vitamin A or D
Large protein: Some very large proteins will not pass through the cell membrane AT ALL!. However, the fact that some people are allergic to certain proteins tells us that these proteins are capable of passing through the epithelial cells of the villi in the small intestine (as intact proteins) - this process involves special movement across membranes by active transport via specialized channels; this is usually an abnormal phenomenon e.g. the passage of protein in the urine (=protenuria) is not good news!
Ions: Some by simple diffusion; others by the presence of an electrochemical gradient; still others by active transport e.g. Na+ reabsorption in the proximal tubule of the kidney using Na+, K+ - ATPase (these cells have many mitochondria (why??) and have microvilli (again, why??) OR by co-transport e.g. glucose transporter (GLUT1) can also carry some ions jointly with the glucose carried across.
Hope this helps!
M (specialist biology tutor)