Algebra Formula Chart

Ask a class in May to write down the quadratic formula and a surprising number will produce something close to it. Close is no good. This algebra formula chart exists because the difference between remembering a formula and half-remembering one is the difference between a mark and no mark, and because the sheets students usually get handed leave out the very parts that decide which of those two happens.

There are 12 reference pages here, six for Algebra 1 and six for Algebra 2, holding 82 named entries between them. Each entry is set out the same way: the name of the rule on a heading band, the formula or statement itself set large and in bold directly beneath it, and under that one or two lines of ordinary English explaining what the symbols stand for or where the rule goes wrong. The English matters as much as the symbols. A student who cannot remember the point of the discriminant is not helped by seeing b squared minus four a c on its own; the note tells them that a positive value means two real roots, zero means one repeated root, and a negative value means a conjugate pair of non-real roots.

The conditions are printed too, and that is the real difference between this and a poster. The quotient rule for radicals only works when the denominator is positive. A zero exponent gives one only when the base is not zero. An infinite geometric series has a sum only when the common ratio is smaller than one in absolute value. An inverse function exists only when the original passes the horizontal line test. Those clauses are the ones a teacher spends the year repeating, and putting them on the chart puts them in front of the student at the moment they are needed rather than in a lesson three weeks earlier.

Several notes are written specifically against the errors that recur. The square root of x squared is the absolute value of x, not x. A sum of two squares does not factor over the real numbers, however much a student wants it to. The notation for an inverse function is not a reciprocal. A shift written inside the function moves the graph the opposite way to the sign that is printed.

Three blank pages close the file. Two of them list the formula names down the left with the space beside them empty, so a student covers the reference pages and writes each one from memory before checking; between them they draw on every one of the twelve charts. The third has a write-on rule beside each heading and twelve empty rows, so a teacher can label it for whatever unit is running and photocopy it all year. All three carry a name, date and class line. Pages are low-ink — black on white with a slim yellow band across each heading and no filled page backgrounds — so a class set costs very little, and the file is 16 pages in total.