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Master essential mathematical concepts and problem-solving techniques in this comprehensive pre-calculus course spanning over 10 hours of instruction. Begin with foundational topics including sets, complex number operations, and quadratic functions through multiple solution methods including factoring, completing the square, and the quadratic formula. Explore nth roots, real exponents, systems of linear equations and inequalities, and matrix operations to build algebraic proficiency. Dive deep into functions within the calculus context, analyzing graphs of relations and functions while examining continuity, end behavior, and limits. Study extrema and average rate of change, parent functions and transformations, function operations and composition, plus inverse functions and relations. Progress through power and radical functions before tackling exponential and logarithmic equations using various approaches including quadratic exponential methods. Apply the Rational Zeros Theorem, upper and lower bounds techniques, and Descartes' Rule of Signs to find polynomial zeros through multiple worked examples. Conclude with practical applications in trigonometry including Heron's formula and area calculations for triangles using the SAS method, preparing you thoroughly for calculus-level mathematics.
