university levels of education Pre-Calculus I — V
Five courses in one reader, from absolute value to the doorstep of the derivative — handmade, no ads, no sign-ups. One hundred written lectures with fully typeset mathematics, three hundred worked examples solved step by step with the reasoning shown, four hundred practice questions with hints and answers, quizzes for every lecture, and three hundred unsolved problems to do on your own, in nineteen ways of studying including a continuous read of a whole course. Start at whichever course you need; the whole-course entry opens all five as one book, and the classic drill studio waits at the end for old times’ sake.
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Pre-Calculus I
Numbers, Algebra & Functions. Absolute value as distance, exponent laws, intervals, radicals and scientific notation; factoring, special products and rational expressions; every standard equation type from linear through radical, inequalities included; and the function idea itself — notation, domain, composition, inverses, and the difference quotient. Twenty lectures, 240 questions. Every lecture carries a written explanation with fully typeset mathematics, the key facts and the classic mistakes to watch for, a formula table, defined terms, worked examples revealed step by step with the reasoning beside each step, practice questions with hints and answers, a quiz, and unsolved problems to do on your own, studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.
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Pre-Calculus II
Graphs, Polynomials & Rational Functions. Distance, midpoint, slope and the circle; shifts, reflections, stretches and piecewise definitions; quadratics through vertex form, the discriminant and complex numbers; polynomial division, the remainder and factor theorems, rational zeros, multiplicity and end behaviour; and rational functions read completely — asymptotes, holes, inequalities and partial fractions. Twenty lectures, 240 questions. Every lecture carries a written explanation with fully typeset mathematics, the key facts and the classic mistakes to watch for, a formula table, defined terms, worked examples revealed step by step with the reasoning beside each step, practice questions with hints and answers, a quiz, and unsolved problems to do on your own, studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.
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Pre-Calculus III
Exponentials, Logarithms & Trigonometry. Growth and decay with compound interest and half-life; logarithms defined, their laws, equations and change of base; then trigonometry from the ground up — degrees and radians, arc length, right triangles, the unit circle, all six functions with their signs, and the full graphing kit of amplitude, period and phase. Twenty lectures, 240 questions. Every lecture carries a written explanation with fully typeset mathematics, the key facts and the classic mistakes to watch for, a formula table, defined terms, worked examples revealed step by step with the reasoning beside each step, practice questions with hints and answers, a quiz, and unsolved problems to do on your own, studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.
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Pre-Calculus IV
Analytic Trigonometry & Applications. The identity families — Pythagorean, sum and difference, double and half angle, product-to-sum; trigonometric equations by factoring, identities and multiple-angle care; inverse functions with their restricted ranges; triangles by the laws of sines and cosines with areas and bearings; and vectors through the dot product, polar coordinates and De Moivre. Twenty lectures, 240 questions. Every lecture carries a written explanation with fully typeset mathematics, the key facts and the classic mistakes to watch for, a formula table, defined terms, worked examples revealed step by step with the reasoning beside each step, practice questions with hints and answers, a quiz, and unsolved problems to do on your own, studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.
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Pre-Calculus V
Systems, Conics, Sequences & Limits. Systems linear and nonlinear with inequalities and the corner principle; matrices, determinants, inverses and Cramer's rule; the conic sections with their focus definitions and parametric curves; sequences through sigma notation to the infinite geometric series; counting and the binomial theorem; and limits and continuity, ending at the tangent line where Calculus I begins. Twenty lectures, 240 questions. Every lecture carries a written explanation with fully typeset mathematics, the key facts and the classic mistakes to watch for, a formula table, defined terms, worked examples revealed step by step with the reasoning beside each step, practice questions with hints and answers, a quiz, and unsolved problems to do on your own, studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.
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The whole of pre-calculus
All five courses opened as one book — one hundred lectures from absolute value to the doorstep of the derivative, with 1,200 questions between them, readable end to end in the continuous view or studied through any of the nineteen modes across the whole sequence at once.
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Pre-calculus studio (classic)
The original pre-calculus drill studio, kept as it was: one hundred arcade modes with three fully solved examples each and endless generated practice, for anyone who prefers the older quick-drill format to the new reader.
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