Problem 1AMC 10
A fair coin is flipped three times, and a fair six-sided die with faces numbered through is rolled once. What is the probability of getting exactly two heads and a prime number on the die?
AMC score calculator
Enter how many problems were right and how many were left blank. The rest count as wrong.
The 2027 AIME cutoffs
| AMC 10 (A or B) | 100 or more |
|---|---|
| AMC 12 (A or B) | 85 or more |
| AIME | February 5 or 6, 2027, at Pearson testing centers; $85 plus taxes, if applicable |
For 2027 the MAA uses set numbers rather than percentages, and a student must also meet its other eligibility rules, including being 13 or older on the day of the AIME.
What it takes
- AMC 10, nothing wrong: 14 right and 11 blank is 84 + 16.5 = 100.5, which qualifies; 13 right and 12 blank is 96.
- AMC 10, nothing blank: 17 right is 102; 16 right is 96.
- AMC 12, nothing wrong: 11 right and 14 blank is 66 + 21 = 87; 10 right and 15 blank is 82.5.
- AMC 12, nothing blank: 15 right is 90; 14 right is 84.
Try 2 problems
Problem 2AMC 10
The mean of five numbers is . A sixth number is added to the list, and the mean of all six numbers is . What is the sixth number?
Next step
Questions people ask
How is the AMC 10 scored?
6 points for each right answer, 1.5 for each blank and 0 for each wrong one, out of 150. The AMC 12 is scored the same way.
What score qualifies for the 2027 AIME?
100 or more on the AMC 10, or 85 or more on the AMC 12, as published by the MAA, plus the other eligibility rules.
Should I leave questions blank on the AMC 10 or AMC 12?
A blank is worth 1.5 points. A blind guess among five choices is worth 6 ÷ 5 = 1.2 points on average, so it pays to guess only after ruling choices out: with two ruled out, a guess is worth 6 ÷ 3 = 2 points.
How is the AMC 8 scored?
1 point for each right answer and 0 for a blank or wrong one, out of 25, so answer every question.
AMC, AMC 8, AMC 10, AMC 12, AIME and American Mathematics Competitions are marks of the Mathematical Association of America (MAA), used here only to name the competitions. UniGenius is not affiliated with or endorsed by the MAA, and every problem here is original.