Extra Exam Exercises (+ solutions) MIDTERM Mathematics for Premaster

Exam exercises Mathematics for Premaster MIDTERM
This is a preview of the extra exam exercises that you can use to prepare for your
midterm. I have successfully passed the premaster in 2019 myself, and since I received a
9 on mathematics, I tutored a bunch of students in 2020. For a crash course, I created
these 30 exercises with extensive elaboration of the answers myself. This might be very
helpful, because you haven’t practiced with these before.


Please note that copyright belongs to the creator of this document.
It is forbidden to freely distribute this file.


If you have bought this document, you can skip the first 6 pages (until ‘END OF
PREVIEW’) as these first pages are adapted with black lines to serve the preview.


Part I


1. Determine the zeros of the following polynomial function: 2𝑥 4 − 7𝑥 2 + 3.


2. Consider the functions 𝑦1 = 5𝑥+3 and 𝑦2 = 3100 + 5𝑥 . Determine the points of
intersection of the graphs of these functions.


3. Solve the following equation: ln(𝑥 + 4) + ln(𝑥 + 8) = 0.


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,Part II


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1 2
28. Determine the intervals on which the function 𝑦(𝑥) = 𝑥𝑒 −2𝑥 is
convex/concave.


29. Determine all 𝑝 for which the function 𝑧(𝑥, 𝑦) = 𝑝𝑥 2 + 2𝑥𝑦 + 𝑦 2 is convex.


1 1
30. Determine all extrema of the function 𝑦(𝑥) = 𝑥 + 4 𝑥 (𝑥 ≥ 1).

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,