Thanks. The programme specification for the University of Surrey's Accounting and Finance BSc (Hons) - 2023/4,
here, confirms that MAN1060 Business Mathematics is a Compulsory module, but not a Core module. It also confirms that it is worth 15 credits. Although the degree is accredited by a variety of different organisations, the programme specification gives no indication that this places any restrictions on how compensation may be applied. (You'll see why I mention that in a moment.)
All that being the case, if you are able to gain at least 30% in this module, then there is every indication that you will receive compensated credits for it, and be allowed to progress to the next year, despite not reaching the 40% pass mark. Regulation 158 might be an issue, but I'll discuss that below.
Here is what their relevant academic regulations,
here, say with respect to compensation:
"
Undergraduate programmes179. Compensation is available following a failure for units of assessment in modules with a value up to and including 30 credits at FHEQ level 4. At FHEQ levels 5, 6 and 7, compensation is available for modules with a value up to and including 15 credits. Circumstances that can affect eligibility for compensation are described in regulation 158 above.
180. Compensation can be applied if the following two conditions are met:
• the weighted level aggregate of all the student's module marks at a level or stage (including the failed modules) is 40.00% or higher (50.00% or higher for FHEQ Level 7 modules on integrated Masters’ programmes); the weighted level aggregate mark is not rounded up
• the lowest overall mark achieved in a failed module is at least 30% (40% in a failed FHEQ level 7 module on Integrated Master’s programmes)"
Regulation 158, which is mentioned above, says:
"
Failure to attend for assessment/examination158. Where a student has failed an assessment, or reassessment, for a module through failing to attend a required examination (or being late by more than 30 minutes), or by attending a required examination (including online timed open book examinations and online examinations available within a defined window), but not making (in the judgement of the Board of Examiners) a reasonable attempt to address the examination questions, and there are no confirmed extenuating circumstances, the student has failed that unit of assessment at that attempt and will be given a mark of zero. If the attempt was the first attempt and the student fails the module overall as a consequence, they may not progress without reassessment, as described in regulation 155 above, and compensation will only be available after a re-assessment."
The fact that you mention "being sick during the exam and having to leave" leaves you vulnerable to an accusation of "not making (in the judgement of the Board of Examiners) a reasonable attempt to address the examination questions". They say that this will only apply where "there are no confirmed extenuating circumstances". You being sick clearly counts as "extenuating circumstances". Are the university aware that this is why you left early? If so, then this would likely count as "
confirmed extenuating circumstances".
If you were to obtain 30% in this module, and 40% in the other resits, would your "weighted level aggregate of all ... module marks ... (including the failed modules)" be at least 40%? If so, and if regulation 158 doesn't apply, then you should receive compensated credits for this module.