Bring a couple of pens or pencils with you for the test. The exam may be optically scanned, so use a pen only if you are supremely confident in not changing your mind.
An extra pencil is affordable fault tolerance. If you want to splurge, the Palomino Blackwing 602 is considered by many to be one of the finest pencils available. The company advertises its key virtue as half the pressure, twice the speed. If that claim is really true, using this product might help you complete the exam quicker.
If you coose not to bring extra pencils, you may want to bring a pencil sharpener. Palamino makes a companion Blackwing Long Point Sharpener. This is somewhat pricey at $24.50. For less money, you can get what looks like a blue-colored clone: the AS2M Long Point Sharpener. Both of these feature two-step sharpening: one for the wood case and another for the graphite core of the pencil.
If you want to go for a high-end model, you’ll want the El Casco Pencil Sharpener, but bringing this to class is overkill, as is spending $700+ on a pencil sharpener (it was only around $300 a few years ago).
If you want to splurge on a beautifully designed pencil with an integrated sharpener, you want the Graf von Faber-Castell Perfect Pencil. This costs $374 for the black edition ($495 for the magnum black edition). You’ll feel bad when you lose it.
Sadly, the only store in the New York City area that was dedicated exclusively to selling pencils, CW Pencil Enterprises, at 15 Orchard St on the lower East Side, closed their doors in 2021. You will have to either shop online or visit a store that sells other products and is unlikely to have any sales staff with specific expertise in pencils.
If you would like to learn the craft of pencil sharpening, there are several fine books available. The best of these may be How to Sharpen Pencils: A Practical & Theoretical Treatise on the Artisanal Craft of Pencil Sharpening for Writers, Artists, Contractors, Flange Turners, Anglesmiths, & Civil Servants by David Rees. I personally own a copy and recommend this if you want to take the time to learn this fine but often neglected craft. Do not be intimidated by the omission of “students” in the title.
You can read more about it at artisinalpencilsharpening.com. You can also watch a video on the topic by David Rees. You are welcome to bring a full pencil sharpening travel kit to the exam, but be aware that a proper sharpening routine may consume far too much time during the exam and may be messy.