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Tackle the SAT's multi-step, context-heavy word problems — defining variables, building equations and systems from a real-world scenario, and answering what's actually asked.
Find the arc length and sector area of a circle using the central angle — in degrees and radians — with diagrams and worked SAT and ACT problems.
Learn when order matters (permutations) and when it doesn't (combinations), the nPr and nCr formulas, and how to count arrangements and selections — with worked SAT and ACT problems.
Understand the imaginary unit i, add, subtract, and multiply complex numbers, and simplify powers of i — with worked SAT and ACT problems.
Recognize and analyze the conic sections — circle, ellipse, parabola, and hyperbola — by their equations, for the ACT and Pre-Calculus, with worked problems.
Use the distance formula and midpoint formula on the coordinate plane — derived from the Pythagorean theorem and averaging — with diagrams and worked SAT and ACT problems.
Understand direct and inverse variation — y = kx and y = k/x — how to find the constant of variation, and how to solve for a new value, with worked SAT and ACT problems.
Master the standard equation of a circle (x − h)² + (y − k)² = r², find the center and radius, and complete the square to convert from general form — with worked SAT and ACT problems.
Model exponential growth and decay — y = a(1 ± r)^t, reading the base, compound interest, and half-life — with a clear graph and worked SAT and ACT problems.
