What are the different methods of transport across a membrane ?

If I remember correctly, there are two main types of transport—passive and active. Passive transport does not require energy or ATP, whereas active transport does.

Types of passive transport include diffusion and osmosis, both of which involve moving down a concentration gradient and thus not requiring energy.

Active transport moves up the concentration gradient and does require energy.

Perhaps someone who has taken bio within the last several years can correct anything I might have misstated here.

Only algae, oak trees, and bermuda grass produce atp by photosynthesis i am almost positive