That depends on your syllabus. Indeed, approaches to Special Relativity are quite varied, and can depend on, e.g., what you are using it for.
I try to understand SR in terms of representations (such as scalars, vectors, tensors, and how to write Lorentz transforms in matrix form) and invariants (such as the speed of light, contractions, and the metric tensor). Then, how are these things physically interpretted.
Depending on how complex and involved your course is, think about:
- metric (tensor): proper length/time, contraction, raising and lowering indices, invariance of
- Lorentz transform: matrix representation, system of equations, gamma and beta, raptidity, pseudo-rapidity, rotations vs. boosts, decomposition into a rotation and a boost, "2x2 matrix" representation (Pauli matrices or quaternions)
- the distinction between: proper time and coordinate time, rest mass and "relativistic mass", proper velocity and coordinate velocity
Some specific issues/applications that could appear:
- resolving the twin paradox (and variaous other paradoxes)
- elegant formulation of electromagnetism: 4-current density, Faraday tensor, Levi-Civita tensor (I would argue that this is of particular importance/relevance to SR, and you should focus on this regardless of what's on the exam.)
- timing and stability in particle accelerators
- kinematical distributions (e.g. in angle, energy, invariant mass, etc.)
