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A cross-class skill is a skill which is not a class skill for any of your classes. When leveling up, each skill point gives only 0.5 rank if put in a cross-class skill for the class you are leveling into. A leftover half-rank is not worth any skill bonus (so, for example, having 2.5 ranks in Intimidate gives only +2 Intimidate skill).
For pure-class characters, the maximum rank for a cross-class skill is (3 + character level) / 2. This number is not rounded. For multiclass characters, that formula applies only if the skill is cross-class for all the character's classes. Taking even a single level of a class that gets a certain skill as a class skill permanently raises that skill's maximum rank to (3 + character level) — the same maximum formula as a pure class skill — even if the character later takes more levels in classes where it's a cross-class skill again. (This is markedly different from PnP rules.) Note that the cost of a rank at each level still depends on whether the skill is class or cross-class for that level-up.
Intimidate is a class skill for Fighters and cross-class for Monks. A level 1 Monk can buy a maximum of 2 ranks in Intimidate. If she stays pure Monk, she can have up to 2.5 ranks at level 2, 3 ranks at level 3, and so on up to 11.5 ranks at level 20. (Note that that last .5 is a waste.)
Alternately, she could splash a level of Fighter at, say, level 4. Her maximum ranks in intimidate at that level would jump from 3.5 to 7, and for that one level-up she could buy full ranks for 1 skill point each. She could then switch back to taking Monk levels for the rest of her build. Her maximum rank in Intimidate would still rise by 1 every level, though it would cost 2 skill points to stay at the max since the skill would be cross-class again. She'd eventually end up as a Monk 19/Fighter 1 with the same 23 ranks in Intimidate as a pure Fighter, though it would cost almost twice as many skill points overall.