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Ojk's Precalculus Study Page: Solving Polynomial Equations
A comprehensive look at the three main ways to find the roots of a polynomial: factoring, formulas, and the rational root theorem.
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Ojk's Precalculus Study Page: Periodic Functions, Stretching and Translating
This online tutorial offers a comprehensive introduction to translating and stretching graphs, and what this implies about the function. Includes lots of pictures and examples.
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Ojk's Precalculus Study Page: Functions of Two Variables
An introduction to functions with two variables, including several examples relating to linear programming. The tutorial includes graphical examples of the functions and also review questions located at the bottom of the page.
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Ojk's Precalculus Study Page: Functions Sample Test
A practice test covering the basics of functions, including domain, range, operations, and graphing. Includes an answer page.
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Ojk's Precalculus Study Page: The Number E and the Function E^x
An introduction to the natural exponential function, beginning with the limit definition of the irrational number e. Includes several examples and exercises with solutions which deal with the compound interest formula.
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Ojk's Precalculus Study Page: Change of Base Formula
An introduction to logarithms with bases other than 10 and e, and how to work with them when solving equations. This tutorial includes lots of examples and exercises with solutions.
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Ojk's Precalculus Study Page: Trigonometry Sample Test
A practice test that covers proving trigonometric identities and solving advances trigonometric equations.
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Ojk's Precalculus Study Page: Easier Trigonometric Equations
An introduction to solving trigonometric equations, including finding general and particular solutions. The connection between the tangent function and the slope of a line is also covered. Includes several examples and graphs.
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Ojk's Precalculus Study Page: Translations of Sine and Cosine Curves
This study tutorial covers more advanced graphing of sine and cosine functions, including horizontal and vertical translations (phase shifts and vertical shifts). Includes several examples and graphs.
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Ojk's Precalculus Study Page: More Difficult Trig Equations
An introduction to solving trigonometric equations by using the reciprocal, negative, Pythagorean, and cofunction identities. Includes several examples and exercises with solutions at the bottom of the page.
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Ojk's Precalculus Study Page: Geometric Representation of Complex Numbers
An introduction to viewing the complex plane in terms of polar coordinates. Assumes knowledge of the conversion formulas. Includes several examples and pictures.
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Ojk's Precalculus Study Page: Powers of Complex Numbers
An introduction to DeMoivre's Theorem for quickly finding the powers of complex numbers. Assumes knowledge of polar form of complex numbers. Includes several examples and pictures.
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Ojk's Precalculus Study Page: Polar Coordinates Sample Test
A practice test covering the polar form of complex numbers, including using DeMoivre's Theorem to find powers and roots of complex numbers.
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Ojk's Precalculus Study Page: Laws of Logarithms
Eight laws reguarding logarithms. The laws include the Law of X, 0, 1, and more. Sample problems and solutions provided.
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Ojk's Precalculus Study Page: Introduction: Average Rate of Change
A precalculus tutorial that explains the average rate of change with formulas and examples. Related links to other concepts.
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Ojk's Precalculus Study Page: Evaluating and Graphing Sine and Cosine
An introduction to graphing the sine and cosine functions by using the 30-60-90 and 45-45-90 right triangle values of the two functions as guides.
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Ojk's Precalculus Study Page: Polar Coordinates and Complex Numbers
An introduction to basic conversion formulas for polar coordinates and complex numbers. Includes several examples.
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Ojk's Precalculus Study Page: Parabolas
Good study tutorial about parabolas. There are examples of finding the equation of the parabola or the focal point and directrix that students can examine and attempt.
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Ojk's Precalculus Study Page: Polynomial Inequalities, One Variable
This tutorial offers two methods to solve polynomial inequalities. Site includes several examples, charts, graphs, and other information for student understanding.