Mathematics
Function: Notations and Rules
Work through function notation, domain, range and the rules for combining functions.
Science & Mathematics
Mathematics, physics, chemistry and biology notes to help you understand a topic, work through examples and revise for your exam.
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The Full Collection
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A Starting Point
These notes take you from mathematical notation to modern physics and the molecules behind living systems.
Mathematics
Work through function notation, domain, range and the rules for combining functions.
Physics
Follow the ideas behind time dilation, length contraction and mass-energy equivalence.
Biology
Understand amino acids, protein structure and the jobs proteins do in living cells.
From Reading to Revision
I recommend starting with one topic you can’t yet explain clearly. Read it, put it away and then try a question on your own.
Read the explanation and follow an example. Check what each symbol means and why each step works.
Close the note and explain the idea in your own words. Reopen the part you couldn’t remember.
Try a question from your textbook or past paper. Compare your working and return to the step that went wrong.
Use your exam board’s current syllabus to choose what to study. This collection supports your revision; it doesn’t replace the syllabus or your course materials.
Before You Start
Need help with a missing topic or a correction? Email me the details.
Yes. The published notes in this collection are free to read, and you don’t need to create an account.
Some notes include a PDF download on their individual page. If a download is available, you can save it for revision. A PDF is not available for every topic.
You can use a note when its topic matches your syllabus and level. The collection includes school and university topics, so check the current syllabus for your exam and practice the required question types.
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Email gaurav@gauravtiwari.org with the topic and your exam or course. For an error, include the note URL and the sentence, formula or step you think needs correcting.
What Are You Studying?
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