Curriculum Development 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 Curriculum Development flashcards as text
How many positive divisors does 72 have?
Answer: 12
72 = 2^3 x 3^2, so it has (3+1)(2+1) = 12 divisors.
What is the value of C(7, 3), the number of ways to choose 3 items from 7?
Answer: 35
7!/(3!4!) = 35.
What is the remainder when 2^10 is divided by 7?
Answer: 2
2^3 = 8 is 1 mod 7, so 2^10 = (2^3)^3 x 2 is 2 mod 7.
What is the greatest common divisor of 84 and 126?
Answer: 42
84 = 2^2 x 3 x 7 and 126 = 2 x 3^2 x 7, so gcd = 2 x 3 x 7 = 42.
How many distinct arrangements of the letters in LEVEL are there?
Answer: 30
5!/(2!2!) = 30 since L and E each repeat twice.
Two fair six-sided dice are rolled. What is the probability their sum is 7?
Answer: 1/6
Six of 36 outcomes sum to 7, giving 1/6.
What is the units digit of 3^2026?
Answer: 9
Units digits of 3^n cycle 3, 9, 7, 1, and 2026 is 2 mod 4, giving 9.
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