2021 AMC 10A Spring Problem 1

Attempt Problem 1 of the 2021 AMC 10A Spring below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10A Spring solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

What is the value of

(2^2-2)-(3^2-3)+(4^2-4)?

1

2

5

8

12

Answer: D

Concepts:order of operations

Difficulty rating: 450

Small hint:

Evaluate each parenthesized expression before combining the signs

Big hint:

Notice that each term has the form

n^2-n

Solution:

\begin{aligned} (2^2 - 2) - &(3^2 - 3) + (4^2 - 4) \\ &= 2 - 6 + 12 \\ &= 8. \end{aligned}

Thus, D is the correct answer.