Grade 12 math

Sum & Difference Formulas

Use the sum and difference identities to find exact values such as sin 75° and to evaluate expressions.

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Average Rate of Change

Find the average rate of change of a function over an interval from a formula, a table, or a graph.

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The Binomial Theorem

Use the Binomial Theorem and Pascal's triangle to find coefficients and specific terms of an expansion.

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Advanced Function Evaluation

Evaluate quadratic functions and simple compositions.

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Sequences & Series

Find a term in an arithmetic or geometric sequence.

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Inverse Functions

Evaluate and find the equation of inverse linear functions.

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Evaluating Piecewise Functions

Evaluate piecewise-defined functions at given input values.

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Conic Sections: Circles, Ellipses & Hyperbolas

Read the center, radius, vertices, and foci from the equations of circles, ellipses, and hyperbolas.

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Domain & Range of Functions

Find excluded values, square-root domains, and ranges of quadratics and graphs.

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Exponential & Logarithmic Models

Use log properties, e and ln, and growth, decay, and interest models.

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Parametric Equations

Find points on a parametric curve, eliminate the parameter to get an equation in x and y, and use parametric equations for projectile motion.

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Partial Fraction Decomposition of Rational Functions

Break a rational expression with distinct linear factors in the denominator into a sum of simpler fractions.

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Rational Functions: Asymptotes & Holes

Find vertical, horizontal, and slant asymptotes, holes, and intercepts of rational functions.

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Sigma Notation & Infinite Geometric Series

Read sigma (Σ) notation with any starting index, decide whether an infinite geometric series converges, and find its sum.

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Double-Angle Formulas

Use sin 2θ, cos 2θ, and tan 2θ formulas to find exact values.

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Transformations of Graphs

Track how shifts, reflections, and stretches move a point on the graph of y = f(x).

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Statistics & Probability

Solve combination and probability problems.

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Expected Value & Binomial Probability

Find expected values of probability distributions and games, and binomial probabilities P(X = k).

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Normal Distribution & z-Scores

Compute z-scores, use the 68-95-99.7 rule, and find standard normal probabilities.

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Trigonometric Ratios

Find sine, cosine, and tangent ratios from a right triangle's side lengths.

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Unit Circle Exact Values

Find exact values of sine, cosine, and tangent for standard angles.

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Law of Sines & Law of Cosines

Use the Law of Cosines with a 60° or 120° angle to find a missing side exactly.

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Complex Numbers in Polar Form & De Moivre's Theorem

Find the modulus and argument of complex numbers, convert polar form to a + bi, and raise to powers with De Moivre's Theorem.

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Inverse Trigonometric Functions

Evaluate sin^-1, cos^-1, and tan^-1 exactly and simplify compositions like sin(cos^-1(3/5)).

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Polar Coordinates

Convert points between polar (r, θ) and rectangular (x, y) coordinates.

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Graphs of Sine & Cosine

Find the amplitude, period, midline, maximum, and phase shift of sinusoids from equations and graphs (x in degrees).

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Solving Trigonometric Equations

Solve linear trigonometric equations for all solutions from 0° up to 360°.

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Trigonometric Identities

Simplify expressions with the Pythagorean, reciprocal, and quotient identities, and use them to find trig values.

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Matrices

Add 2×2 matrices and find determinants.

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Introduction to Vectors

Find vector magnitude, sum, and dot product.

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Matrix Multiplication

Multiply 2×2 matrices and multiply a matrix by a scalar.

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Inverse Matrices & Cramer's Rule

Find inverses of 2×2 matrices, tell when a matrix has no inverse, and solve 2×2 systems with Cramer's rule.

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Vectors: Direction, Unit Vectors & Angles

Find direction angles, unit vectors, component form, linear combinations, and the angle between two vectors.

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Vectors in 3D: Dot & Cross Products

Find magnitudes, dot products and cross products of three-dimensional vectors, and use them to test for perpendicular vectors.

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Introduction to Limits

Evaluate limits of polynomial functions by direct substitution.

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Product, Quotient & Chain Rules

Use the product, quotient, and chain rules to find the value of a derivative at a point.

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Antiderivatives & Definite Integrals

Find antiderivatives of polynomials with the power rule and evaluate definite integrals and areas under curves.

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Limits: Factoring & Limits at Infinity

Evaluate 0/0 limits by factoring or rationalizing, and find limits of rational functions as x → ∞.

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One-Sided Limits & Continuity

Find left-hand and right-hand limits of piecewise functions, decide whether a limit exists, classify discontinuities, and find the constant that makes a function continuous.

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Derivatives: The Power Rule

Differentiate polynomials (and negative powers) with the power rule and evaluate derivatives at a point.

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Slope & Equation of a Tangent Line

Use the derivative to find the slope and equation of the tangent line, and where the tangent is horizontal.

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Word Problems

Sequence and function word problems.

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