AP Precalculus : Accelerated Program
SAT Score Range
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5 sessions
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PB
About
AP Precalculus: Accelerated Program
The AP Precalculus: Accelerated Program is a rigorous, fast-paced course designed for highly motivated students seeking a comprehensive and in-depth understanding of precalculus concepts. This program moves at an advanced pace, covering the full AP Precalculus curriculum in a condensed timeframe to prepare students for college-level mathematics and the AP Precalculus Exam.
Course Overview
This accelerated program delves into the essential topics of precalculus, focusing on the sophisticated analysis of functions as they model dynamic real-world phenomena. Students will develop a deep conceptual understanding of various function types and their applications, examined through graphical, numerical, analytical, and verbal representations.
Key areas of study include:
Polynomial and Rational Functions: Exploring end behavior, asymptotes, zeros, and modeling real-world scenarios.
Exponential and Logarithmic Functions: Understanding inverses, modeling data, and solving exponential and logarithmic equations.
Trigonometric and Polar Functions: Analyzing periodic phenomena, transformations, inverse trigonometric functions, and graphing with polar coordinates.
Functions Involving Parameters, Vectors, and Matrices (Optional, but often included in accelerated programs): Expanding the understanding of functions to new types and their applications in motion and transformations.
Throughout the course, students will hone critical mathematical practices, including procedural and symbolic fluency, translating between multiple representations, and precise mathematical communication and reasoning.
Who Should Enroll?
This accelerated program is ideal for students who have successfully completed Algebra 2 (or an equivalent integrated math sequence) and demonstrate a strong aptitude and passion for mathematics. It is particularly beneficial for those aiming to:
Prepare for AP Calculus (AB or BC): Develop an exceptionally strong foundation in precalculus concepts, which are crucial for success in higher-level calculus.
Earn College Credit or Placement: Potentially fulfill a college math requirement, allowing them to focus on other major-specific courses.
Pursue STEM Fields: Build foundational mathematical skills essential for careers in mathematics, physics, engineering, computer science, and other STEM disciplines.
Challenge Themselves Academically: Engage with a demanding curriculum that fosters advanced problem-solving skills and critical thinking.
Benefits of the Accelerated Program
Students in the Accelerated Program will gain:
Advanced Preparation: A more intensive and comprehensive preparation for the AP Precalculus Exam and subsequent college-level math courses.
Enhanced Critical Thinking: Development of higher-order thinking skills through rigorous problem-solving and conceptual exploration.
Time Efficiency: The ability to complete the precalculus curriculum efficiently, potentially freeing up their senior year schedule for other advanced courses or electives.
Competitive Edge: A strong transcript demonstrating readiness for demanding college coursework and a commitment to academic excellence.
A College Board-approved graphing calculator is required for this course.
✋ ATTENDANCE POLICY
Attendance is optional but encouraged.
SESSION 1
21
Jul
SESSION 1
AP Precalculus
AP Precalculus
Mon 11:00 PM - Tue, 12:00 AM UTCJul 21, 11:00 PM - Jul 22, 12:00 AM UTC
Topic 1.1: Change in Tandem
This section introduces the fundamental concept of how two quantities relate to and influence each other.
1.1A Introduction to Covariation:
Description: We will define covariation as the simultaneous change in two quantities. This means as one quantity changes, the other quantity also changes in a related way. We'll discuss how this relationship forms the basis of functions.
What we'll cover: Understanding that functions describe how an output quantity covaries with an input quantity.
1.1B Independent and Dependent Variables:
Description: We will identify and differentiate between the independent variable (the input, which causes change) and the dependent variable (the output, which responds to change). Understanding which variable is which is crucial for setting up and interpreting functions.
What we'll cover: Recognizing the roles of input and output in various real-world scenarios.
1.1C Real-World Examples:
Description: We'll explore practical examples to illustrate quantities changing in tandem. This helps solidify the abstract concept of covariation with concrete, relatable situations.
What we'll cover: Examples like how the distance traveled changes with time, how a plant's height changes with the amount of sunlight, or how the cost of a product changes with the number of items purchased.
SESSION 2
22
Jul
SESSION 2
AP Precalculus
AP Precalculus
Tue 11:00 PM - Wed, 12:00 AM UTCJul 22, 11:00 PM - Jul 23, 12:00 AM UTC
Topic 1.2: Rates of Change
This section focuses on quantifying how quickly one quantity changes with respect to another.
1.2A Defining Average Rate of Change:
Description: We will formally define the average rate of change as the ratio of the change in the dependent variable (Δy) to the change in the independent variable (Δx). This is essentially the "slope" between two points on a function.
