Recover an original amount and interpret percentiles
Reverse a percentage multiplier · Interpret a percentile as a position in a distribution · Use an explicitly stated percentile convention
Exam scope and assessment notes
Extended content; not a Core requirement. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Forward percentages
- Ordered data
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Reverse a percentage multiplier
- Interpret a percentile as a position in a distribution
- Use an explicitly stated percentile convention
Undo a multiplier
If an original amount P becomes Q after multiplier m, then P = Q/m, not Q minus the same percentage of Q. For an increase of 20%, Q = 1.2P; for a decrease of 20%, Q = 0.8P.
Position is not percent correct
A percentile describes relative position among ordered observations. A 75th-percentile threshold places roughly three quarters of observations at or below it; ties and calculation conventions affect the exact interpretation. It does not mean 75% of exam questions were correct.
For the nearest-rank convention used in these tasks, sort N values and use rank ceil(pN/100), numbered from 1. Other interpolation or percentile-rank conventions exist. Use the question's stated rule rather than treating one method as universal.
Sources for this lesson
Pause and explain
Does a 90th-percentile result mean 90% of questions were answered correctly?
Worked example
After a 20% discount, a price is 72. Recover the original.
Show the worked solution
- 72 = 0.8P.
- P = 72/0.8 = 90; 20% of 90 is 18, leaving 72.
Answer Original price 90.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A price after a 25% increase is 150. Find its original value.
Give me a hint
The multiplier is 1.25.
Compare my reasoning
- 1.25P = 150.
- P = 150/1.25 = 120.
120.
Look for these in your work
- Use the original base
- Check forwards
Find the nearest-rank 75th percentile of 2, 4, 4, 6, 8, 10, 12, 20.
Give me a hint
Use rank ceil(0.75 × 8).
Compare my reasoning
- Rank = 6.
- The sixth ordered value is 10; six of eight are at or below it.
10 under the stated nearest-rank convention.
Look for these in your work
- Sort first
- State the convention
A school calls a result '80th percentile' but gives no raw score or calculation rule. May you infer 80% correct or an exact count of students below it?
Give me a hint
Distinguish relative position from raw performance.
Compare my reasoning
- 80% correct does not follow: the raw score is unknown.
- The group size, ties and convention are unknown, so an exact count below the result cannot be inferred.
No to both. It indicates relative position; obtain the comparison group and convention for precise interpretation.
Look for these in your work
- Avoid an unsupported score inference
- Account for ties and definitions
Common mistakes
- Reverse a change by division, not by changing its sign.
- Percentile and percentage score measure different things.
What can you explain now?
Does a 90th-percentile result mean 90% of questions were answered correctly?
Compare with the explanation
No; it describes relative position in the comparison distribution.
The comparison group and convention matter; it is not a percentage score.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Does a 90th-percentile result mean 90% of questions were answered correctly?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.