Practice Structure vs Computation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The distinction between recognizing mathematical structure and patterns versus performing step-by-step arithmetic computations.
Seeing that x^2 - 1 = (x+1)(x-1) is structural. Computing 7^2 - 1 = 48 is computational.
Example 1
easyWithout computing, which is larger: 101^2 - 99^2 or 200?
Example 2
mediumCompute 1 + 2 + 3 + \cdots + 100 using structure, not brute force.
Example 3
easySimplify \frac{x^2 - 4}{x - 2} structurally (don't substitute values).
Example 4
mediumIs 37 \times 43 closer to 1500 or 1600? Use structure.