What if school makes it mandatory to take algebra and geometry during middle school? What would the mathematical order be in high school?
Depends on the school.
Our local public in OH had the option to do algebra and geometry in middle school. The progression in HS was Alg II, Trig/Precalc, Stats, AP Calc
In our new area the progression is Alg II, Trig/Pre-calc, AP calc, MV Calc
Check your HS’s course progression.
You need to discuss this with your local school – either the guidance counselor or math teacher.
Most common sequence (regardless of whether starting in 7th, 8th, or 9th grade):
Algebra 1, Geometry, Algebra 2, Precalculus / Trigonometry, Calculus
An alternative variation is switching the order of Geometry and Algebra 2. Some students try to accelerate by taking Geometry and Algebra 2 together. At some high schools, topics may be rearranged so that Trigonometry is included in Algebra 2, while other concepts are moved from Algebra 2 into Precalculus.
Integrated Math variation:
Integrated Math 1, Integrated Math 2, Integrated Math 3, Precalculus / Trigonometry, Calculus
The concepts of Algebra 1, Geometry, and Algebra 2 are taught in the three Integrated Math courses, although the most Geometry-heavy course is usually Integrated Math 2.
In a few high schools, an accelerated or honors sequence is offered that covers Trigonometry and other Precalculus topics by the end of Algebra 2 or Integrated Math 3, so that students who do well can go directly to Calculus after that.
You should check your specific school district about what its math sequence is.
I took A1 and Geometry in middle school, then A2, precalc/trig, AP Calc AB, and AP Calc BC and AP Stats senior year. I know of a few very advanced students who took dual enrollment Calc 3/ Multivariable Calc or DiffEq
In my area, algebra first then geometry
I’m not sure that when you start matters. My D and a couple friends accelerated to Algebra 1 in 6th but took the same Algebra 1, Geometry, Algebra 2, PreCalc, Calculus sequence that everyone takes.
Calculus can be just AB, just BC, or a sequence of both. After any of those could be AP Stats or a multivariate Calc course if your school offers it.
It’s also possible to inject Stats somewhere between PreCalc and the end of Calculus courses.
(There are a outliers that have in-school or DE offerings of Linear, DiffEq, etc, but those aren’t “typical”.).
This is the progression here : Algebra 1, Geometry, Algebra 2, Precalculus / Trigonometry, Calculus AB, Calculus BC although some will opt out of Calc and take Statistics.