In fact, we can't generalize the difficulty of mathematics in American high schools, because American high schools follow the principle of teaching students in accordance with their aptitude and adopt different educational methods for students with different learning abilities. For students with mathematical ability, schools can offer AP courses in American high schools to meet students' learning needs, so it is impossible to generalize whether mathematics in American high schools is simple or easy.
Mathematics courses in American high schools are generally taught in the order of basic algebra-geometry-advanced algebra-calculus preparatory course-calculus. That is to say, after finishing junior high school in China, you can take calculus preparatory course directly, which mainly involves some functions (especially trigonometric functions). After taking the pre-calculus course, you have theoretically completed the mathematics in American high schools.
Let me tell you about the AP(Advanced Placement) course in American high schools, which is a basic freshman course for high school students. AP calculus can be divided into AB and BC, and the latter has more contents about sequence, convergence judgment and Taylor expansion than the former.
AP calculus course is composed of learning tasks for a whole school year in middle school, which is equivalent to calculus course in university. For the students who take AP calculus course, they expect to get credits or skip grades, or both.
AP courses in American high schools include two calculus courses, and detailed descriptions of the exams of these two courses. These two courses and the corresponding exams are called Calculus AB and Calculus BC.
For students with certain mathematical ability, the school can offer calculus AB as AP course. In design, calculus AB needs to be taught for a whole school year in middle school. But in this school year, I should be able to learn some elementary functions and complete the corresponding calculus AB course. However, if students want to take the AB exam of calculus, then most of the school year must focus on the corresponding calculus course topics. These topics are the focus of AP exam questions.
If students can complete all the listed preparatory courses, then the school can offer calculus BC. Calculus BC is a year-round calculus course about unary functions. It includes all the questions and additional questions in Calculus AB, but these two courses are very challenging and demanding, which require similar in-depth understanding of the same topic. The report of calculus AB score line is based on the score line of calculus AB topic in calculus BC exam.
These two courses represent university-level mathematics courses, and most universities give them the advantage of advanced placement and/or increasing credits. Most universities will offer a series of calculus courses, and students who enter the university will be arranged to skip classes according to their preparation and mastery of the courses (that is, AP test scores or other standards). According to different local policies, universities will give appropriate credits and advanced placement. Compared with Calculus AB, Calculus BC can give students more credits or advanced placement advantages. Many universities provide statements about AP policies in their subject catalogs or websites.
The key to the success of AP calculus learning is closely related to students' preparation for AP course. Before studying calculus, students should be able to master the curriculum materials equivalent to four years of mathematics in middle school. These courses should include algebra, geometry, coordinate geometry and trigonometry, and in the fourth year of study, they also include advanced topics such as algebra, trigonometry, analytic geometry and elementary functions.
It can be seen from the above introduction that "the mathematics learned by American high school students is very simple" is a false proposition. One of the great benefits of American education to students is that it allows young people to spend extra time and energy on what they like to do. Usually studying philosophy, history, art, playing orchestral music and physical education is very helpful for students' growth.