Free worksheets
(my favourite available online, in alphabetical order!)
Target audience: IB and IGCSE Mathematics students.
Focus: Conceptual practice and exam-style questions for IB and IGCSE curricula.
Cost: Free
Description: An excellent collection of IB and IGCSE Mathematics worksheets and videos, carefully designed to develop both procedural fluency and conceptual understanding. Christos Nikolaidis’s resources are particularly useful for reinforcing syllabus topics and practising under exam-style conditions.
Target audience: GCSE, IGCSE, and early IB or A-Level Mathematics students.
Focus: Practice videos, worksheets, and exam-style questions.
Cost: Free
Description: Corbettmaths provides hundreds of worksheets, tutorials, and daily practice sheets across all major mathematics topics. Its “5-a-day” sets are ideal for building consistency and confidence through short, regular revision sessions.
Target audience: IGCSE, GCSE, and A-Level Mathematics students.
Focus: Topic-based worksheets and revision booklets.
Cost: Free resources with optional premium materials.
Description: Created by an experienced mathematics teacher, Dr Austin Maths offers clearly structured worksheets organised by topic and difficulty. These resources are perfect for targeted independent study or classroom reinforcement.
Target audience: GCSE and IGCSE Mathematics students.
Focus: Practice and revision for UK examination boards.
Cost: Subscription-based, with sample materials available
Description: A comprehensive site providing exam-style worksheets, topic revision, and problem sets. JustMaths is widely used in UK schools and offers clear, teacher-developed resources that mirror real exam formats.
Target audience: GCSE, IGCSE, and early A-Level Mathematics students.
Focus: Printable worksheets and problem sets for classroom and independent use.
Cost: Free
Description: Maths4Everyone offers well-designed, printable worksheets with detailed answer keys. The topics are broad and graded by difficulty, making it a great platform for self-paced revision and foundational practice.
Target audience: GCSE, IGCSE, and A-Level Mathematics students.
Focus: Interactive worksheets and teaching resources.
Cost: Subscription-based, with some free samples
Description: MathsPad provides interactive, visually engaging worksheets that promote deep conceptual learning rather than rote practice. Excellent for students who want to visualize relationships and patterns in mathematics.
Target audience: IB and AP Physics students.
Focus: Lesson notes, practice problems, and teacher-curated worksheets.
Cost: Free
Description: A collaborative physics teaching resource built by experienced IB and AP educators. Pretty Good Physics offers topic-by-topic notes, worksheets, and lab activities, making it an outstanding resource for independent study or classroom reinforcement.
Target audience: High-school and early university physics students (IGCSE, IB, AP)
Focus: Concept explanations, practice problems, and interactive simulations
Cost: Free
Description: A long-standing favourite for physics learners, The Physics Classroom combines clear conceptual tutorials, self-check quizzes, and interactive lessons. It’s ideal for reviewing core mechanics and electricity topics in a student-friendly format.
Interactive Websites
(in alphabetical order)
These platforms offer structured lessons, interactive exercises, and exam-style practice to support self-directed learning in mathematics, physics, and related subjects. Each resource has been selected for its clarity, reliability, and alignment with international curricula such as IB, IGCSE, A-Level, and AP.
Target audience: Upper secondary and university students, or adult learners interested in data science, statistics, and programming.
Cost: Subscription-based, with limited free courses available
Description: Interactive, hands-on courses in Python, R, SQL, statistics, and data analysis. Great for applying mathematical and statistical concepts to real-world data problems. The built-in coding environment lets learners progress without extra software. Excellent bridge for STEM, economics, and CS students into data-driven thinking.
Target audience: Secondary and pre-university students studying physics and combined science (IGCSE, GCSE, IB).
Cost: Free
Description: Interactive quizzes and quick-fire MCQs to test understanding and build recall. Ideal for exam prep and topic review, helping learners build speed and confidence with short, focused practice.
Target audience: IB Mathematics and Physics students (DP level, HL & SL).
Cost: Free access for most tools; premium upgrades available
Description: Generate custom IB-style exam questions by topic and difficulty. Perfect for targeted revision and mock-exam preparation, enabling practice under exam-like conditions.
Target audience: Middle school to university-entry level (IB, IGCSE, AP learners).
Cost: Free
Description: Structured lessons, practice exercises, and instructional videos across mathematics, physics, and more. Ideal for self-paced learning and concept reinforcement, especially for foundational skills before advancing.
Target audience: IB DP and IGCSE students (Mathematics AA/AI, HL & SL; IGCSE Mathematics).
Cost: Subscription-based, with limited free content
Description: Comprehensive IB & IGCSE Maths revision: video tutorials, question banks, practice exams, and grade predictors. Especially strong IB alignment with exam-style questions and mark-scheme standards—great for aiming at top grades.
