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In USA, there is a course called College Algebra and a course description may look like the following:

This course provides students an opportunity to gain algebraic knowledge needed in many different fields such as engineering, business, education, science, computer technology, and mathematics. Graphical, numerical, symbolic, and verbal methods support the study of functions and their corresponding equations and inequalities. Students will study linear, quadratic, rational, exponential, logarithmic, inverse, composite, radical, and absolute value functions; systems of equations and inequalities modeling applied problems; and curve fitting techniques. There will be extensive use of graphing calculators.

How about in other places such as UK, Russia, India, China, Japan, Brazil, Germany, etc.? What course will be roughly equivalent to College Algebra in other countries?

I am not expecting a complete answer. A few examples will be greatly appreciated.

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    $\begingroup$ Even in the US, College Algebra is really just a euphemism for pre-calculus. It's a term used at community colleges and other schools that have nonselective admissions. It's really a high school course, and high schools call it pre-calculus. At the community college where I teach, the first sentence of the catalog description for College Algebra defines it using the word "pre-calculus." At UC Berkeley, the class is Math 32, Precalculus. $\endgroup$
    – user507
    Commented Apr 25, 2020 at 13:42
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    $\begingroup$ @BenCrowell: A CUNY, there are separate College Algebra and Precalculus courses (separate steps in the standard sequence). Another example: OpenStax has separate College Algebra and Precalculus textbooks (openstax.org/subjects/math). So I'd say they're not generally, exactly synonymous. $\endgroup$
    – Daniel R. Collins
    Commented Apr 27, 2020 at 1:59

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In the UK, what you describe lies somewhere in between GCSE and A-Level Maths. Both of these exams are intended for secondary school students.

It is unusual for these topics to be taught at the university level, and if they are taught, it is often not by the Maths department. For example, the Economics department might have such a course for their first year undergraduates with insufficient maths background. A small number of British universities offer a 'Foundation Year' before beginning an undergraduate degree. A Foundation Year for a scientific degree would cover these topics.

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I am going to list the topics from the Russian Algebra/PreCalc school program, and you decide for yourself. The material below is mandatory for all students. I did not include optional material.

Russia has 11-year grade school; it used to have 10-year until late 1990s. No K class. The age to enroll 1st grade is between 6.5 and 8 years old.

There is no "college algebra" in Russia. The lowest university math course is calculus.

8 grade: [14-16 years]

  • Simple functions
  • Functions and graphs
  • Functions $y=x$, $y=x^2$, $y=\frac 1 x$
  • Square roots
  • Quadratic and rational equations
  • Linear, quadratic and reciprocal functions
  • Systems of linear equations

9 grade:

  • Inequalities
  • Linear one-variable inequalities
  • Quadratic one-variable inequalities
  • Rational inequalities
  • Power
  • Function $y^n$
  • n-th root
  • Sequences
  • Arithmetic progression
  • Geometric progression
  • Intro to theory of probability, statistics and combinatorics
  • Approximations
  • Descriptive statistics
  • Permutations, combinations, partitions
  • Experiments, outcomes, events

10 grade:

  • Roots, powers, logarithms
  • Trigonometric formulas and functions
  • Sine and cosine
  • Tangent and cotangent
  • Trigonometric identities
  • Trigonometric functions
  • Trigonometric equations and inequalities
  • Intro to probability theory
  • Probability
  • Conditional probability
  • Frequency of events

11 grade

  • Functions, derivative, integral
  • Functions and their graphs
  • Limit of a function, continuity
  • Inverse functions
  • Derivative
  • Application of derivative
  • Antiderivative and integral
  • Equations, inequalities, and systems of them
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  • $\begingroup$ Just one unimportant correction. The switch from 10 to 11 years of grade school hapenned in 1990 (when it was still Soviet Union, technically speaking), not in the late 1990s. That's why I graduated from 11th grade after 10 years of schooling -- our year went from 9th grade straight to 11th. :-) $\endgroup$
    – zipirovich
    Commented May 25, 2020 at 16:14
  • $\begingroup$ It's also very common for schools to "skip" 4th grade (so 5th comes right after 3rd), so education still takes 10 years. $\endgroup$
    – Dan M.
    Commented Apr 22, 2021 at 11:23
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[Too long to fit in comments and addressing your meta-questions, versus just a square peg for square question response.]

