I never waste an opportunity to teach using data, and a perfect example is this histogram of scores from the latest AMC 10. Notice the spikes at regular intervals among the lower scores to the left. What is going on here?
These students do not understand how the AMC is scored, in particular that you receive 1.5 points for each answer left blank. While you receive 6 points for each correct answer, you receive no points for each wrong answer.
Take a look at the spike occurring at 30 points. You can earn 30 points by answering 5 questions correctly and the rest are wrong, with no questions left unanswered. A student can choose the correct answer to 5 problems on a multiple choice exam with 25 questions and 5 answer choices, by selecting answers at random.
As an exercise, try to generate scores 24, 36, and 42 as a naive student who does not leave any question blank. There is no excuse to not know this scoring rubric, as it is explained on the front of each exam booklet:
I coach all my AMC students to write a “clean exam.” That is one where all answered questions are correct and no questions are answered incorrectly. All other questions are left unanswered to achieve the highest possible score. (Notice the higher scoring students to the right are savvy to this strategy.)
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