AMC 12 Assessment Strategies 5

Question 1

Which integer is closest to √2026?

Accepted Answer

45

Answer

45² = 2025, so √2026 is just above 45.

Question 2

Your computed answer to a probability problem is 7/5. What is the best response?

Accepted Answer

Recheck the work, since a probability cannot exceed 1

Answer

A sanity check shows probabilities must lie between 0 and 1, so an error occurred.

Question 3

Testing n = 1, 2, 3 gives 2, 4, 8 for the number of subsets of an n-element set. Which formula fits?

Accepted Answer

2^n

Answer

The small cases double each time, matching 2^n.

Question 4

P is any point inside an equilateral triangle with side length 2. What is the sum of the distances from P to the three sides?

Accepted Answer

√3

Answer

By Viviani's theorem the sum equals the altitude, which is √3; placing P at the center confirms it quickly.

Question 5

What is the probability of getting at least one head in 4 fair coin flips?

Accepted Answer

15/16

Answer

Complementary counting gives 1 − (1/2)⁴ = 15/16.

AMC 12 - - American Mathematics Contest 12 Practice Test