AP Precalculus Sprint

Find the score drag, then turn it into today's coaching plan.

This sprint checks the AP Precalculus skills that usually leak points fastest: function notation, graph features, logs, trig models, and FRQ interpretation.

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Burst 1

Functions and Domain

Composition, inverse notation, and domain restrictions. These are fast points if the setup is disciplined.

Progress is saved on this device. Burst progress: 0/3 answered; 0/5 bursts scored.

Question 1 - Functions and Models

Composition with domain awareness

75s target

Let f(x) = sqrt(x - 1) and g(x) = 2x + 5. Which value is f(g(2))?

Question 2 - Functions and Models

Inverse function notation

80s target

If q(4) = 11 and q is one-to-one, what must be true about q^-1(11)?

Question 3 - Functions and Models

Transformation sequence

80s target

Compared with y = f(x), which description matches y = -3f(x + 2) + 7?

Coach Queue

Unlock after scoring

Run the mixed diagnostic under time and record whether errors came from concept, setup, or execution.

Move directly into FRQ setup practice after the MCQ burst; AP Precalculus rewards clear interpretation.

Use the 12-hour plan as a sprint, then retest with a fresh mixed set.

12-Hour Sprint Plan

Hour 1

Function notation, composition, inverse notation, domain restrictions

Hour 2

Transformations and model translation from words to equations

Hours 3-4

Polynomial zeros, multiplicity, end behavior, rational graph features

Hours 5-6

Exponential and logarithmic rewrite drills with model interpretation

Hours 7-8

Trig parameters, period, phase shift, polar basics

Hour 9

Parametric position, vectors, and matrix context

Hours 10-11

FRQ setups: state, solve, justify, interpret

Hour 12

Timed mixed set, error audit, and final formula-free recall pass

FRQ Readiness

Short-answer habits that raise the score ceiling

Discontinuities, graph behavior, and justification

Rational Function Model

A rate model is R(x) = (x^2 - 9)/(x - 3). Identify any discontinuity, simplify the model where possible, and explain what the hole means in context.

Factors numerator as (x - 3)(x + 3)

Names x = 3 as a removable discontinuity

Uses R(x) = x + 3 only for x not equal to 3

Explains the contextual restriction instead of only giving algebra

Amplitude, period, phase shift, and prediction

Sinusoidal Model Interpretation

A Ferris wheel height is modeled by H(t) = 35 cos((pi/20)(t - 6)) + 42. Interpret each parameter and describe when the rider is first at maximum height after t = 0.

Identifies amplitude as 35 and midline as 42

Computes period as 40

Interprets the shift t - 6 correctly

Connects maximum height to the cosine maximum

Model setup, growth factor, and solving with logs

Exponential Model and Log Solve

A bacteria culture starts with 800 cells and grows by 18% each hour. Define a model B(t), interpret the growth factor, and determine when the culture first exceeds 2,000 cells.

Defines t and writes B(t) = 800(1.18)^t

Interprets 1.18 as 18% growth per hour

Uses logarithms or a calculator table to solve the inequality

Rounds the time in context and explains first exceeds

Parameter values, coordinate interpretation, and displacement

Parametric Motion and Vector Displacement

A drone path is modeled by x(t) = 2t + 1 and y(t) = t^2 - 4 for 0 <= t <= 5. Find the position at t = 3, compute the displacement from t = 1 to t = 3, and interpret the displacement vector.

Substitutes t = 3 into both coordinate functions

Computes positions at t = 1 and t = 3 before subtracting

Reports displacement as a vector with direction

Interprets the result in the drone context

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