考 first meant 'aged father' — the 耂 radical is an old man leaning on a stick. Because elders questioned and examined the young, 考 slid from 'the old one' to 'the one who tests'. Every exam carries a white-haired examiner inside it.
科举 the imperial exam ran for 1300 years and made 考 the hinge of Chinese life; its descendant 高考 the college entrance exam still stops traffic every June — literally, streets near exam sites close so students can 考 in silence.
An elder 耂 with questions stuck 丂 in his throat — about to TEST you.
考古 'examine the ancient' is archaeology — the exam where the questions are buried and the answers are shards.