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Precalculus
The bridge between algebra and calculus: functions studied for their own sake — polynomial, rational, exponential, logarithmic — plus the complex numbers, sequences and series, conic sections and vectors that calculus will assume you know.
درسها
Core
Complex numbers
i² = −1, arithmetic in the complex plane, modulus and conjugates.
(1 + 2i)*(3 - i)
Core
Polynomial functions
Degree, end behaviour, zeros, turning points, and what the graph must look like.
y = x^3 - 3x
Core
Rational functions
Asymptotes, holes and domain — where a fraction of polynomials blows up.
y = 1/(x^2 - 1)
Core
Sequences and series
Arithmetic and geometric sequences, partial sums, and the geometric series formula.
sum of 2^k for k = 0 to 10
Core
The binomial theorem
Expanding (a + b)ⁿ with Pascal's triangle and binomial coefficients.
expand (a + b)^5
Advanced
Conic sections
Circles, ellipses, parabolas and hyperbolas as equations and as surfaces sliced.
x^2 + y^2 - 25
Core
Vectors
Magnitude, direction, components, and adding vectors head to tail.
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＋ Arithmetic𝑥 Algebra△ Geometry∿ Trigonometry∫ Calculus⊞ Linear Algebraσ Statistics & Probability⊢ Discrete Math & Logicℕ Number Theoryẏ Differential Equationsε Analysis∞ Frontiers