Henry Wan, Ph.D.
Core Principle:
Don’t guess randomly — only guess after eliminating two options.
If you guess, pick D or C. Avoid A and E.
1. Scoring Rules
| Correct | Wrong | Blank |
| +6 | 0 | +1.5 |
Key point: A blank answer earns 1.5 points. A wrong guess earns 0. So guessing has an opportunity cost — you give up 1.5 points if you guess wrong.
2. Why You Shouldn’t Guess Randomly
| Strategy | Expected Score | vs. Blank |
| Leave blank | 1.5 | — |
| Random guess | 1.2 | Lower |
| Choose D | 1.45–1.48 | Slightly lower |
| Choose C | 1.36–1.40 | Lower |
| Choose A | 0.87 | Much lower |
| Choose E | 0.86–0.97 | Much lower |
If you have no idea at all, leaving it blank (1.5) beats guessing.
3. Three-Step Decision Process
Step 1: How many options can you eliminate?
| Eliminated | Action | Reason |
| 0 | Leave blank | 1.5 > guess expected value |
| 1 | Guess or skip | Expected value = 1.5 (tie) |
| 2 | Must guess! | Expected value = 2.0 > 1.5 |
| 3 | Must guess | Expected value = 3.0 |
Step 2: Which remaining option should you pick?
| Remaining options include | Pick |
| D | Pick D |
| No D, but C | Pick C |
| No D, no C, but B | Pick B |
| Only A and E | Pick either; low expected value |
Step 3: After guessing
Use the saved time to check the questions you know how to do — that pays off more.
4. Option Frequencies (AMC 10 and AMC 12)
| Option | AMC 10 | AMC 12 |
| A | 14.57% | 14.50% |
| B | 23.62% | 21.90% |
| C | 23.32% | 22.73% |
| D | 24.23% | 24.70% |
| E | 14.26% | 16.16% |
Pattern: D appears most often, followed by C and B. A and E appear least often.
5. Exam Mantra
AMC 10/12: don’t guess randomly,
Only guess after eliminating two;
Pick D first, then C,
A and E are traps.
6. Reminders
- Mark questions you have no idea about and handle them at the end.
- If you can eliminate 2 options, guess — don’t hesitate.
- Spend at most 15 seconds per guess.
- Leaving blank is also a strategy — not giving up.
- Before submitting, check your known questions first — securing those points matters more than guessing.
Appendix: Statistical Tables
Table 1. AMC 10 Answer Frequency
53 contests, 1,325 questions
| Option | Count | Percentage |
| A | 193 | 14.57% |
| B | 313 | 23.62% |
| C | 309 | 23.32% |
| D | 321 | 24.23% |
| E | 189 | 14.26% |
| Total | 1,325 | 100.00% |
Ranking: D > B > C > A > E
Table 2. AMC 12 Answer Frequency
53 contests, 1,324 questions
| Option | Count | Percentage |
| A | 192 | 14.50% |
| B | 290 | 21.90% |
| C | 301 | 22.73% |
| D | 327 | 24.70% |
| E | 214 | 16.16% |
| Total | 1,324 | 100.00% |
Ranking: D > C > B > E > A
Note: The AMC 12 total is 1,324 rather than 1,325 because the MAA officially removed 2025 AMC 12A Problem 25 from scoring due to a flaw in the question. All contestants received full credit, and no official A–E answer exists for that problem.
Key Takeaways from the Tables
| Finding | AMC 10 | AMC 12 |
| Most frequent option | D (24.23%) | D (24.70%) |
| Least frequent option | E (14.26%) | A (14.50%) |
| Middle options (B, C, D) combined | 71.17% | 69.33% |
| Extreme options (A, E) combined | 28.83% | 30.67% |
Conclusion: Both AMC 10 and AMC 12 show a preference for middle answer choices in these historical datasets. Options B, C, and D account for approximately 70% of the correct answers, while A and E account for approximately 30%.
Important Note:
These are historical frequencies, not guarantees about future answer keys. Students should prioritize mathematical reasoning and eliminate incorrect choices rather than rely on answer distributions.
Good luck on your AMC 10 / AMC 12!
Further Reading
The strategic framework presented in this card builds on the expected-value approach discussed in:
Henry Wan. (2026). When Should You Guess on the AMC 10/12? A Mathematical Guide to Scoring Strategy.
Note: This card extends the original guide by incorporating empirical answer-frequency data from 53 AMC 10 contests and 53 AMC 12 contests administered between 2000 and 2025. While the original guide assumed that all answer choices were equally likely, the historical data reveal a different distribution: the middle options (B, C, and D) collectively account for approximately 70% of the correct answers.
Important distinction: Historical answer frequencies describe past contests; they do not guarantee the distribution of answers on future exams. Students should use mathematical reasoning and systematic elimination as their primary guessing strategies.
