Could anyone familiar with Singapore please tell me what is the name of a common textbook used for Math in Singapore's secondary schools? I am looking for topics covered for ages 14-18. I am very interested in what I have heard about Singapore's math education, so it's mostly to see their approach since I also do not like the vast majority of American math textbooks.
I'm only moderately familiar with Singapore, but here is what I know.
There was an older textbook series for ages 12 to 16 called "New Elementary Mathematics: Syllabus D" Books 1 to 4. I doubt all schools used it, but I think it was from the same publishing company that put out the elementary-level books that were eventually sold in the U.S. I'm not sure what they use now.
The series was formerly sold in the United States. Here is a review by, I assume, a homeschooling U.S. parent: https://cathyduffyreviews.com/homeschool-reviews-core-curricula/math/math-grades-7-8/new-elementary-mathematics
If you do a search for "Ordinary Level mathematics" (about the top 60% at ages 12-16), "Additional Mathematics" (for some proportion of students aged 14-16) and "Advanced Level Mathematics" (ages 16-18), you'll turn up some materials used now.
See here for the official curricula at O-Level: https://en.wikipedia.org/wiki/Singapore-Cambridge_GCE_Ordinary_Level
For A-Level, you ought to be able to find syllabi by searching for H1 Mathematics, H2 Mathematics, H2 Further Mathematics and H3 Mathematics. According to this thread, textbooks aren't widely used at this level, but there are textbooks for similar exams offered by "Cambridge International" up to the "Further Maths" level: https://www.reddit.com/r/SGExams/comments/jzz91o/a_levels_h2_maths_and_further_maths_textbook/
The entire Singapore curriculum at the secondary level is modelled on older curricula in use in England (probably about pre-1985). So if you want more textbooks like that, you can look at the books in use in England in that period. They were very different from the ones used now because at that time the top 25% had their own curricula and were sometimes educated in separate schools. Beware of pre-1970 books, though, as they use Imperial units and non-decimal (!) currency.
If you want to see what was typical in the early 1980s for ages 11 to 15 or 16 in England (in the top 25%), there are some books on the Internet Archive called "New General Mathematics for West Africa" by Channon and McLeish Smith. These are basically the same as the British textbooks but with "London" replaced with "Lagos" and pounds with local currencies, etc. (I'm not saying these are the best textbooks, but at least you can look at them.) For "Additional Mathematics" for advanced students at ages 15-16, see "Pure Mathematics: A First Course" by Backhouse, also on the Internet Archive. This was also a first-year book at Advanced Level (age 16-17) for those who hadn't taken Additional Mathematics. I believe all of this is quite similar in approach to the Singapore curriculum.
The main difference between the Singapore syllabus and most English syllabi about pre-1980 appears to be that some pure geometry was taken out and some vectors and transformations added in.
Edit: Here are some links to official syllabi and additional information provided to me in the comments. (Thank you.)
2022 syllabus for H2 Mathematics (generally with Additional Mathematics as prerequisite)
2022 syllabus for H2 Further Mathematics (with H2 Mathematics as corequisite)
2022 syllabus for H3 Mathematics (with H2 Mathematics as corequisite)
2022 Syllabus for H1 Mathematics (a proper subset of H2 mathematics, not taken by those offering H2 Mathematics)
Edit: Here is some additional information from the deleted comments.
here's a slightly cleaner summary:Additional Mathematics (100% Pure Mathematics) is a prerequisite for H2 Mathematics (Pure Mathematics : Probability&Statistics = 3:1), which is a co-requisite for H2 Further Mathematics and H3 Mathematics (both 100% Pure Mathematics)
H1 (Pure Mathematics : Probability&Statistics = 4:6) is restricted to non-H2 candidates, and a comparison of its syllabus with that of Additional Mathematics above reveals that about 30% of the former overlaps with the latter, and about 60% of the latter overlaps with the former. The H1 content is a proper subset of the H2 content; there is no other overlap among these various Mathematics courses.
The O-level (Elementary) Mathematics course takes place over four years (13-16yo), and the Additional Mathematics alongside it over the final 2 years (15-16yo); they are designed to occur in parallel, so the texts don't overlap, although some pre-requisite stuff from EM does get reviewed at the beginning of the relevant AM chapters, and complementary topics across the two subjects occur alongside each other.
About half of all 16-year-olds take Additional Mathematics, a minority which will go on to take H1 instead of H2, which will have been taken by half of all the college students (all the STEM ones and some of the non-STEM ones). Further Mathematics is a very unpopular course; almost nobody takes H3 Mathematics.