That article appears to conflate "mastering algebra" with passing an Algebra 1 course (or passing an Algebra 2 course, in places). Is that a reasonable conflation, in the US system? In the UK, a student needs to get grade A-C at GCSE mathematics (exam taken age 16) in order to be counted in certain "success" statistics for the school, and in order to go to university (any subject). The GCSE syllabus includes a lot of what you call Algebra 1 or Geometry e.g. solve quadratics, do stuff with the equation of a straight line, work with exponents, calculate volumes and areas of various 3D shapes, prove simple things using circle theorems, etc. However, getting a C at GCSE is a pretty low hurdle, and by no means proves that you've "mastered" all that material.

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