The following are correct -
Medical exams can help people live longer lives.
This is true because through medical exams possible health issues can be detected which can be treated and enable the person to live longer.
Medical exams are mandatory for all employment.
This is true because potential employees need to know about any existing health conditions in employees for insurance reasons.
Medical exams can help record changes in health over time.
This is true because keeping a record of health changes allows medical practitioners to monitor the health of a patient and allows the patient to know the state of their own health.
Medical exams can prevent existing issues from getting worse.
This is true as stated above in the first statement.