Precalculus

Precalculus is the course that consolidates everything a student has done with functions and prepares them for the limit-based thinking of calculus. The bulk of the year is split between an extended look at function families (polynomial, rational, exponential, logarithmic, piecewise) and a full treatment of trigonometry, including the unit circle, identities, and inverse functions. Most courses also touch on sequences, series, polar coordinates, vectors, and conic sections.

It usually lands in 11th or 12th grade, after algebra II and geometry. A student who finishes precalculus solidly is ready for AP Calculus AB, dual-enrollment Calculus I, or a college STEM track. A student who skates through it tends to hit a wall in the first month of calculus, because calculus assumes fluent algebra and instant recall of trig values.

The hard part of precalculus is not any single idea, it's the sheer volume of small skills a student has to keep on tap at once. A trig identity problem might require factoring, fraction manipulation, and three identities used in sequence. Kids who struggle here usually have shaky algebra II foundations, not a precalculus problem per se. Before piling on more drill, check whether they can simplify rational expressions and solve exponential equations without hesitation.

Video-based courses (Khan Academy, Professor Leonard, Organic Chemistry Tutor) work well for the lecture half, but students need a separate problem set to actually build fluency. A good textbook with worked solutions, or a workbook like the Schaum's outline, is worth more than another video. Have your student teach the unit circle back to you from a blank sheet of paper. If they can't, they don't know it yet.