Pennies made after 1982 are made of Zinc with a thin copper coating.
To find out if a penny is made of copper or zinc, try the magnet test.
Pennies made of copper are not attracted to magnets, but pennies made of zinc with a copper coating are attracted to magnets. Therefore, if a magnet sticks to the penny, it's made of zinc. If the magnet doesn't stick, it's made of copper.