At the link below, The Tablet offers an excellent guide to the Catholic elementary schools in Brooklyn and Queens. There are two improvements this year: a disclosure of basic tuition rates, which vary considerably by neighborhood; and excellent maps.
Please see https://thetablet.org/back-to-school-2023/
The Archdiocese of New York (seven counties), the Diocese of Brooklyn (two counties), and the Diocese of Rockville Centre (two counties) generally require the test offered on the website https://tachsinfo.com/
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The test is taken by computer at home. It costs $71. The student selects three high schools to which the testing company will send results. The test is apparently scheduled for early November, 2023. Apparently there is some way the downloaded program knows that is is the registered eighth grade student and not a learned grandma answering the test questions.
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The abbreviated name for the test is TACHS. Much more information is at https://tachsinfo.com/
