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A. Burning a piece of paper is technically called combustion. It represents a chemical reaction whereby the carbon compounds in the paper are oxidized into different chemicals like carbon dioxide and water vapor. This is a chemical change.
As the molecules jostle each other, a few get to higher than average energy (and some to lower, keeping the average) and can get over the hump. Thus paper will slowly oxidize (go brown) and hydrogen peroxide will slowly decompose (building up a pressure of oxygen gas if the container does not have a vent or pressure release). However if you raise the temperature so that enough molecules have more energy than the activation energy then the reaction will proceed, and the heat released will activate more molecules.