AP Precalculus measures whether a student can recognise functions in different representations and model a situation with the right one. The exam is very regular in structure, so preparation can be planned.
Unit order
The course has four units but only the first three are tested: polynomial and rational functions, exponential and logarithmic functions, and trigonometric and polar functions. The fourth unit (functions involving parameters, vectors and matrices) is taught but not assessed.
Order matters: rate of change is built in the first unit and reused in every function family after it. A student who cannot tell linear from exponential growth gets stuck in the second unit; one without a secure grasp of radians gets stuck in the third.
The calculator
Part of the multiple choice section bans calculators and part of it requires a graphing calculator. In the free response section, two questions are solved with a calculator and two without.
The calculator must be in RADIAN mode. A calculator left in degree mode turns a correctly set up trigonometry question into a wrong number, and that is the cheapest way to lose marks.
The four free response questions
The free response section uses the same four question types every year, each worth 6 points:
Function concepts (calculator): reading a function's behavior from a table, a graph or an equation.
Modeling a non-periodic context (calculator): choosing the right function family for given data and justifying it.
Modeling a periodic context (no calculator): building a rotation, tide or Ferris wheel situation with sine or cosine.
Symbolic manipulations (no calculator): rewriting exponential, logarithmic and trigonometric expressions in equivalent forms.
The three most common mistakes
Forgetting to simplify a rational function. Not every value that makes the denominator zero is an asymptote; a cancelling factor leaves a hole.
Choosing a model without justification. Equal differences over equal intervals mean linear, equal ratios mean exponential; a model chosen without that sentence loses part of the credit.
Not describing rate of change in words. The exam asks for exact phrases such as increasing, decreasing, and increasing at a decreasing rate.
How long it takes
That depends on the starting point rather than on a fixed number of months. For a student who knows the Turkish curriculum well, most topics are familiar and the real work is modeling and writing justifications; that is settled with a diagnostic rather than an estimate.