At the end of school life, those attending US schools leave with a High School Diploma, which is a reflection the 14 years of work proceeding it.
Having a high school diploma is essential for university entrance, but also in some ways also irrelevant. Getting into US university is not based on a final grade at high school. Rather US universities take a distinctly less academic view, looking at your profile as a whole: The number of courses you have taken (how academically interested are you), how you're expected to do in those courses (US universities will offer you a place before you sit your final exams), and your extra curricular activities (what are you going to contribute to college life, not just your course).
The US is also less focused on what you have studied. To some degree this reflects the fact that you don’t usually decide what your main focus at a US college until the end of your second year. In the UK, and Europe as a whole, you focus almost immediately on one subject.
Finally, perhaps the "real" exam or pass you are looking for for for US universities is not the US high school diploma, but your SAT, or “Scholastic Assessment Test”. This is a compulsory test, and determines your abilities in writing, mathematics and “critical reading” or reasoning.
In other words your high school diploma matters only in as much it reflects what you have done with your time at school, which in turn will reflect how a university sees you as a human being. It will be one facet of what a college will be looking for.
This for example is what Columbia University says matters:
- The student’s curriculum and grades - we hope to see that a student is challenging herself or himself with a rigorous course load
- The context of a particular candidate, including family circumstances, secondary school, community, interests and access to resources
- The quality of a student’s involvement in activities beyond the classroom
- The character and personality of a candidate, and the impact she or he will make on our diverse, residential campus
- The candidate’s fit for the distinctive Columbia experience, which includes the Core Curriculum; a both traditionally collegiate and unmistakably urban campus life; and an Ivy League school where curious thinkers come to grow
- Recommendations - which provide evidence of intellectual curiosity and promise, classroom and school and community participation, and overall potential for the candidate to make an impact at Columbia, in the classroom and beyond
Criteria to actually obtain your high school diploma will vary from state to state - one of the reasons why talking about a "US education" or curriculum is difficult. It will require at a minimum the continued study of core subjects and a minimum grade point average.
Note: Academically gifted students at US high schools will also look to take Advanced Placement (AP) exams. Again, how well you do at these exams will not determine your success or otherwise in university admission. It will however send a statement regarding how much you challenge yourself academically, your intellectual ambition, and perhaps your overall potential. Students capable of doing well at the AP exam will also take it because it will give you college credit.