AP Precalculus Review on Sections 1.1, 1.2, and 1.3 (Reteaching and Test Practice Problems)
4.4 هزار بار بازدید -
11 ماه پیش
-
Please subscribe:
Please subscribe: @nickperich
Unit 1: Polynomial and Rational Functions
1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
In this video, I thoroughly describe and reteach the main components of the sections listed above found in the official College Board AP Precalculus course description found at https://apcentral.collegeboard.org/me.... Afterwords, I provide multiple examples and give descriptive solutions to AP Precalculus-style problems. Topics in this video include…
1. Concave Up: A graph is concave up when it curves upward like the letter "U." In calculus, this indicates that the second derivative is positive, and the function is generally increasing.
2. Concave Down: A graph is concave down when it curves downward like an upside-down "U." In calculus, this indicates that the second derivative is negative, and the function is generally decreasing.
3. Inflection Points: These are points on a graph where the concavity changes, often from concave up to concave down or vice versa. They are associated with the roots of the second derivative.
4. Rate of Change on a Graph: This refers to how fast a function's output (y-value) changes concerning its input (x-value). It can be calculated as the slope of a tangent line at a specific point on the graph.
5. Average Rate of Change: This is the overall rate of change of a function over an interval. It's calculated as the difference in the function's values at two endpoints of the interval divided by the difference in their x-values.
6. Determining Linearity or Quadratic Nature: The rate of change of a linear function is constant, meaning it has a constant slope. The rate of change of a quadratic function (a polynomial of degree 2) is not constant; it changes with the input value. By analyzing the rate of change, you can determine if a polynomial is linear or quadratic.
I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: nickperich
Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
.
.
#math #maths #mathskills #mathsucks #mathstudent #mathsmemes #mathstudents #mathsteacher #mathsisfun #gcsemaths #quickmaths #mathstutor #mathsclass #mathstricks #mathsjokes #brunomathsson #mathstations #mathslover #mathsproblems #mathsfun #alevelmaths #earlymaths #mathsquiz #mathsmeme #mathsmock #mathsnotes #mathsbeauty #ilovemaths #lovemaths #addmaths #mathsforlife #mathsweek #mathsgames #mathsexam #eyfsmaths #mathsrevision #primarymaths #ihatemaths #mathslesson #mathstuition
Unit 1: Polynomial and Rational Functions
1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
In this video, I thoroughly describe and reteach the main components of the sections listed above found in the official College Board AP Precalculus course description found at https://apcentral.collegeboard.org/me.... Afterwords, I provide multiple examples and give descriptive solutions to AP Precalculus-style problems. Topics in this video include…
1. Concave Up: A graph is concave up when it curves upward like the letter "U." In calculus, this indicates that the second derivative is positive, and the function is generally increasing.
2. Concave Down: A graph is concave down when it curves downward like an upside-down "U." In calculus, this indicates that the second derivative is negative, and the function is generally decreasing.
3. Inflection Points: These are points on a graph where the concavity changes, often from concave up to concave down or vice versa. They are associated with the roots of the second derivative.
4. Rate of Change on a Graph: This refers to how fast a function's output (y-value) changes concerning its input (x-value). It can be calculated as the slope of a tangent line at a specific point on the graph.
5. Average Rate of Change: This is the overall rate of change of a function over an interval. It's calculated as the difference in the function's values at two endpoints of the interval divided by the difference in their x-values.
6. Determining Linearity or Quadratic Nature: The rate of change of a linear function is constant, meaning it has a constant slope. The rate of change of a quadratic function (a polynomial of degree 2) is not constant; it changes with the input value. By analyzing the rate of change, you can determine if a polynomial is linear or quadratic.
I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: nickperich
Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
.
.
#math #maths #mathskills #mathsucks #mathstudent #mathsmemes #mathstudents #mathsteacher #mathsisfun #gcsemaths #quickmaths #mathstutor #mathsclass #mathstricks #mathsjokes #brunomathsson #mathstations #mathslover #mathsproblems #mathsfun #alevelmaths #earlymaths #mathsquiz #mathsmeme #mathsmock #mathsnotes #mathsbeauty #ilovemaths #lovemaths #addmaths #mathsforlife #mathsweek #mathsgames #mathsexam #eyfsmaths #mathsrevision #primarymaths #ihatemaths #mathslesson #mathstuition
11 ماه پیش
در تاریخ 1402/06/18 منتشر شده
است.
4,491
بـار بازدید شده