The Ultimate GOAT AP Precalculus Practice Test: Section 2 Free Response Questions (FRQ) #1 - 4

You made it to the ULTIMATE GOAT AP PRECALCULUS PRACTICE TEST!!! I made this test by taking problems from the official CollegeBoard AP Precalculus practice tests and slightly manipulated each problem to make them different. I'm no hero, just a humble math teacher trying to make a few dollars on the internet.

The 4 six-point free-response questions on the AP Precalculus Exam include content topics from Units 1, 2, and 3. Two of the four questions incorporate a realworld function modeling context. A graphing calculator is required for the first 2 questions (Part A). Calculators should be in radian mode for the AP Exam. Refer to the “Technology Needs” section on page 7 for a list of calculator capabilities that are necessary for the AP Exam.

Here's a breakdown of the real exam:

Unit 1: Polynomial and Rational Functions (30%–40% of the exam)
Unit 2: Exponential and Logarithmic Functions (27%–40% of the exam)
Unit 3: Trigonometric and Polar Functions (30%–35% of the exam)

Unit 4 is not assessed on the AP exam.

The sections from AP Precalculus that are tested are...

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application
2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

/ nickperich

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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[adanaamun]

hey love the video but shouldn't 3A be 4/3 for the time not 3/4? because its 3 quarters per second which would make the time 4/3?

[mikewazowski]

Quick question. For A(i), we are trying to find k(4), making x = 4. Why are you plugging x = 1 into h(x) instead of h(4) to get 4?