How can I attend university without any formal higher education?

In the United States, many Universities use an privately written and scored entrance examinations.  They are the ACT or the SAT (I don't know what the acronyms mean).  A few years ago, a school would require scores from at least one of these exams.  Today, many schools allow applicants to apply without have scores from either. If you want to attend a US college and earn a baccalaureate degree, I'd suggest you do some homework on which schools would provide you with the training you need (e.g., which majors they have, what types of experiences they offer their students).  Then look at their application requirements.  Do they require ACT or SAT scores?  Does their application require a fee?  There are many schools, among them my employer (Truman State University) that have a free application. Once you know which schools meet your needs, apply.  If you're accepted, that's a sign that the school thinks you will succeed.  Go for it!

Study for and take the SAT. This test and how you score, could make or break your University attempts. In the USA, getting into University after scoring well on the SAT will be easy. They may still require you to take "basics". They will want you to prove that you know "Intermediate Algebra" and "College Algebra". I would try to test out of classes so that they will place you more appropriately. In the USA, they are very ignorant as to what you learn by age 16.  They think that you learn what they learn, in the same year. This would mean Algebra II may or may  not have been taken yet depending on the school district. This would also mean that you never graduated from school. They will assume that you are missing 2 years of maths, social science, English and so on. They will assume that you are lacking in "high school level" Chemistry and Physics, as opposed to the A levels Chemistry and Physics (that we in the USA get at University at age 18-20 on average).  Well, they are closer to what we get at University. From a UK perspective, you will have to look up at the specific University you are looking at applying to. Oxford does require an entrance test. Computer Science will have you taking the MAT test (Mathematics Admissions test). https://www.maths.ox.ac.uk/study-here/undergraduate-study/maths-admissions-test%20 Very good information about past tests. Studying: I would make sure you understand and can solve quickly, quadratic equations, graphing cubics, quadratics and other algebraic equations and inequalities, sequencing and series,  differentiation, integration, logarithms and powers, geometry and trigonometry,  and algebra. I'd work out some mathematical logic problems too. Find a book for studying the MAT (UK version, or  you'll get the silly Miller's Analogy Test book which is not the same thing). My dad taught math. I used to study math textbooks because I thought they looked cool. When I was 3, I vowed someday I will learn this - I was looking at my dad's Calculus book from 1963. I didn't get his math skills. Thus, I still can't do Calculus. I just happen to know some of the maths terms, and have some idea as to what is taught when.