Curated OER
Slope and Tangent
Students differentiate between the slope and the tangent of the horizontal. In this precalculus instructional activity, students examine slopes created by tangent lines. They observe the angle formed using properties of the unit...
Curated OER
Intersecting Lines and Segments of Measures
Mathematicians measure intersecting lines-and circles, and create chords. In this geometry activity, students explore interrior and exterior chords created by tangent and secant lines. These segments can be inside the circleor outside...
Curated OER
Mathemafish Population
It's shark week! In this problem, young mathematically minded marine biologists need to study the fish population by analyzing data over time. The emphasis is on understanding the average rate of change of the population and drawing...
West Contra Costa Unified School District
Introduction to Trigonometric Functions
Scholars first learn the definitions of the sine ratio, the cosine ratio, and the tangent ratio. After mastering these definitions, they use the new information to solve triangles.
Concord Consortium
Outward Bound
Just how far can I see? The short assessment question uses the Pythagorean Theorem to find the distance to the horizon from a given altitude. Scholars use the relationship of a tangent segment and the radius of a circle to find the...
Mathematics Assessment Project
Circles in Triangles
Circles, and triangles, and tangents, oh my! In the assessment task, learners first answer questions leading to the radius of an inscribed circle for a given right triangle. They then use the result to independently determine the...
Curated OER
Senior Analysis: Review Functions and Tangents
In this function learning exercise, students find the equation of a line tangent to a given function. They identify the derivative of functions, This one-page learning exercise contains 11 multi-step problems. Answers are provided on...
Curated OER
Tangents and Circles
In this tangents and circles learning exercise, 10th graders solve 10 different problems that include various tangents and circles. First, they determine in each diagram whether the segments shown are tangents or not. Then, students...
Curated OER
Differential Equations
In this differential equations worksheet, students solve and complete 3 different parts of a problem. First, they sketch a slope field for the given differential equation on the axes provided. Then, students write an equation for the...
Flipped Math
Calculus AB/BC - Average and Instantaneous Rate of Change
Ramp up the average rate of change—instantly. Learners use their knowledge of the formula to find the average rate of change to find the instantaneous rate of change. The presenter shows pupils an interactive that demonstrates finding...
Flipped Math
Calculus AB/BC - Estimating Derivatives of a Function at a Point
It seems like it should be about three. Pupils learn to get an estimate of the derivative of a function at a point by using the derivative functionality of their graphing calculators. They take that information to determine the equation...
Flipped Math
Calculus AB/BC - The Power Rule
There has to be a quicker way. Pupils learn the power rule that allows for a shortcut to take the derivative of terms to a power. Using the newly found rule, scholars find the slope of the tangent line to a function at a given x value....
Curated OER
Three Calculus Overview Problems
For this calculus overview worksheet, students: find the equation of a tangent line, curve sketch, and find limits. Students should have covered continuity as well.
Curated OER
Math 155 - Worksheet 7. Function
In this function worksheet, students compute the derivative of given functions. They find the equation of a tangent line to a curve and compute the implicit differentiation. This two-page worksheet contains six problems.
CK-12 Foundation
Newton's Method
Does the accuracy of the first guess make a difference down the line? Learners investigate the effects of the iterative process of finding roots, using Newton's Method. By moving the initial guess of a root on a graph, pupils observe the...
Curated OER
Sine
In this sine worksheet, 10th graders solve 10 different problems that include finding the sine in each figure shown. They determine the value of x in each situation. Then, students use the tangent line of the given angle to solve the...
Curated OER
Arc and Angles Formed by Secants and Tangents
In this calculus worksheet, students solve problems by finding the line of tangency and measure of the arcs and angles form by a secant line. There are 9 questions.
Curated OER
Relationship between tangent, secant side length
In this calculus worksheet, learners calculate the relationship between a line of tangency and a secant side length. They are given the formulas to solve their problems. There are 9 problems.
Curated OER
Implicit Differentiation
In this implicit differentiation instructional activity, students use the chain rule to solve for the derivative. The find the equation for the tangent line at a given point and determine if the line is vertical. This two-page...
Mathed Up!
Area and Circumference of Circles
Don't go around and around, help your class determine amounts around and in a circle with a video that connects circumference to the perimeter or the distance around an object. The resource includes 14 questions dealing with circles and...
EngageNY
Mid-Module Assessment Task: Pre-Calculus Module 4
Challenge scholars to show what they know about properties and addition and subtraction formulas for trigonometric functions. The resource provides a mid-unit check on the progress toward mastery of trigonometric concepts. The areas...
CK-12 Foundation
Derivatives of Trigonometric Functions: Derivative of sin(x)
Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...
College Board
2005 AP® Calculus AB Free-Response Questions Form B
Grab a peak inside the test. The 2005 free-response questions from the AP® Calculus exam allow learners to see how topics appear on the tests. Topics cover differential equations, bounded areas, particle motion, and slopes of tangent lines.
Curated OER
Tangent Properties
In this geometry worksheet, 10th graders solve problems based on the properties of lines tangent to one or more circles. Constructions are included. The one page worksheet contains eight questions. Answers are...
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