AP Calculus AB Pacing and Alignment Guide

Chapter 1 Solutions Manual (Access Restricted)

1.1 Learning Targets

I can estimate from a graph and find algebraically functional values, domain, range, and intervals of increasing and decreasing functions.

I can evaluate the difference quotient.

I can write an equation of a function given various information about the function in terms of one variable.

I can determine and interpret even and odd functions.

1.2 Learning Targets

I understand the modeling process, (developing, analyzing, and interpreting a mathematical model) and can use it to write and interpret a linear equation.

I can classify functions: linear, power, rational, algebraic, trigonometric, exponential and transcendental functions.

I can identify the special characteristics (shape, transformations, y-intercept, increasing/decreasing) of each class of functions.

1.3 Learning Targets

I understand the mechanics and geometry to compose functions.

I understand the mechanics and geometry to add, subtract, multiply, and divide functions.

I understand the mechanics and geometry to transform functions.

1.4 Learning Targets

I understand graphing calculators can give misleading or wrong answers.

I understand some functions don't have any single viewing window that will give all the important details of the function.

I understand when graphing an arbitrary function, some viewing windows are more appropriate than others, depending upon the context of the inquiry and some analysis of the actual equation.

1.5 Learning Targets

I can write and solve exponential equations that represent models for population growth and decay.

I can identify and transform exponential functions, specifically focusing on symbolic and geometric perspectives.

1.6 Learning Targets

I can find the exact value of the inverse trigonometric functions.

I can use the product, quotient, and power properties of logarithms to simplify or solve logarithmic equations.

I can use multiple representations (verbal, numeric, visual, algebraic) to understand and find the inverse of a one-to-one function, always coming back to the central idea of reversing inputs and outputs.