Questions & Answers about Jeg har eksamen i norsk neste måned.
Norwegian uses the fixed expression å ha eksamen for talking about exams in general:
- Jeg har eksamen neste måned. – I have an exam next month.
- Hun har eksamen i dag. – She has an exam today.
You can also say å ta eksamen, but that focuses more on the act of sitting / taking the exam at that moment:
- Jeg skal ta eksamen i norsk neste måned. – I’m going to take the Norwegian exam next month.
Å gjøre eksamen is not idiomatic in this context.