Practice Recomposition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Combining solved sub-problems back into a coherent solution for the original, larger problem.
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.