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Public learning track
Advanced Cartesian Lines, Circles, and Tangent-Normal Systems
12th Grade · Track 639 of 698 · 10 lessons
10 lessons
Goal
Analyze straight lines, general and standard forms of circles, and solve geometric problems involving tangents, normals, and intersections.
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Point-Slope and General Linear Equations in Cartesian Space
Public learning track
Advanced Methods of Proof and Mathematical Reasoning
12th Grade · Track 640 of 698 · 11 lessons
11 lessons
Goal
Construct, analyze, and evaluate formal mathematical arguments using deduction, exhaustion, contradiction, contrapositive, and induction across number theory and algebra.
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Direct Proof and Deductive Reasoning in Algebra
Public learning track
Advanced Quadratics, Discriminant Analysis, and Inequalities
12th Grade · Track 641 of 698 · 7 lessons
7 lessons
Goal
Analyze quadratic functions in depth, evaluate discriminants across real and complex roots, and solve quadratic and linear inequalities in one and two variables.
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Completing the Square with Arbitrary Leading Coefficients
Public learning track
Advanced Sample Spaces, Combinatorics, and Geometric Probability
12th Grade · Track 642 of 698 · 6 lessons
6 lessons
Goal
Model complex random phenomena using set operations, advanced combinatorial counting, and geometric area representations.
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Set Notation for Unions, Intersections, and Complements in Sample Spaces
Public learning track
Advanced Univariate Distributions and Summary Statistics
12th Grade · Track 643 of 698 · 7 lessons
7 lessons
Goal
Represent, summarize, and interpret univariate datasets using graphical representations, measures of central tendency, position, and dispersion.
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Representing Univariate Data Using Dot Plots and Box Plots
Public learning track
Circular Trigonometry, Radians, and Rotational Kinematics
12th Grade · Track 644 of 698 · 6 lessons
6 lessons
Goal
Master radian measure, circular sector geometry, unit circle evaluations, and angular-to-linear velocity kinematics.
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Radian Measure and Arc-Length Proportionality
Public learning track
Exponential and Logarithmic Functions, Inverses, and Rates of Change
12th Grade · Track 645 of 698 · 6 lessons
6 lessons
Goal
Analyze exponential and logarithmic functions, apply logarithmic laws to solve complex equations, and apply the derivative property of exponential functions.
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The Natural Exponential Function and Natural Logarithm
Public learning track
Limits, First Principles, and Derivative Foundations
12th Grade · Track 646 of 698 · 7 lessons
7 lessons
Goal
Understand derivatives as limits of difference quotients, differentiate fundamental functions from first principles, and interpret first and second derivatives geometrically.
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Limits and the Definition of the Derivative
Public learning track
Numerical Methods for Root Finding
12th Grade · Track 647 of 698 · 9 lessons
9 lessons
Goal
Locate and approximate roots of algebraic and transcendental equations using sign-change tests, fixed-point iteration, and Newton-Raphson methods while evaluating convergence criteria and failure conditions.
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Locating Roots by Sign Change Tests and Continuity
Public learning track
Real Number Systems, Density, and Completeness
12th Grade · Track 648 of 698 · 6 lessons
6 lessons
Goal
Analyze decimal and non-decimal representations of real numbers, prove irrationality, and demonstrate the structural density and completeness properties of number systems.
Featured Diagrams
Structural Hierarchy of Number Systems