How Every Worksheet Is Checked

Every worksheet on Math Pages is made by code, from the settings on the page, at the moment you ask for it. Nobody types the problems in and nobody types the answers. This page says what is checked and how; each statement on it describes a test or a script in the site's code.

The answer key is printed from the same problems as the worksheet, in the same order. The problems are not drawn a second time for the key, so the two cannot disagree. The answer pages come after the worksheet pages.

Each kind of sheet has its own tests for what its answers depend on. A few of them: every addition, subtraction and multiplication answer is worked out again from its two numbers; a division sheet without remainders always divides exactly, and with remainders the remainder is always smaller than the divisor; fraction answers are always in lowest terms; money answers are exact to the cent; and on the Pythagorean theorem pages every "yes" is a right triangle and every "no" is a triangle that is not one.

Every number of problems per page the settings panel offers is laid out by the real PDF renderer, full page and half page, with and without the answer key. A choice that runs onto a second page fails, and so does text printed over other text or over the footer. This runs for every kind of sheet except the mixed spiral review, whenever a layout or a kind of sheet changes. One known overlap is listed rather than hidden: on the three-digit addition color-by-number sheet, a line of the color key runs under its swatch.

When a page describes its sheet, a test makes sheets from that page's settings and checks the description on each one. On the Pythagorean theorem page, for example, it checks that every answer is a whole number. More than seventy pages carry claims checked this way, and when a claim fails, the words on the page change, not the test.

The code in a sheet's footer, such as K4T9M2, is the seed its problems were drawn from. With the same settings, the same code gives the same problems in the same order, and tests check that. Type it into "Rebuild a printed sheet" to get a lost sheet or its key back. A copied sheet link carries the settings and the code together.