MHB Most Important Precalculus Topics

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Key precalculus topics essential for success in Calculus 1 include a strong understanding of trigonometry, basic geometric facts, and analytic geometry. Mastery of algebra is crucial, particularly in solving linear and quadratic equations and finding polynomial roots. Familiarity with the relationship between function equations and their graphs is also important. Resources like Stewart's Calculus textbook can provide diagnostic exams to assess readiness. A solid foundation in these areas will significantly enhance a student's ability to tackle calculus concepts effectively.
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In your opinion, what are the most important topics in precalculus needed before entering calculus 1? What must a student know well after taking precalculus?
 
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Definitely need to know your trig really well. See http://mathhelpboards.com/trigonometry-12/trigonometry-memorize-trigonometry-derive-35.html for some help on that. You need to know basic geometric facts like areas of squares, rectangles, triangles, and trapezoids. You need analytic geometry - so you're very familiar with going between the equation defining a function and its graph. You also need a significant mastery of basic algebra: finding roots of polynomials, solving equations including linear and quadratic. If you look at Stewart's Calculus book, he has a Diagnostic Exam in the beginning that should help you understand very well what the most important things to know are.
 
Ackbach said:
Definitely need to know your trig really well. See http://mathhelpboards.com/trigonometry-12/trigonometry-memorize-trigonometry-derive-35.html for some help on that. You need to know basic geometric facts like areas of squares, rectangles, triangles, and trapezoids. You need analytic geometry - so you're very familiar with going between the equation defining a function and its graph. You also need a significant mastery of basic algebra: finding roots of polynomials, solving equations including linear and quadratic. If you look at Stewart's Calculus book, he has a Diagnostic Exam in the beginning that should help you understand very well what the most important things to know are.

Thanks but I was looking for a list. I am now waiting for my James Stewart textbook to arrive in the mail. I think precalculus is super cool. It covers so many interesting topics that most students need to master.

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By the way, the great calculus professor, James Stewart, passed away in December 2014.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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