How to Get a 5 in AP Precalculus

What we have for Precalculus

Everything below is free to work through and is organized against the same units as the official course framework, so you can go straight to the unit you are weakest in.

How the country actually scores

Approximate national results on AP Precalculus from recent score reports. Use these as context, not as a prediction — the exact curve is set fresh each year.

• 3 or higher82%
• 4 or higher58%
• Scored a 529%
• Scored 1 or 218%

Read that honestly: a 5 on Precalculus is a minority outcome, earned by roughly one student in 3. It is not out of reach — but it is not the default outcome of finishing the class either, which is why the review phase below matters more than the coursework.

What a 5 in Precalculus takes

The specific habits that separate a 5 from a 3 on this exam, drawn from the scoring patterns for Precalculus.

• Always check for extraneous solutions.
• Know your unit circle cold.
• On the calculator sections, use your grapher to check zeros, intersections, and regression models — but always write the setup (the equation being solved) on FRQs, since the setup earns points even if an arithmetic slip follows.
• Memorize the horizontal-asymptote degree rules and the unit circle cold; Units 1–3 questions repeatedly hinge on end behavior and exact trig values with no time to re-derive them.
• When a modeling FRQ says “interpret,” answer with a sentence that includes units and context (e.g. “the population grows by about 26% each hour”) — a bare number does not earn the interpretation point.
• For rational functions, always factor first: identify canceled factors as holes and surviving denominator factors as vertical asymptotes before sketching or answering anything else.
• Expect log solving to require the power rule (bringing exponents down); check for extraneous solutions by confirming every log’s argument stays positive.
• In Unit 4, verify parametric and matrix answers by plugging in a concrete value (a specific t, or the unit vectors) — it takes seconds and catches most sign and order errors.

The 4 units of AP Precalculus

Unit names and exam weights follow the published course framework. Weights are the share of the multiple-choice section each unit is worth, so they tell you exactly where to spend time: Unit 1 (Polynomial & Rational Functions), Unit 2 (Exponential & Logarithmic Functions), Unit 3 (Trigonometric & Polar Functions) are worth roughly 85–115% between them.

A unit-by-unit study order

Work the units in framework order for your first pass — later units in Precalculus lean on earlier ones — then let your error log, not the unit numbers, drive the review phase. Each row below opens the first lesson of that unit.

1. 1Polynomial & Rational Functions30–40% of the exam · 14 lessons · starts with “End Behavior of Polynomials”
2. 2Exponential & Logarithmic Functions25–40% of the exam · 13 lessons · starts with “Exponential Growth & Decay”
3. 3Trigonometric & Polar Functions30–35% of the exam · 14 lessons · starts with “The Unit Circle”
4. 4Functions Involving Parameters, Vectors & MatricesNot assessed on the exam · 9 lessons · starts with “Parametric Equations”

Formulas and relationships to know

Pulled from the Precalculus lessons. The same list is on the printable Precalculus cheatsheet.

On exam day

The exam-specific warnings our Precalculus lessons flag as you go.

• On the AP exam, state end behavior with limit-style language: “as x → ∞, f(x) → ∞.” Naming the degree parity and the sign of the leading coefficient is the reasoning that earns the point.
• When a graph is given, read multiplicity from the shape: a straight-through crossing is multiplicity 1, a flattened crossing is multiplicity 3+, and a bounce is even. This lets you rebuild the factored form directly from a picture.
• Always factor fully first. The exam loves a rational function whose denominator “looks like” two asymptotes but where one factor cancels into a hole. Simplify, then read vertical asymptotes and holes off the reduced form.
• When several transformations combine, handle inside changes (horizontal shifts, y-axis flips) separately from outside changes (vertical shifts, x-axis flips). Describe each precisely — the AP rubric awards the direction and the axis, not just the word “shift.”
• When a free-response question says "average rate of change," it wants a computation and units. When it says "describe the rate of change," it usually wants *increasing or decreasing, and whether that rate is itself increasing or decreasing* — a different question, taken up in the next lesson.
• Free-response questions ask you to *justify* concavity, not just assert it. A justification cites evidence: "the average rates of change on successive intervals are 3, 6, 9, 12, which are increasing, so f is concave up." Naming the evidence is where the point is earned.
• Non-real zeros are examinable on AP Precalculus, but building polynomials from complex zeros shows up far more often than computing with i. Practice the reconstruction direction — given some zeros, produce the polynomial.
• A favorite exam setup: a rational function whose x-intercept appears to be at the hole. In the worked example above, x = −2 makes the numerator zero, yet it is **not** an x-intercept — the point is missing from the graph. Always check candidate intercepts against the domain.
• Symmetry halves your work. If you know a function is even, analyzing x ≥ 0 determines the whole graph by reflection. Free-response questions sometimes hand you symmetry precisely so you can transfer a computed value from one side to the other.
• When a question asks you to "justify the choice of model," a numerical fit is not enough for full credit. Name the structural feature — constant ratio, constant second difference, fixed period — and, where the context allows, the reason that feature makes sense.

Everything for Precalculus, in order of use

Interactive labs for Precalculus

Frequently asked questions