Practice Recomposition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Recomposition is the process of combining simpler parts, sub-results, or solved sub-problems back together to form a complete solution or to understand the whole structure from its pieces.
After decomposing a problem, you must reassemble the pieces correctly — like completing a jigsaw puzzle, the boundary conditions between parts must match.
Example 1
easyAfter decomposing x^2 + 5x + 6 = (x+2)(x+3), recompose to solve x^2+5x+6 = 0.
Example 2
mediumPartial fractions gave \frac{5x+1}{(x+1)(x-2)} = \frac{4}{3(x+1)}+\frac{11}{3(x-2)}. Recompose to verify by adding the fractions.
Example 3
easyYou find x=3 and y=1 from solving a system. Recompose by substituting back into both equations to verify.
Example 4
mediumGiven the identity \sin^2\theta = \frac{1-\cos 2\theta}{2}, recompose: use it to evaluate \int \sin^2\theta\, d\theta.