Since everybody seems to have missed it when Oblique posted the FAR, allow me to reiterate:
14 CFR 61.35 requires, for all written exams, identification which shows that the written results will not expire before the applicant is old enough to take the practical. This means that you must be 15 to take the private pilot written, 16 to take the commercial written, etc - even if those ages aren't specifically spelled out in the FARs.