Target audience: IGCSE, A-Level, and IB students (mathematics and physics).
Cost: Subscription-based, with free sample materials available
Description: High-quality topic summaries, exam-style questions, and detailed mark schemes. Ideal for learners who benefit from structured practice and worked solutions, particularly for Cambridge IGCSE, A-Level, and IB.
Full course materials (in alphabetical order)
Target audience: Advanced high-school and university-level students interested in in-depth STEM learning.
Cost: Free
Description: An extensive library of university-level courses, lectures, and problem sets created by the Massachusetts Institute of Technology. Perfect for highly motivated students who wish to go beyond the standard curriculum, explore topics like multivariable calculus, linear algebra, or physics, and experience authentic university-style learning from one of the world’s top institutions.
Target audience: University and pre-university students studying Calculus, Algebra, or Differential Equations.
Cost: Free
Description: An exceptional free resource offering clear, well-organized notes, examples, and practice problems in core university mathematics topics. Paul’s Online Math Notes is ideal for students who want to review or self-study calculus, algebra, or differential equations at their own pace, with concise explanations and worked examples similar to high-quality lecture notes.
Educators and Science Communicators on YouTube
(in alphabetical order)
These amazing creators represent some of the best in online science and mathematics education. Each channel offers a unique teaching style — from curriculum-aligned tutorials to conceptual storytelling that brings abstract ideas to life.
Target audience: IB HL, A-Level, and university mathematics, physics and engineering students.
Focus: Visual, conceptual explanations of advanced math.
Description: Grant Sanderson’s animations reveal the geometry and intuition behind topics like calculus, linear algebra, and neural networks—ideal for deep understanding.
Target audience: Curious learners of all ages.
Focus: Hands-on science demos and thought experiments.
Description: Memorable experiments that make physics and chemistry ideas tangible and fun.
Target audience: IB Physics (MYP & DP, HL/SL).
Focus: IB-aligned lessons and exam prep.
Description: Clear explanations and past-paper style walkthroughs aligned to the IB syllabus.
Target audience: Secondary and pre-university mathematics students (GCSE, IGCSE, IB, and early university).
Focus: Engaging, concept-driven mathematics lessons.
Description: Eddie Woo, an award-winning Australian mathematics teacher, makes complex ideas accessible through clear explanations and relatable examples. His channel, Wootube, covers topics ranging from algebra and trigonometry to calculus and problem-solving strategies. Ideal for students who appreciate an enthusiastic, human approach to learning mathematics and for anyone seeking to strengthen conceptual understanding in a friendly, classroom-style environment.
Target audience: High-school, AP physics & IB Physics students.
Focus: Engaging lessons with demos and humor. Description: Jonathan Thomas-Palmer’s lively approach makes core mechanics and exam prep stick.
Target audience: Middle-school through early university students (IB, IGCSE, AP, and first-year university).
Focus: Clear, curriculum-aligned lessons in mathematics, physics, and related subjects.
Description: The official Khan Academy YouTube channel offers concise, easy-to-follow explanations across thousands of topics — from algebra and calculus to mechanics and statistics. Lessons are designed for self-paced learning and review, making this channel an excellent companion for independent study or quick concept refreshers before exams.
Target audience: Advanced high-school & university students.
Focus: Elegant explanations of higher math.
Description: Visually rich lessons on calculus, linear algebra, and mathematical methods for physics.
Target audience: General audiences & high-school learners.
Focus: Accessible, curiosity-driven physics.
Description: Dianna Cowern explores everyday phenomena and sparks scientific curiosity.
Target audience: IGCSE/GCSE & A-Level physics.
Focus: Exam-oriented tutorials and tips.
Description: Lewis Matheson offers crisp videos aligned with UK syllabi and exam technique.
Target audience: University mathematics students (and advanced pre-university learners).
Focus: Rigorous university-level math (e.g., real analysis, linear algebra, abstract algebra, differential equations).
Description: Full-course style lectures with proofs and careful reasoning—excellent for building a solid theoretical foundation.
Target audience: General audiences to university level.
Focus: Big scientific ideas and paradoxes via storytelling.
Description: Derek Muller blends evidence, curiosity, and narrative to challenge intuition and deepen understanding.
Simulators & Interactive Tools (in alphabetical order)
Modern learning is at its best when students can see ideas come to life. Interactive simulations and online tools make abstract mathematical and physical concepts more tangible, allowing learners to experiment, visualize relationships, and deepen their intuition. Below is a selection of trusted simulators and interactive resources I regularly recommend to students — excellent companions for self-learners who want to connect theory with experience.
Target audience: High-school and early university students studying probability / statistics.
