What kind of psychological test yields information about cognitive functioning and the presence of learning disabilities?

When a psychologist wants to evaluate cognitive functioning in a person, he does a psychological assessment. The psychologist can then evaluate that person to see if everything is functioning normally. However, there is another test for learning disabilities. If a teacher detects them in a child, he can refer this child so he can take specialized testing done by a psychologist or another professional, like a teacher, who has received the formation in order to give out those kinds of tests.