters! 🎢
- Power and efficiency—why do some machines waste energy? ⚡

**Week 5: Momentum—The Physics of Impact!**
- Why do car crashes depend on mass and speed? 🚗💥
- Conservation of momentum—nothing ever truly stops! 🔄
- Collisions: elastic vs. inelastic—bouncy vs. sticky! 🎾

**Week 6: Circular Motion & Gravitation—Why Everything Orbits!**
- How do planets stay in motion? 🌍
- Centripetal force—the hidden force in every turn! 🔄
- Newton’s Law of Universal Gravitation—why gravity rules all! 🛰️

**Week 7: Rotational Motion—The Physics of Spinning!**
- Torque—how force makes things rotate! 🔧
- Angular momentum—why figure skaters spin faster! ⛸️
- Rolling motion—why do wheels keep going? 🚴

**Week 8: Properties of Matter—Solids, Liquids, and Gases!**
- Density, pressure, and buoyancy—why boats float! 🚢
- Pascal’s and Archimedes’ principles—how fluids exert force! 💧
- Real-world applications—hydraulics, submarines, and weather balloons! 🎈

**Week 9: Thermodynamics—The Science of Heat & Energy!**
- Temperature vs. heat—what’s the difference? 🌡️
- The Laws of Thermodynamics—why energy never disappears! ♻️
- Entropy—why disorder always increases! 🔥

**Week 10: Waves & Sound—The Physics of Vibrations!**
- What are waves, and how do they move? 🌊
- Sound waves—why do we hear music? 🎵
- Doppler Effect—why sirens change pitch as they pass! 🚓

**Week 11: Light & Optics—The Science of Seeing!**
- Reflection & refraction—how light bends and bounces! 🔦
- Lenses & mirrors—how do glasses and telescopes work? 🔍
- The electromagnetic spectrum—why we only see a tiny part of light! 🌈

**Week 12: Electricity & Magnetism—The Invisible Forces!**
- Electric charge, current, and circuits—how power flows! ⚡
- Magnetic fields—how magnets and electricity are connected! 🧲
- Electromagnetic induction—how we generate electricity! 🔋

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✩░▒▓▆▅▃▂▁𝟏𝟐-𝐖𝐞𝐞𝐤 𝐇𝐢𝐠𝐡 𝐒𝐜𝐡𝐨𝐨𝐥 𝐂𝐡𝐞𝐦𝐢𝐬𝐭𝐫𝐲 𝐂𝐨𝐮𝐫𝐬𝐞 – 𝐔𝐧𝐥𝐨𝐜𝐤 𝐭𝐡𝐞 𝐄𝐥𝐞𝐦𝐞𝐧𝐭𝐬! ▁▂▃▅▆▓▒░✩

**Week 1: Chemistry—The Science of Everything!**
- What is chemistry, and why does it explain everything? 🌍
- Matter and its states—solid, liquid, gas, and plasma! 🔥
- Physical vs. chemical changes—what’s really happening? 🧪

**Week 2: The Building Blocks—Atoms & Elements!**
- What are atoms, and why are they so small yet powerful? ⚛️
- The periodic table—how elements are organized! 📜
- Atomic structure—protons, neutrons, and electrons! 🔬

**Week 3: Chemical Bonding—The Glue That Holds Matter Together!**
- Why do atoms stick together? 🧲
- Ionic vs. covalent bonds—what’s the difference? 🔗
- Metallic bonding—why metals are so strong! 🏗️

**Week 4: Chemical Reactions—How New Substances Form!**
- What happens when chemicals react? 💥
- The types of chemical reactions—synthesis, decomposition, and more! 🔄
- Balancing chemical equations—why atoms must be conserved! ⚖️

**Week 5: The Mole Concept—Counting the Uncountable!**
- What is a mole, and why do chemists love it? 🐹 (not that mole!)
- Avogadro’s number—how big is **6.022 × 10²³**? 🤯
- Stoichiometry—how we calculate chemical quantities! 🧮

**Week 6: Gases & Their Laws—The Science of Air!**
- Pressure, volume, and temperature—how gases behave! 🎈
- Boyle’s, Charles’, and Avogadro’s Laws—what do they tell us? 🔥
- The Ideal Gas Law—how gases follow simple math! 🧑‍🔬

**Week 7: Solutions & Mixtures—What’s Dissolving?**
- Solutes, solvents, and solutions—why does salt dissolve in water? 🌊
- Concentration—how strong is a solution? 🧂
- Factors affecting solubility—temperature, pressure, and polarity! 🧪

