Assessment Strategies Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Assessment Strategies flashcards as text
A problem asks which expression equals 1 + 3 + 5 + ... + (2n − 1). Testing n = 2 quickly identifies which choice?
Answer: n²
For n = 2 the sum is 4, which matches only n² among these.
What is the units digit of 7^2026?
Answer: 9
Units digits of powers of 7 cycle 7, 9, 3, 1, and 2026 ≡ 2 (mod 4) gives 9.
Which of the following could be the sum of five odd integers?
Answer: 2027
An odd number of odd integers always has an odd sum.
Using a mod 9 (digit sum) check, which could be the value of 123 × 456?
Answer: 56088
123 ≡ 6 and 456 ≡ 6 (mod 9), so the product ≡ 0, and only 56088 has digit sum divisible by 9.
Find the positive integer x with x³ − x = 120.
Answer: 5
Testing choices: 5³ − 5 = 120, while 4 gives 60 and 6 gives 210.
Two fair dice are rolled. What is the probability the first die shows a strictly larger number than the second?
Answer: 5/12
Ties have probability 1/6, and by symmetry the remaining 5/6 splits evenly, giving 5/12.
A problem asks for an identity that holds for all real x. What is usually the fastest way to eliminate wrong answer choices?
Answer: Substitute simple values like x = 0 or x = 1
Plugging in easy values quickly rules out choices that fail the identity.
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