Calculus
Differentiation Basics
Course pathway

A level Calculus · 8MA0 / 9MA0

Understand it. Remember it. Practise it. Explain it. Apply it.

This site is designed to take you from first understanding a calculus idea to using it confidently in unfamiliar problems. Each topic is organised as a learning journey rather than a list of notes: explore the idea, retrieve the key facts, practise the standard methods, explain the mathematics, then apply it.

You do not have to use every section every time. If a topic is already secure, move quickly to the practice you need. If something breaks down, use Need a reminder? to jump back to the right explanation, fact or practice activity.

First steps

A good way to use the site

For a new topic, work from understanding towards independence. The order is deliberate, but you can move backwards whenever you need to.

  1. 1 Choose your topic

    Use the Topics panel to find the part of the course you are studying. The pathway separates Year 12 content from the additional Year 13 material.

  2. 2 Start with Understand

    Read the Topic goals, then work through the explanations, diagrams and interactives until the main ideas make sense.

  3. 3 Make the facts retrievable

    Use Memorise for notation, rules, definitions and key facts. Flashcards, games and review activities are there to make recall quick.

  4. 4 Move through AO1 → AO2 → AO3

    First practise the technique, then reasoning and explanation, then harder applications and modelling.

  5. 5 Use feedback to loop back

    Check answers, reveal hints when useful and follow targeted reminder links instead of simply repeating the same question.

The five learning modes

What each section is for

Most topics use the same five-part structure. Some foundation or review topics deliberately use fewer modes when another section would add no value.

Understand · Explore

Build the idea

Concept explanations, worked examples, visual models and interactive diagrams. Use this when the mathematics is new or when a method has stopped making sense.

Ask: “Do I understand why this works?”
Memorise · Recall

Make key knowledge available

Definitions, notation, standard results and method cues are turned into active-recall tasks, flashcards, games and mixed review.

Ask: “Can I recall this without looking it up?”
AO1 · Practise

Use and apply standard techniques

AO1 is about carrying out familiar mathematical procedures accurately and efficiently: algebra, differentiation, integration and other standard methods.

Ask: “Can I execute the method correctly?”
AO2 · Explain

Reason, interpret and communicate

AO2 asks you to justify choices, interpret results, connect representations, diagnose errors and communicate mathematical reasoning clearly.

Ask: “Can I explain or justify the mathematics?”
AO3 · Apply

Solve problems in context

AO3 is about choosing and connecting mathematics in less familiar problems, including modelling and problems set in mathematical or real-world contexts.

Ask: “Can I decide what mathematics to use?”

Tools around the course

What the other site functions do

The controls around each activity are there to help you navigate, practise independently and recover when you get stuck.

Topic goals

Shows what you should be able to understand or do by the end of the topic. Check these at the start and again when reviewing.

Need a reminder?

Takes you to targeted support for the exact gap: an Understand explanation, a Memorise item or suitable AO1 practice.

Word Bank

Collects important vocabulary and notation as you meet it. Use it to check definitions and mark terms that need more review.

ClassWiz

Appears only where calculator support is genuinely useful. It shows how a Casio ClassWiz can be used to check or support the mathematics without replacing the method.

Generated questions

Practice questions can generate fresh examples. Use New question, hints, answer checking and worked solutions to build independence rather than memorising one example.

Progress & Data

Topic markers show what you have visited and completed. Progress is stored locally in your browser; the Data tool lets you export, import or reset it.

Course pathway

How the course is organised

Year 12 · 8MA0

The first part of the pathway develops the core ideas of differentiation and integration and ends with a Year 12 review and mastery checkpoint.

Additional Year 13 · 9MA0

The second part extends those ideas into the additional differentiation and integration techniques required for the full A level.

Review & mastery

Review sections mix topics so you must recognise the structure yourself. They are designed for consolidation once individual topics are reasonably secure.

Topic goals

In this topic you will learn to…

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Progress data

Your completion, practice history and Word Bank are saved locally on this device. Security is stored separately from completion.

Storage Saved on this device
Schema Version 1
Activity records 0
Word Bank 0 words

Export

Save a small JSON backup that can be restored on another browser or device.

Import

Select a Calculus Website progress file. Nothing is replaced until you confirm the import.

No file selected

Reset

Clear saved progress and Word Bank records on this browser. This cannot be undone unless you exported a backup.