This is a common USMLE question. Here's some help
Exclusively in the Mitochondria:
Exclusively in the Cytoplasm:
- Fatty acid oxidation (Beta-oxidation).
- Oxidative phosphorylation and Electron transport chain.
- Ketone body synthesis, AKA Acetyl Co A synthesis.
- Krebs cycle, AKA TCA cycle.
Both mitochondria and cytoplasm:
- Gluconeogenesis (basically the reverse of glycolysis though you need the malate shuttle to bring oxaloacetate from the mitochondria.
- Hexose Mono Phosphate (HMP) shunt.
- Cholestrol synthesis (as it needs the above two to supply Acetyl CoA and NADPH respectively).
- Protein synthesis (RER).
- Steroid synthesis (SER).
- Heme synthesis.
- Urea cycle (Where you have ornithine and citrulline jumping between the two sides).
- Gluconeogenesis (this is listed here in FA, but see note above).
- Fatty acid synthesis (this is not listed here in FA but citrate shuttle needed between the mitochondria and the cytoplasm).