You do not need to memorize the periodic table. You need to memorize four trends and the electron-shell reasoning that produces them.
Atomic radius: decreases across a period, increases down a group. Reason: more protons pull the same shell tighter across a period; a new shell adds distance going down a group.
Ionization energy: increases across a period, decreases down a group. Reason: harder to remove an electron from a tightly-held small atom; easier from a large, loosely-held outer shell.
Electronegativity: increases across a period, decreases down a group. Fluorine is the peak. Cesium is near the floor.
Metallic character: decreases across a period, increases down a group — the mirror of electronegativity.
Any exam question on trends reduces to picking the right two elements and applying one of these four rules. Do not try to memorize specific values.