**Week 8: Acids & Bases—The Chemistry of pH!**
- What makes something acidic or basic? 🧃⚗️
- The pH scale—how acidic is lemon juice? 🍋
- Acid-base reactions—neutralization and titration! ⚖️

**Week 9: Thermochemistry—The Energy of Reactions!**
- Endothermic vs. exothermic—how reactions absorb or release heat! 🔥❄️
- Enthalpy and entropy—how do they drive reactions? ♻️
- Gibbs free energy—will a reaction happen or not? ⚡

**Week 10: Chemical Kinetics & Equilibrium—Speed & Balance of Reactions!**
- What makes reactions go faster? ⏳
- Activation energy—why some reactions need a push! 🔥
- Le Chatelier’s Principle—how reactions shift to balance! ⚖️

**Week 11: Electrochemistry—The Power of Chemistry!**
- Redox reactions—how do batteries work? 🔋
- Electrolysis—splitting water into hydrogen and oxygen! 💧
- Corrosion & galvanization—why do metals rust? 🏗️

**Week 12: Organic Chemistry—The Chemistry of Life!**
- Hydrocarbons—how do carbon chains form fuels? ⛽
- Functional groups—how small changes make big differences! 🏗️
- Polymers & biomolecules—how plastics and DNA are built! 🧬

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✩░▒▓▆▅▃▂▁𝐏𝐡𝐲𝐬𝐢𝐜𝐬 & 𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐂𝐨𝐦𝐩𝐮𝐭𝐢𝐧𝐠▁▂▃▅▆▓▒░✩

🔹 **𝐂𝐥𝐚𝐬𝐬𝐢𝐜𝐚𝐥 & 𝐌𝐨𝐝𝐞𝐫𝐧 𝐏𝐡𝐲𝐬𝐢𝐜𝐬**
📌 Mechanics, Electrodynamics, Optics, Thermodynamics
📌 Special Relativity, Nuclear Physics

🔹 **𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐌𝐞𝐜𝐡𝐚𝐧𝐢𝐜𝐬 & 𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐂𝐨𝐦𝐩𝐮𝐭𝐢𝐧𝐠**
📌 Foundations of Quantum Mechanics
📌 Qubits, Superposition, Entanglement
📌 Qiskit basics
📌 Quantum Gates & Circuits
📌 Quantum Algorithms (Grover’s, Shor’s)
📌 Quantum Machine Learning & VQAs
📌 QKD

Subjects

  • SAT (Scholastic Assessment Test)

  • Physics IGCSE-Bachelors/Undergraduate

  • Geometry Beginner-Expert

  • Precalculus Grade 10-Grade 12

  • Mathematics IGCSE-A level

  • Trigonometry Beginner-Expert

  • Key Stage 3 Mathematics Grade 7-Grade 9

  • IB board Maths Beginner-Expert

  • Algebra 1 and 2 Beginner-Expert

  • Calculus 1 AS level-Bachelors/Undergraduate

  • Quantum Computing Beginner-Expert

  • Algebra and Trigonometry Grade 5-A level

  • Advanced Functions Grade 9-Grade 12

  • KS3 Science (Year 7-Year 9) Grade 7-Grade 9

  • Pure Mathematics AS level-A2 level

  • Algebra 1, 2, 3 Grade 5-O level

  • GCSE Edexcel Science

  • KS3 Maths British Curriculum Grade 7-Grade 9

  • Cadet College Entrance Test Grade 5-Grade 11

  • Quantum computation Beginner-Expert

Experience

  • Teacher (Jun, 2020–Present) at online tutoring
    I've been teaching students online from USA, Canada, UK, Oman and KSA for past five years.
  • Teacher (Jun, 2016–Present) at home tutor
    I have been working as a home tutor for the past 8 years and I have taught various curricula such as, O levels, Matric, IGCSE, F.Sc, A levels, Cadet colleges entrance exam prep, NET, ECAT and SATs.

Education

  • MS physics (Sep, 2021–May, 2024) from NUST, Islamabad Pakistan
  • MSc Physics (Oct, 2017–Jun, 2020) from University of The Punjab Lahore
  • BSc ( Mathematics, Physics, Computer) (Dec, 2015–May, 2017) from University of The Punjab Lahore
  • Higher Secondary (Jun, 2012–Jul, 2014) from Military college murree
  • Secondary (Jun, 2010–May, 2012) from Military college murree

Fee details

    Rs40,000–80,000/month (US$143.60–287.20/month)

    I charge fee for 1 hours class, 5 days a week. It can vary based on the number of subjects a student needs help with or the time required.

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