Cristae = inner membrane infoldings of the mitochondria a) ..

The inner membrane of a mitochondrion is folded into cristaehas a large surface area.

Mitochondria- Cristae, Matrix - Mrs. Graham's AP Biology

You should already know from your GCSE studies that mitochondria are the sites of ATP production, but for “A” level you must be able to explain where all the chemical reactions of tissue respiration take place. Glycolysis, the breakdown of glucose to form acetyl coenzyme A, takes place in the cytoplasm outside mitochondria. The Kreb’s cycle, breaking down acetyl coenzyme A into carbon dioxide and NADPH, takes place in the matrix of the mitochondrion. Some ATP is generated directly during the Kreb’s cycle, but most of the ATP produced in tissue respiration is generated by the electron transfer chain which takes place across the membranes of the mitochondrion. Stalked particles on the inner surface of cristae contain the enzymes required to make ATP from ADP and phosphate.

Macromolecular organization of ATP synthase and …

The host cell can not make ATP by electron transport in aerobic respiration without
mitochondria, but it does carry out glycolysis in the cytosol and then transports the end product, pyruvate, into the
mitochondria where it is used in Kreb's cycle which takes place in the mitochondrial matrix (the 'mitochondrial cytosol').

The cristae increase the surface area for packing in many electron transport
systems and ATPase molecules - the mitochondria is specialised for electron transport and uses oxygen to drive the ETS and
uses the resultant proton gradient to make ATP for the whole eukaryotic cell.