Cost: Free
Description: This GeoGebra page provides interactive visualizations for multiple probability distributions (normal, binomial, Poisson, etc.). Students can adjust parameters (mean, variance, etc.) and immediately see how the curve changes. Ideal for learners who want an intuitive, visual grasp of how distributions behave under parameter shifts.
Target audience: Physics students from high school through early university.
Cost: Free
Description: OPhysics offers interactive physics simulations and visualizations of classical mechanics, electromagnetism, and wave phenomena. It helps learners see in real-time how changing variables (forces, mass, velocity) influences physical behavior — great for building conceptual intuition beyond equations.
Target audience: Statistics learners at high school and introductory university levels.
Cost: Free
Description: This tool simulates sampling distributions by letting users draw repeated samples from a population and observe the distribution of sample statistics (e.g. sample mean). It visually reinforces central limit theorem ideas and sampling variability. Excellent when you want to link theory to empirical behavior.
Target audience: Students at many levels — middle school, high school, and introductory university science and math learners.
Cost: Free
Description: PhET provides a vast library of interactive physics, chemistry, biology, and mathematics simulations. Each simulation allows students to manipulate sliders, visual parameters, and input variables, making abstract ideas hands-on and explorative. Ideal for deepening conceptual understanding in a playful and exploratory environment.
My Favourite Textbooks
(in alphabetical order)
Textbooks remain some of the most valuable companions for mastering mathematics and physics. A well-written textbook offers clarity, structure, and depth that allows the student to be self-taught and self-reliant. I choose textbooks that explain, not just present: books that teach as if a private teacher were sitting beside you.
The following books and series are those I personally use and recommend as resources that have shaped my own learning and teaching, and that I frequently share with students. Each combines rigorous content, clear explanations, and abundant practice opportunities.
Asimov & Maxwell – Probability and Statistics with Applications:
A Problem Solving Text (2nd Edition)
Target audience: University students studying calculus-based probability and statistics.
Subjects: Probability and Statistics.
Format: Digital (via ActuarialUniversity.com) and print editions available.
Description: This outstanding text completely changed my view of statistics and probability. Despite not being my favourite field originally, I found this book exceptionally clear, rigorous, and engaging. It provides comprehensive coverage, carefully structured problem sets, and a strong focus on conceptual understanding through application, making it ideal for advanced high-school and university-level learners seeking a calculus-based treatment of the subject.
Chris McMullen – Mathematics & Physics Practice Series
Target audience: High-school to early university students; independent learners wanting extensive practice.
Subjects: Mathematics and Physics (both algebra- and calculus-based).
Format: Available in print and digital formats.
Description: A practical and affordable series featuring hundreds of progressively challenging problems across core mathematics and physics topics. These books are excellent for self-directed learners or students wishing to reinforce their skills through repetition and application, with clear step-by-step solutions and explanations.
Haese Mathematics (Haese Publications)
Target audience: IB MYP and DP students, IGCSE (0607), AS and A-Levels learners, and teachers using international curricula.
Subjects: Mathematics for IB (MYP & DP), IGCSE, and Australian curricula.
Format: Digital (via Snowflake) and print editions available.
Description: My all-time favourite and go-to mathematics textbooks for structured learning. Anyone who has ever learned mathematics with me has received material from a Haese textbook. The Haese series is comprehensive, conceptually clear, and beautifully organized, aligning perfectly with IB, IGCSE, and A-Level curricula. Their Snowflake digital platform is affordable, reliable, and intuitive: an excellent resource for both students and teachers. I recommend them especially for the self-taught.
Kuldeep Singh – Linear Algebra Step by Step
Target audience: University students or advanced high-school learners studying linear algebra.
Subjects: Linear Algebra.
Format: Print and digital editions available; publisher provides online worked solutions.
Description: An exceptionally student-friendly book that breaks complex linear algebra topics into manageable, logically ordered sections. Singh’s approachable style and the availability of worked solutions make it ideal for learners who want to build intuition and fluency in one of the most abstract areas of mathematics.
Kumon Workbooks (Kumon Publishing)
Target audience: Primary through early secondary students; self-learners developing arithmetic or pre-algebra fluency.
Subjects: Arithmetic, Pre-Algebra, Algebra, Geometry, and Calculus.
Format: Print only.
Description: A series of rigorous, self-paced workbooks that emphasize mastery through consistent, incremental practice. Written for a U.S. audience, they include both imperial and metric units. Highly affordable and methodical, they are ideal for building solid foundational skills in mathematics through repetition and gradual progression.
Lowe & Rounce – Calculations for A-Level Physics
Target audience: A-Level, IB, and pre-university physics students.
Subjects: Physics (mathematical methods and applied problem-solving).
Format: Available in print and digital formats.
Description: An excellent bridge between mathematics and physics, this book is filled with quantitative problem-solving exercises that sharpen mathematical reasoning in physical contexts. It’s one of the best resources for developing numerical fluency and confidence when working with data, equations, and units in exam-style situations.
