Theory that answers the problem in front of you.

The last release put the Theory one tap from a wrong answer. This one makes sure what you find there is the right rule, properly explained.

We checked all 156 subtopics against the problems they actually generate and filled the gaps: the difference of cubes behind a 0/0 limit, working back to the price before tax, reference angles and quadrant signs on the unit circle, convergence tests beyond the geometric series. That is 39 new cards. Another 62 had an explanation that only restated, in smaller type, the formula printed above it. Each of those now says what the formula cannot, such as why a rare cause makes even an accurate test mostly false positives.

Also fixed: a correct answer written a different way could be marked wrong. Swapping the order of the two terms in a product rule answer, or leaving out a multiplication dot, was enough to be rejected, and the product rule and integration by parts were the worst affected. An answer that was already fully expanded could also be told to expand further.

And 16 integral problem types that had been written but never reached practice are now in rotation, and math is rendered entirely on device, so problems appear instantly and offline.