Flipped Math
Calculus AB/BC - Using the Second Derivative Test to Determine Extrema
Take a second look at extrema of functions. Pupils learn how to use the second derivative to determine whether a critical point is a maximum or a minimum. Learners use concavity to identify critical points as either a max or a min and...
Flipped Math
Calculus AB/BC - Connecting a Function, Its First Derivative, and Its Second Derivative
Uncover what the first and second derivatives reveal about the function. Pupils move beyond sketching graphs to determine what derivatives tell about the function itself. The video reminds learners about particle motion and how to...
Flipped Math
Calculus AB/BC - Defining the Derivative of a Function and Using Derivative Notation
Pupils learn how to find the derivative of a function by applying the definition using limits. Learners understand that the derivative provides the slope of the tangent line and use that information to find the equation of the tangent...
CK-12 Foundation
Higher Order Derivatives—Acceleration and Jerk
Accelerate your class through finding the second derivative. Using a bank of equations, pupils determine the equations for distance, velocity, and acceleration and their associated function notations. With the equations, learners answer...
Flipped Math
Calculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area
Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...
Flipped Math
Calculus AB/BC - Determining Concavity of Functions over Their Domains
Time to take a second look at derivatives finding concavity. While watching the video, learners find out the definition of concavity. Individuals see how to determine whether an interval is concave up or concave down using graphs and the...
College Board
Vectors: A Curriculum Module for AP® Calculus BC
It is all in a matter of time. The model curriculum module uses parametric equations and vectors to solve problems dealing with particle motion along a curve. At the beginning of the lesson, the unit reviews parametric equations and...
Flipped Math
Calculus AB/BC Unit 3 Review: Differentiation
It's time to take stock of the class's knowledge of derivatives. Individuals review how to take the derivatives of composite, implicit, and inverse functions. They complete some problems involving the Chain Rule, implicit...
Flipped Math
Calculus AB/BC - Exploring Behaviors of Implicit Relations
Put everything together implicitly. Pupils use their knowledge of implicit differentiation to determine whether a curve is increasing or decreasing or its concavity. Given a differential equation, scholars determine whether a specific...
EngageNY
Modeling Video Game Motion with Matrices 2
The second day of a two-part lesson on motion introduces the class to circular motion. Pupils learn how to incorporate a time parameter into the rotational matrix transformations they already know. The 24th installment in the 32-part...
Flipped Math
Calculus AB/BC - Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Move the video on motion to the front of the line. The second of eight lessons in Unit 4 - Contextual Applications looks at straight-line motion. Scholars learn how position, velocity, and acceleration are related by derivatives before...
College Board
2011 AP® Calculus BC Free-Response Questions Form B
Take a second look. Form B of the AP® Calculus BC free-response questions allow pupils and teachers to see another set of items. The six questions expand the set of items from the 2011 free-response questions. Form B items include a...
EngageNY
Overcoming a Second Obstacle in Factoring—What If There Is a Remainder?
Looking for an alternative approach to long division? Show your classes how to use factoring in place of long division. Increase their fluency with factoring at the same time!
EngageNY
Complex Number Division 2
Individuals learn to divide and conquer complex numbers with a little help from moduli and conjugates. In the second lesson on complex number division, the class takes a closer look at the numerator and denominator of the multiplicative...
EngageNY
Formal Definition of a Function
Formalize the notion of a function. Scholars continue their exploration of functions in the second lesson plan of the module. They consider functions as input-output machines and develop function rules for selected functions.
EngageNY
End-of-Module Assessment Task: Pre-Calculus Module 2
Assess pupil understanding of the relationship between matrices, vectors, linear transformations, and parametric equations. Questions range from recall to more complex levels of thinking. Problems represent topics learned throughout the...
EngageNY
Ordered Pairs
Scholars learn to plot points on the coordinate plane. The lesson introduces the idea that the first coordinate of a coordinate pair represents the horizontal distance and the second coordinate represents the vertical distance.
EngageNY
When Can We Reverse a Transformation? 3
When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third lesson plan on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous two...
EngageNY
Proving the Area of a Disk
Using a similar process from the first lesson plan in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the...
EngageNY
Mid-Module Assessment Task: Grade 8 Module 6
Make sure pupils have the skills to move on to the second half of the module with a mid-module assessment task. The formative assessment instrument checks student learning before moving on to the rest of the lessons in the unit.
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 2)
Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...
EngageNY
When Can We Reverse a Transformation? 2
The second lesson on finding inverse matrices asks class members to look for a pattern in the inverse matrix and test it to see if it works for all matrices. The teacher leads a discussion to refine the process in finding inverses,...
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
EngageNY
Interpreting Rate of Change and Initial Value
Building on knowledge from the previous lesson, the second lesson in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate how slope expresses the...