Final answer:
The term that matches the synonyms 'arouse', 'excite', and 'sharpen' is 'stimulate', as they all imply an action that incites or enhances activity or interest.
Step-by-step explanation:
The synonyms provided: arouse, excite, and sharpen, are associated with the term stimulate. When using a thesaurus, stimulate is a term that often appears with these synonyms, indicating that it makes a match for the description given. To use it in a sentence: The teacher's intriguing question about the solar system managed to stimulate the student's curiosity, leading her to conduct further research on the topic.