Algebra
Factor, substitute and let Vieta do the heavy lifting.
- 12Algebraic ManipulationsreadySquare, cube, factor and combine: the identities and equation tricks that let you find exactly what a problem asks for without solving for every variable.
0% - 13Vieta's Formulas for PolynomialsreadyRead the sum and product of a polynomial's roots straight off its coefficients, and answer root questions without ever finding the roots.
0% - 14Polynomial RootsreadyWrite a polynomial through its roots, find remainders without long division, flip and shift roots, and climb power sums with Newton's identities.
0% - 15Arithmetic SequencesreadyAdd the same number again and again: find any term, count the terms, and sum them all with Gauss's pairing trick.
0% - 16Geometric SequencesreadyMultiply by the same ratio again and again: find any term without listing them, add a whole sequence in one line, and sum infinitely many terms to a finite number.
0% - 17Special SequencesreadyClosed forms for sums of integers, odd numbers, squares and cubes, plus telescoping sums and products and sequences that repeat.
0% - 18Mean, Median, ModereadyThree ways to describe the middle of a list: the mean is a balance point, the median sits in the middle, the mode is the crowd favorite. Then the geometric, harmonic and quadratic means, and how they line up.
0% - 19System of EquationsreadyName the unknowns, turn every fact into an equation, and combine them: systems, mixtures and work-rate problems the contest way.
0% - 20Speed, Distance, and TimereadyDistance equals speed times time, and almost everything else follows: average speed (it is not the average of the speeds!), meeting and catching up, and walking on escalators and moving walkways.
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