high, top
a piece of high-grade building land
He still wants to play top-grade football.

low, poor
low-grade steel

final
The oral exam constitutes 10% of the final grade.

A, B, etc.
an A-grade essay

excellent, good, high
bad, low, poor
failing, passing (both AmE)
She got a failing grade for that assignment.

course (AmE)

achieve, attain, earn, get, have, receive
She got good grades in her exams. (BrE)
She got good grades on her exams. (AmE)

bring up (esp. AmE), improve, raise (esp. AmE)
I need to improve my grades.

award (sb), give sb

grade point average (AmE)
You've maintained a 3.9 grade point average.

high, senior
He has asked to be put onto a higher grade.
large pay increases for senior grades

junior, low
pay

at a/the … grade
She was offered a job at a lower grade.

on a/the … grade
The majority of staff are on the same grade.

sixth, third, etc.
Sam is in (the) second grade.

enter, start
My son will be starting third grade this fall.

complete, finish
skip
He skipped a grade so he finished high school early.

reach
teach

level
school

in … grade
My daughter is in (the) fifth grade.

carefully
a series of stories carefully graded for beginner to intermediate students (esp. BrE)

finely
finely graded nuances of language

according to
The timber is graded according to its thickness.

by
The containers are graded by size.

from … to …
Eggs are graded from small to extra large.

fairly, objectively
I don't think he graded our essays fairly.

Grade is used with these nouns as the object:
exam, homework, test