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Conics are curved algebraic forms that come from slicing a cone with a plane. Use these equations to graph algebraic conics, such as circles, ellipses, parabolas, and hyperbolas: [more…]
Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]
Algebra can help you add a series of numbers (the sum of sequences) more quickly than you would be able to with straight addition. Adding integers, squares, cubes, and terms in an arithmetic or geometric [more…]
In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn't matter [more…]
Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs. [more…]
In algebra, multiplying binomials is easier if you recognize their patterns. You multiply the sum and difference of binomials and multiply by squaring and cubing to find some of the special products in [more…]
You can find solutions for quadratic equations by factoring, completing the square, guessing, or everyone's favorite — using the quadratic formula. The best thing about the quadratic formula [more…]
Working with radicals can be troublesome, but these equivalences keep algebraic radicals from running amok. Finding the root of product or quotient or a fractional exponent is simple with these formulas [more…]
Logarithms help you add instead of multiply. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1. [more…]
Algebra is all about formulas, equations, and graphs. You need algebraic equations for multiplying binomials, dealing with radicals, finding the sum of sequences, and graphing the intersections of cones [more…]
If you’re studying pre-calculus, you’re going to encounter triangles, and certainly the Pythagorean theorem. The theorem and how it applies to special right triangles are set out here: [more…]
In pre-calculus you deal with inequalities and you use interval notation to express the solution set to an inequality. The following formulas show how to format solution sets in interval notation. [more…]
Even though you’re involved with pre-calculus, you remember your old love, algebra, and that fact that absolute values then usually had two possible solutions. Now that you’re with pre-calculus, you realize [more…]
Of course you use trigonometry, commonly called trig, in pre-calculus. And you use trig identities as constants throughout an equation to help you simply problems. The always-true, never-changing trig [more…]