M8.4 Negative Enlargement, Similarity and Dependent Probability
Negative enlargement, similar 3D length-area-volume relationships and complex probability including dependent tree diagrams.
How to study for CCEA GCSE Mathematics
Secure fluent methods, explain mathematical reasoning and solve unfamiliar problems with a route-aware balance of non-calculator and calculator practice.
Core concepts
Concept 1
A negative enlargement places the image on the opposite side of the centre while its magnitude controls size.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
Similar solids connect corresponding length, surface-area and volume ratios by first, second and third powers.
Exam cue: Track the sign and magnitude of the scale factor, convert between dimensional ratios and update every dependent tree denominator.
Concept 3
Without-replacement events are dependent because branch probabilities change after each selection.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Leaving tree probabilities unchanged after an item is removed and not replaced.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Importing a topic boundary, formula sheet or paper convention from an England 9-1 board.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Giving a calculator display or unsupported answer without the reasoning, units or accuracy the question requires.
Guardrail: M5-M8 Paper 1 is non-calculator; Paper 2 and every M1-M4 assessment use a permitted calculator.
Memory anchors
Negative scale factor
An enlargement factor that reverses direction through the centre as well as changing size.
Similar solids
Solids with corresponding lengths in a constant ratio and matching shape.
Surface-area ratio
The square of the corresponding linear ratio for similar solids.
Volume ratio
The cube of the corresponding linear ratio for similar solids.
Dependent events
Events where one outcome changes the probability of a later event.
Without replacement
A selection process in which chosen items are not returned before the next draw.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
An enlargement with centre the origin and scale factor −3 maps (2,−1) to which point?
Under an enlargement, A=(1,2) maps to A′=(7,8) with scale factor 3. Find the centre.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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