1.2B Geometric Interpretation:
Description: We will visualize the average rate of change on a graph. It represents the slope of the secant line connecting two points on the function's curve. This helps connect the algebraic definition to a graphical understanding.
What we'll cover: Drawing secant lines and understanding their significance.
1.2C Calculation from Data/Equations:
Description: We will practice calculating the average rate of change using different forms of function representation: from tables of values, directly from a function's equation, and by selecting points from a graph.
What we'll cover: Step-by-step calculations and interpreting the meaning of the calculated rate in context.
SESSION 3
23
Jul
SESSION 3
AP Precalculus
AP Precalculus
Wed 11:00 PM - Thu, 12:00 AM UTCJul 23, 11:00 PM - Jul 24, 12:00 AM UTC
Topic 1.3: Rates of Change in Linear and Quadratic Functions
This section applies the concept of rate of change specifically to two fundamental function types.
1.3A Linear Functions:
Description: We will discuss that linear functions are characterized by a constant average rate of change. This constant rate is precisely the slope of the line.
What we'll cover: How the slope of a line directly represents its constant rate of change, and why this is unique to linear functions.
1.3B Quadratic Functions:
Description: We will explore how quadratic functions have a non-constant average rate of change. However, we'll discover a pattern: the rate of change of the rate of change (often called second differences in tables) is constant for quadratic functions. This is a key insight leading to calculus concepts.
What we'll cover: Analyzing how the slope of the secant line changes across different intervals for a quadratic function, and observing the constant second differences in numerical tables.
1.3C Numerical and Graphical Analysis:
Description: We will use both numerical tables and graphical representations to illustrate and compare the distinct rate of change behaviors of linear and quadratic functions. This visual and numerical comparison reinforces the theoretical understanding.
What we'll cover: Plotting points, observing curve shapes, and calculating rates from data to highlight the differences.
SESSION 4
24
Jul
SESSION 4
AP Precalculus
AP Precalculus
Thu 11:00 PM - Fri, 12:00 AM UTCJul 24, 11:00 PM - Jul 25, 12:00 AM UTC
Topic 1.5: Polynomial Functions and Complex Zeros
This section introduces the characteristics of polynomial functions, focusing on their roots.
1.5A Defining Polynomials:
Description: We will formally define polynomial functions, including their general form, degree, and leading coefficient. We'll clarify what makes an expression a polynomial.
What we'll cover: Identifying polynomial functions and understanding the significance of their degree.
1.5B Fundamental Theorem of Algebra:
Description: We will introduce the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n zeros in the complex number system (counting multiplicity). This theorem provides a foundational understanding of the number of roots a polynomial can have.
What we'll cover: The concept that the degree of a polynomial dictates the total number of its zeros.
1.5C Real vs. Complex Zeros:
Description: We will differentiate between real zeros (where the graph crosses or touches the x-axis) and complex (non-real) zeros. We'll explain that complex zeros always occur in conjugate pairs, meaning if a+bi is a zero, then a−bi must also be a zero.
What we'll cover: Identifying real and complex zeros and understanding the conjugate pairs property.
1.5D Finding Zeros (Algebraic Methods):
Description: We will review and apply algebraic methods for finding zeros of polynomial functions. This includes factoring techniques (such as factoring by grouping, difference of squares/cubes, and trinomial factoring), and briefly introduce or review the Rational Root Theorem and synthetic division as tools to find potential rational zeros.
What we'll cover: Step-by-step procedures for algebraically determining all zeros of a given polynomial.
SESSION 5
25
Jul
SESSION 5
AP Precalculus
AP Precalculus
Fri 11:00 PM - Sat, 12:00 AM UTCJul 25, 11:00 PM - Jul 26, 12:00 AM UTC
Topic 1.6: Polynomial Functions and End Behavior
This section focuses on how polynomial functions behave as the input values become very large or very small.
1.6A Leading Term Test:
Description: We will explain how the leading term (the term with the highest degree) of a polynomial function dictates its end behavior. This means we can predict how the graph will look as x approaches positive or negative infinity.
What we'll cover: The influence of the leading coefficient's sign and the degree's parity (even or odd) on the graph's direction at its ends.
1.6B Four Cases of End Behavior:
Description: We will analyze and illustrate the four distinct patterns of end behavior for polynomial functions based on their leading term:
1.6C Limit Notation:
Description: We will introduce and use formal limit notation to precisely describe the end behavior of polynomial functions. For example, lim
x→∞
f(x)=∞ means "as x approaches infinity, f(x) approaches infinity."
What we'll cover: Correctly writing and interpreting limit statements for polynomial end behavior.