Schaum’s Outline Series (McGraw-Hill Education)
Target audience: Advanced secondary and university students seeking concise, practice-oriented guides.
Subjects: College Physics, Calculus, Linear Algebra, and other foundational STEM topics.
Format: Print and digital (via major eBook platforms)
Description: The Schaum’s Outlines series combines succinct theoretical explanations with hundreds of worked examples and exercises. These books are ideal for students who prefer focused, problem-driven learning, and they serve as excellent supplements to standard course textbooks.
Serway & Vuille – College Physics (Cengage Learning)
Target audience: Upper secondary and early university students studying algebra-based physics.
Subjects: Algebra-based introductory physics.
Format: Print and digital (Cengage MindTap platform).
Description: My all-time favourite physics textbook. Serway and Vuille’s College Physics delivers clarity, depth, and strong conceptual grounding without requiring calculus. Ideal for students transitioning to university-level physics, this text balances explanation, intuition, and mathematical precision beautifully.
Stewart – Calculus Series (Cengage Learning)
Target audience: University students studying calculus or advanced secondary learners preparing for STEM degrees.
Subjects: Calculus (Single & Multivariable).
Format: Print only.
Description: The Stewart Calculus series remains a gold standard for calculus instruction, valued for its rigorous problem sets and pedagogical clarity. While these books are unfortunately expensive and rarely available digitally, they remain among the most comprehensive and well-structured calculus texts available.
Tsokos – Physics for the IB Diploma (Cambridge University Press)
Target audience: IB Diploma Programme Physics students (HL & SL).
Subjects: IB Physics.
Format: Print and digital (via Cambridge GO).
Description: A cornerstone text for IB Physics, Tsokos’s book offers precise derivations, conceptual depth, and exam-aligned practice. Its clarity and structure make it one of the most respected resources for Diploma Programme learners seeking mastery and top-tier performance.
Oxford IB Physics (Oxford University Press)
Target audience: IB Diploma Programme Physics students (HL & SL).
Subjects: IB Physics.
Format: Print and digital (Oxford Digital platform).
Description: A highly approachable and student-friendly counterpart to Tsokos. The Oxford IB Physics textbook provides clear explanations, visual aids, and practice questions aligned to IB assessment criteria — ideal for lesson planning, review, and exam preparation.
Reading for Pleasure
(in alphabetical order, by title)
Scientific curiosity doesn’t end when lessons do. These books invite readers to explore the human side of discovery — the mistakes, surprises, and moments of insight that have shaped our understanding of the world.
Each of these titles combines storytelling, history, and science in ways that make complex ideas feel alive and accessible.
American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer by Kai Bird and Martin J. Sherwin
Target audience: General readers, high-school and university students interested in history, physics, or ethics in science.
Description: A deeply researched and compelling biography of J. Robert Oppenheimer, the brilliant physicist behind the Manhattan Project. This book weaves together the history of 20th-century physics, the moral questions surrounding scientific discovery, and the human complexity of one of history’s most consequential scientists. Perfect for readers who enjoy history told through the lens of scientific progress. I highly recommend reading the book and watching the movie, in that order.
A Short History of Nearly Everything by Bill Bryson
Target audience: General readers and students aged 15+, especially those curious about how scientific ideas evolved.
Description: Bill Bryson’s humorous and insightful exploration of science — from the Big Bang to quantum mechanics — is both educational and entertaining. With his trademark wit, Bryson recounts how scientists made their discoveries (and their mistakes), offering a hilariously human take on the story of science. A wonderful read for anyone who wants to learn and laugh at the same time.
The Joy of x, Infinite Powers, and Sync (three different books) by Steven Strogatz
Target audience: Curious high-school students, university learners, and teachers interested in the beauty of mathematics in everyday life.
Description: Steven Strogatz (Cornell University) writes about mathematics with warmth, humor, and extraordinary clarity. His books explore how patterns, connections, and relationships underpin everything from biology and physics to love and language. Whether explaining calculus as the language of motion (Infinite Powers) or revealing the hidden order in chaos (Sync), Strogatz helps readers see the elegance and humanity in mathematics. I would highly recommend all his books for those looking for topics for the IB IAs.
Humble Pi (UK edition) / Math Gone Wrong (US edition) by Matt Parker
Target audience: Advanced secondary students, educators, and mathematically curious readers.
Description: A fascinating and often hilarious collection of real-world disasters caused by mathematical errors, from engineering oversights to digital failures. Matt Parker (a comedian and former math teacher) shows how even small miscalculations can have big consequences. This book is particularly engaging for ambitious IB students looking for topics for their Mathematics IA or Extended Essay, as it demonstrates how mathematical literacy impacts the real world.
