Formula
c × m − (a − c) × p ≥ Tc ≥ (T + a × p) ÷ (m + p), rounded upbreak-even accuracy = p ÷ (m + p)
- c — correct answers needed
- a — questions attempted
- m — marks per correct answer
- p — marks lost per wrong answer
- T — target score
Every attempt is either right (+m) or wrong (−p); solve for how many must be right.
Worked example
Reach 150 by attempting 100 questions (+2 / −0.5)
- Target score
- 150
- Questions you plan to attempt
- 100
- Marks per correct answer
- 2
- Marks lost per wrong answer
- 0.5
Correct answers needed
80 of 100 attempted
Accuracy needed: 80%
Wrong answers you can afford: 20
Score at that accuracy: 150
How it works
With negative marking, attempting more questions is not automatically better: each wrong answer takes marks away. If you attempt a questions and get c of them right, your score is c × m − (a − c) × p. Setting that equal to the target and solving gives the smallest number of correct answers that reaches it, rounded up to a whole question.
The planner also reports the accuracy that implies, how many wrong answers you can afford, and the break-even accuracy for guessing: p ÷ (m + p). With a penalty of a quarter of the marks, for example, a guess is worth making on average only when your chance of being right is above 20%. Below that, guessing costs marks over time.
It treats each attempted question as right or wrong and assumes you skip the rest, so it does not predict difficulty or time. Use it with a scheme from the exam calculators, such as CAT Score Calculator or UPSC Prelims Score Calculator, or with Exam Score Calculator and Required Marks Calculator for simpler cases.
Assumptions and limits
- Every attempted question is either right or wrong; unattempted questions score nothing.
- The target must be reachable with the number of attempts entered; otherwise the tool says so.
- It does not model sectional cut-offs, time limits or partial marking.