Basics of differentiation
Learning workspace
Explore the idea
See the derivative as a gradient function
Start from what the graph is doing, then connect that visual change to the derivative rather than beginning with a rule to memorise.
Explore, notice and make sense of the mathematics before formalising the method.
The linked-function explorer will live here; the mathematics remains the visual focus of the workspace.
Learn
Build a compact mental reference
Key facts from this topic are collected here before retrieval.
Flashcards
Recall before you reveal
Say or think the answer first. Reveal it, then judge whether you knew it without help.
Games
Retrieval games
Same core knowledge, different retrieval formats.
Match
Connect each cue to its partner
Choose one item from each column.
Build the rule
Build the right-hand side of the general power rule.
Select tokens in order. Use Undo or Reset whenever you want to change the construction.
Missing piece
Which expression belongs in the missing exponent?
Choose one piece, then check it.
Sort
Sort each expression by what you should do before applying the power rule.
Select an expression, then choose its bucket. This is the keyboard/touch alternative to dragging.
Spot the impostor
One derivative is incorrect. Which is the impostor?
Choose the one statement that breaks the rule.
Review
Mix the retrieval, not the content
Use an untimed mixed review, or focus on rapid recall or diagram recall. The timer is always optional.
Rapid recall
Recall one fact at a time.
Choose the best answer. Accuracy comes before speed.
Diagram recall
Which label points to the tangent line?
Read the diagram first, then choose the callout label.
Build the rule
Build the right-hand side of the general power rule.
Select tokens in order.
Missing piece
Which expression belongs in the missing exponent?
Choose one piece, then check it.
Spot the impostor
One derivative is incorrect. Which is the impostor?
Choose the one statement that breaks the rule.
Question
Differentiate with respect to x.
Diagnostic mastery
Your evidence and next steps
Evidence is grouped by the exact Year 12 micro-skill. This is diagnostic feedback, not a single score.
Complete questions in this mastery set to build your diagnostic picture.
Strengths shown
Specific next steps
Differentiation mastery
Method recognition and execution
Evidence is grouped by exact micro-skill. Recognition errors and execution errors are counted separately and routed to precise support.
Complete questions in this mastery set to build your diagnostic picture.