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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...
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Calculus AB/BC - Derivatives of tan(x), cot(x), sec(x), and csc(x)
Continue to differentiate the rest of the trigonometric functions. Pupils see the derivatives of the other four trigonometric functions and begin to memorize the rules. Learners see examples that show that the calculus portion of a...
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Calculus AB/BC - The Quotient Rule
Some differentiation rules are just better to memorize. The ninth lesson in a unit of 11 presents the quotient rule to pupils for them to memorize. Learners use the quotient rule to determine the derivative of two quotients after seeing...
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Calculus AB/BC - The Product Rule
There's more to derivatives of multiplication than simply the product of the derivatives. A helpful video gives learners the product rule of finding the derivative of the product of two functions. Pupils find the derivatives of functions...
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Calculus AB/BC - Derivatives of cos(x), sin(x), e^x, and ln(x)
The shortcuts are not just for polynomial functions. Pupils learn the derivatives of the two basic trigonometric functions, cosine and sine. The video provides the derivatives for exponential and logarithmic functions. Learners work...
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Calculus AB/BC - Derivative Rules: Constant, Sum, Difference, and ​Constant Multiple
Use derivatives to find equations of lines. Pupils learn more rules to use as shortcuts to find derivatives. Using the rules, they find the equations of the tangent line and the normal line at a given point. Scholars then apply the new...
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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....
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Calculus AB/BC - Connecting Differentiability and Continuity
Despite what you thought, you can differentiate between continuity and differentiability. Using a short lesson, pupils learn how differentiability and continuity relate to each other. It provides three descriptions of when a function is...
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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...
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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...
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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...
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More Probability
Multiply the amount of probability using addition. Pupils use probabilities to make predictions in problems. They find shortcuts to find probabilities instead of listing the entire sample space. The learners then use the multiplication...
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Introduction to Probability
Chances are high that the class will probably like the lesson. Pupils view an introduction to probability and use the information to find probabilities of simple events based on the sample space. Scholars then use their knowledge of area...
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Unit 11 Review: Circles
Solve problems around a circle. Pupils watch a video that shows how to apply concepts about circles and related angles and segments to find solutions to word problems. Learners then review the different concepts from the unit in...
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Secants and Tangents
Put the vertex in, put the vertex out. Pupils explore theorems about the relationships of lengths of segments and angles of line segments that intersect inside or outside the circle. Learners use the theorems to solve problems involving...
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Intercepted Arcs
Intercept the class's learning on circles. Pupils learn the relationship between intercepted arcs and inscribed angles. The scholars use that information to find the relationship of angles in an inscribed quadrilateral and an angle...
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Chords and Arcs
Congruence breeds congruence. Pupils learn three more circle theorems dealing with congruent chords and arcs. Learners use the theorems to find the measures of chords and arcs in circles by applying previously learned concepts in the...
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Tangents to Circles
Touch a circle once. Individuals watch a video and learn two theorems related to tangents and circles. The pupils then apply the theorems to find missing angle measures and lengths in figures. At the end, they practice their skills on...
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Unit 9 Review: Area of Polygons
It's time to show what you know! Individuals first review finding the area of polygons using the formulas from parallelograms to regular polygons. They then brush up on finding the area and circumference of circles, as well as reviewing...
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Sectors and Segments
It's a piece of pizza! Pupils learn about a sector of a circle as a slice of the circle and determine how to find its area. Scholars continue to find out how to calculate the segment of a circle based on the sector's area. At the end,...
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Circles and Arc Lengths
Discuss all things round and round. Pupils review finding area and the circumference of circles and use them to solve problems. Next, they learn about central angles and their relationships to measures of arcs. Learners then find out how...
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Area of Trapezoids, Kites, and Rhombi
Everything will add up. Learners find the areas of trapezoids, kites, and rhombi by using the area formulas. Scholars find any missing information needed to use within the formula and continue to use prior knowledge and practice...
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Parallelograms and Triangles
Expand area problems to incorporate prior knowledge. Pupils begin by reviewing the formulas for finding the area of parallelograms and triangles. The scholars apply previous learning of trigonometric ratios and the Pythagorean Theorem to...
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Rotations
Turn the class around. Scholars define rotations of multiples of 90 degrees and create algebraic mappings for them. After an introduction to symmetry, pupils determine which letters of the alphabet have rotational and reflectional...