POLAR COORDINATES (Optional – if time permits)Ĭhange polar coordinates into rectangular ones and vice versa (points and equations) Review from 10H: counting principle, addition principleīernoulli Experiments – Exactly r success in n trials: at least at mostīinomial Theorem – Pascal’s triangle in relation to coefficients (theorem) finding a specific term Location Principle: is continuous on, and, at least one real root between a and b Rational Roots Theorem:, if is a root of, p is a factor of k and q is a factor of aĭescartes Rule of Signs: number of positive roots from, number of negative roots from Remainder Theorem: is the remainder when is divided by Solve for all zeros – GCF, grouping, factor theorem, factoring, quadratic form, “ a is a root if and only if is a factor” (See limits in Brown, Advanced Mathematics, chapter 13) If, use highest exponent in numerator and denominator If, look for a re-write, then substitute types covered: by factoring, radical expressions, Geometric sequences: common ratio r (closed rule) (recursive rule)įinding common difference/ratio, specific terms, number of terms, arithmetic and geometric means verbal problem applicationsĪrithmetic series: other related formulasĪpplications throughout include verbal applicationsįinding limits, including one-sided limits from graphs from rational expressions neitherĪrithmetic sequences: common difference d (closed rule) (recursive rule) , sum and difference, double angle, half angle applications – solving trigonometric equations, proving identities, evaluating (e.g., ) Solving the triangle all angles and sidesĪmbiguous case finding the number of possible triangles (0, 1, or 2) – solving for possible triangles use altitude for comparisonĭerive and apply angle formulas: e.g. Inverse trigonometric functions, including graphs use with calculatorĪpplications when solving harder trigonometric equationsĪrea of a triangle:, given SAS extension – force problems Impact of a, b, c, d on graphs of functions Graphing of sine, cosine, and tangent e.g., include vertical and horizontal shifts Incorporate use of the graphing calculator Solving trigonometric equations – incorporate later again with Pythagorean identities, double angle formulas Pythagorean identities – derive from the unit circle, and algebraic derivation
Radian measure converting from degrees to radians, and vice versa Reciprocal functions: cosecant, secant, cotangent Sine, cosine and tangent of angles whose reference angles are from special triangles Sine, cosine and tangent of special angles Translating all conics finding equationsĭefinition of sine, cosine and tangent off the unit circleįinding reference angles, via distance from x-axis Rectangular hyperbolas – horizontal and vertical: graphing, finding equation from graph, center, asymptotes, foci Parabola – review derive and apply equation: finding equation, graphing, focus, directrix CONIC SECTIONS – Equations, Vitals, GraphingĮllipse via locus definition: finding orientation, vertices, minor, major axes, foci and area ( ) Solving fractional equations (polynomial denominators) Review of logarithms, including an extension to natural logarithmsĭifference of two squares, perfect squares, GCF includedĪdding, subtracting, multiplying, dividing (up through different polynomial denominators)
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