Ergänzungsprüfung Mathematik in Graz (VGUH): the written exam, calculators and a worked problem

The supplementary maths exam in Graz is for anyone admitted by the University of Graz or another Graz university on condition that they pass mathematics. It's run by VGUH, the preparatory course of Graz's universities, and whether you've been assigned it is stated in your admission decision, the Zulassungsbescheid.

In Graz this exam is written only: there's no oral part. VGUH doesn't publish a points threshold; you pass if your paper is graded positively. You can prepare on the VGUH maths course, but you're admitted to the exam without it too, and you can see what the papers look like before your first attempt.

How the Graz maths exam is structured

The written paper runs 180 minutes.¹

It's marked by two examiners, and the result has to be communicated within four weeks at the latest. Grades run from 1 to 5, where 5 means a fail; the rules don't say how many points or what percentage you need for a 4.²

The course syllabus is divided into nine topics: algebra, functions, trigonometry, sequences, vectors in the plane and in space, derivatives, integrals, probability and complex numbers. The syllabus file was created in 2018. The eight papers from 2023–2025 contain no tasks on complex numbers or sequences.³

The papers fall into five blocks: trigonometry, vectors, growth and decay, calculus, and probability, and all five appear in each of the eight papers. Curve sketching, extrema, area by integration, volume of a solid of revolution and the normal distribution come up in all eight papers; the binomial distribution, the sine rule and planes in space in seven.

Calculators and formula booklet in Graz

Four calculator models are allowed: TI 30 X II S, TI 30 X II B, TI 30 X a and TI 30 ECO RS. You don't need to bring your own formula booklet: the AHS school formula booklet published by ÖBV is handed out at the exam.⁴

A worked VGUH problem: caffeine breakdown

This problem is from the June 2025 paper, in the growth and decay block. Caffeine breaks down in the body exponentially, with a half-life of about four hours. A woman drinks a coffee with 100 mg of caffeine at 7:00, a cola with 40 mg at 13:00, and another cup of coffee at 15:00. How much caffeine is in her body right after that, and when will it be down to 50 mg?

First the decay constant: from $e^{-4\lambda }=\frac{1}{2}$ we get $\lambda =\frac{\ln 2}{4}\approx 0.1733$ per hour. It's easy to go wrong here by letting every portion decay from 7:00. Each one decays for its own time: the morning coffee for eight hours, the cola for two, and the second cup hasn't started yet. The sum of the three portions at 15:00 works out like this.

From then on all three portions decay together, and what's left is to solve $153.28\cdot e^{-\lambda s}=50$. That gives $s=\frac{\ln (153.28/50)}{\lambda }\approx 6.46$ hours, so at about 21:28.

VGUH dates, registration and retakes

The next maths exam takes place on 14 October 2026, and registration for it has already closed. You register through your VGUH account and, within the same window, send proof of payment to office@vguh.at. You can withdraw up to five working days before the exam; if you're registered and don't turn up, the attempt still counts and the fee isn't refunded. VGUH hasn't published the further dates for 2026/27 yet.¹

The fee is €66 per exam.⁴

You can retake a failed exam three times, so you have four attempts in total. The third retake is held before a commission.²

How to prepare for VGUH maths

1. Do one past paper in full in 180 minutes, with one of the allowed calculators and the AHS formula booklet.
2. Check it against the worked solutions and note which of the five blocks cost you the most.
3. Work on that block in the VGUH trainer: the tasks there are sorted by the same topics, and your answer is checked straight away.
4. Do the next paper and compare the blocks.

How Graz differs from Vienna overall, from course fees to housing, is covered in the article on Graz.

Sources

· 4 checked 01.10.2026

1. 1Anmeldung Ergänzungsprüfungen, 2. Termin WS 2026/27, VGUH · checked 01.10.2026
2. 2Prüfungsordnung VGUH, gültig ab Sommersemester 2026 · dated 01.01.2026, checked 23.09.2026
3. 3Lehr- und Lerninhalte MATHEMATIK, VGUH · checked 01.10.2026
4. 4VGUH — Prüfungen, Vorstudienlehrgang der Grazer Universitäten · checked 23.09.2026