It's basically the same thing as "Algebra 2" in US high school. The funny thing is it is an anachronism to call it College Algebra. Prior to WW2, it was common that US high schools only had first year algebra and geometry. Thus "Algebra 2" was a college course as was trigononmetry. And College Algebra really was college algebra.

However, the stereotypical norm now is for kids to do 9th grade algebra one (lines mostly), 10th geometry, 11th algebra two (logs, exponents, etc.), 12th trig and other precalculus. Calculus is the normal first year college course. Of course some kids are accelerated and do calc in HS. But it is still considered college material. Thus the AP test.

A kid who takes College Algebra in college is remedial now. He should be nominally taking first semester calculus as he starts freshman year if he is neither remedial nor accelerated track.

P.s. Some kids will even have had some calculus in HS (it is probably the most commonly accelerated subject) in either an AP class or some easier version. However, many of them still have to take calc as freshmen as they really didn't master it in high school (can't pass an AP, can't pass a college-specific placement exam) but just got some exposure. Some weaker ones even end up in precalculus although they were in a "calculus class" in HS.

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  • $\begingroup$ This is interesting, but not an answer to the question. $\endgroup$
    – user507
    Commented Apr 25, 2020 at 18:37
  • $\begingroup$ -1 College Algebra is not remedial. At community colleges it is generally referred to as the "gateway" (first credit-bearing) math course in the calculus track. $\endgroup$
    – Daniel R. Collins
    Commented Apr 27, 2020 at 2:02
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    $\begingroup$ @DanielR.Collins: Defining "remedial" is ultimately subjective and politicized. Community colleges are anxious to spare the egos of students by labeling things as college-level when they're really high school classes. The word "remedial" is taboo at my school for this reason, and we speak of "developmental" classes. It doesn't change the reality that college freshmen are not supposed to have to be taught algebra. $\endgroup$
    – user507
    Commented Apr 28, 2021 at 13:44
  • $\begingroup$ @BenCrowell: Read "remedial" as "non-credit" if that helps in your case. $\endgroup$
    – Daniel R. Collins
    Commented Apr 28, 2021 at 14:13
  • $\begingroup$ @DanielR.Collins Could you clarify? Your two statements don't seem to agree. Are you saying that college algebra can be credit bearing, in which case it is not remedial, or can be non credit bearing, it which case it is remedial? And this depends on an institution. Is this what you are saying? $\endgroup$
    – Rusty Core
    Commented Apr 29, 2021 at 6:37
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In Spain these things are generally not taught at the university level and there is no course comparable to what you call College Algebra, as these topics form part of the high school curriculum. Some degree programs offer a "Zero Course" that reviews mathematical material from high school, but such a course usually focuses on graphing functions using basic calculus.

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    $\begingroup$ These are also taught in high school in the US. But not all high school students take advantage of it. And some of those students later go to a college or university and need to learn that material. That is "College Algebra". One description I heard: high school material taught at college speed. This is similar to beginning foreign language courses offered in colleges and universities: the same as high school courses, but done with higher speed. $\endgroup$
    – Gerald Edgar
    Commented May 16, 2020 at 14:50
  • $\begingroup$ @GeraldEdgar "These are also taught in high school in the US. But not all high school students take advantage of it." — which means it is not compulsory. Dan Fox says, that it is compulsory in Spain, so no need to re-take it in college. $\endgroup$
    – Rusty Core
    Commented May 21, 2020 at 4:29
  • $\begingroup$ In Spain: every child takes it, or only those in certain "advanced" or "technical" schools or tracks? What an idea: every cab driver, every baker, every gardener knows algebra! In the US, most gardeners do not know algebra; but some of them decide later to advance their education, so universities offer remedial courses like "College Algebra". $\endgroup$
    – Gerald Edgar
    Commented May 21, 2020 at 9:39
  • $\begingroup$ @GeraldEdgar I did not say these things are compulsory. I said they are not taught in the university and they are part of the high school curriculum. A student going to the university has completed the Bachillerato and taken an entrance exam. There are various tracks - Sciences, Social Sciences, Humanities, and Arts. The first two require math including linear algebra, calculus, basic probability, basic linear programming, etc. and these subjects are examined in the university entrance exam. Any university level degree program requiring use of mathematics draws from the tracks that require it. $\endgroup$
    – Dan Fox
    Commented May 21, 2020 at 15:00

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