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Ap Calc Oct22
The document discusses the definite integral and how to estimate distances traveled from a velocity-time graph. It includes a table of velocity values and asks the reader to (1) sketch the velocity-time graph, (2) estimate the lower and upper distances traveled in 5 seconds, (3) estimate the actual distance traveled, and (4) represent the lower estimate as a shaded region on the graph. The document also asks why we began by looking at the picture of rectangles.
AP Calculus October 7th, 2008
The document discusses derivatives and second derivatives of functions. The first derivative f' of a function f assigns values to inputs where f is differentiable. The second derivative f'' can then be calculated by taking the derivative of the first derivative function f' and defines f''(a) using a formula involving limits.
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The document is a short text that simply repeats the date "February 26, 2009" three times without providing any other context or information.
Pre-Cal 20S September 18, 2004
The document describes the process for a pre-test on polynomials and factoring. It states that students will spend 20 minutes individually completing the pre-test without calculators. They will then spend 10 minutes discussing the results in groups of three. Each group will submit one sheet of paper with their best answers. Remaining time will be used to go over unanswered questions as a class. The actual test on the material will take place the next day.
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Ap Calc Oct22
The document discusses the definite integral and how to estimate distances traveled from a velocity-time graph. It includes a table of velocity values and asks the reader to (1) sketch the velocity-time graph, (2) estimate the lower and upper distances traveled in 5 seconds, (3) estimate the actual distance traveled, and (4) represent the lower estimate as a shaded region on the graph. The document also asks why we began by looking at the picture of rectangles.
AP Calculus October 7th, 2008
The document discusses derivatives and second derivatives of functions. The first derivative f' of a function f assigns values to inputs where f is differentiable. The second derivative f'' can then be calculated by taking the derivative of the first derivative function f' and defines f''(a) using a formula involving limits.
Quiz Corrections
The document is a short text that simply repeats the date "February 26, 2009" three times without providing any other context or information.
Pre-Cal 20S September 18, 2004
The document describes the process for a pre-test on polynomials and factoring. It states that students will spend 20 minutes individually completing the pre-test without calculators. They will then spend 10 minutes discussing the results in groups of three. Each group will submit one sheet of paper with their best answers. Remaining time will be used to go over unanswered questions as a class. The actual test on the material will take place the next day.
Pre-Cal 20S September 29th
The problem asks to find the length of DC given that AB is 3 units long, BC is 4 units long, and DE is 10 units long. The midpoint formula is used to find the coordinates of point B given that the midpoint M of AB is (1/2, 6) and the coordinates of A are (3, 7).
Applied Math 20S October 8th, 2008
This document provides instructions for students to transition from Investigation 1 to Investigation 2 in their science class, suggests making graph paper if none is available, and assigns homework of questions 1 through 6 on pages 207 to 209 for their teacher, Mrs. Karras, which is due tomorrow.
AP Calculus October 3rd, 2008
The document discusses finding the derivative of a function f(x) = x^2 at x = a in multiple ways. It lists methods such as the slope program, difference quotient, symmetric difference quotient, drawing the tangent line, using a numerical derivative program, and the limit definition of the derivative. The document provides instructions on deriving a derivative through various mathematical techniques.
AP Calculus October 6th, 2008
This document lists homework problems assigned from a textbook or class. The homework problems that were assigned are problems 1, 7, 9, 11, 15, 19, 22, 23, and 25.
Completing the Square
La ecuación original es y = x2 - 4x + 3, luego se agregan términos constantes para obtener y = x2 - 4x + 3 + 16x + 8 = x2 + 12x + 11. Finalmente, se factoriza como y = (x - 2)(x - 5) = 2x2 - 12x + 13.
Probability04
The document discusses homework assignments involving using experiments and simulations to determine probabilities. The first assignment involves simulating a 6 question multiple choice test by guessing answers. The second asks to simulate a 10 question true/false test using coins to find the probability of scoring at least 70% by guessing. The third asks to find the probability of flipping 3 pennies and getting at least 1 head. Guidance is provided on using the calculator's randBin function and the Random.org website to perform the simulations.
Ch8 Lesson03
The document discusses volumes of revolution and provides formulas to calculate volumes. It mentions volumes can be found by rotating a function about the x-axis and using a function that represents the changing cross-sectional areas. The document also references homework problems and calculating the volume of a cone but provides minimal details or explanations.
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The document contains several math and probability word problems and examples presented as homework assignments. It provides the questions, working, and answers for problems involving Pascal's triangle, counting paths, probability, coin flipping, and spinners. The document is a collection of homework questions and solutions on topics of combinatorics, probability, and experimental vs theoretical probability.
Ch8 Lesson02
This document provides instructions for calculating the volumes of various 3D shapes using integrals. It discusses finding the volume of a revolving cube, calculating the area between curves, and using a function for the changing radii to determine the volume of a cone.
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The document discusses translations and stretches of graphs, with sections on the role of parameters a and b in shifting graphs right or left (parameter a) and up or down (parameter b). It also covers stretches and compressions along the x and y axes depending on whether parameters a or b are greater than, less than, or between 0 and 1.
Ch8 Lesson01
A car leaves Winnipeg traveling east or west on a highway at 35 miles per hour. The document discusses using integrals to calculate how far the car is from Winnipeg after 4 hours, taking into account the car's average speed and time traveled. It provides some examples of potential velocity functions that could model the car's motion and notes the driver's poor driving abilities may impact the results.
Slides February 24th
The document discusses translations of graphs and functions. It provides examples of translating graphs by sliding them along the x-axis. It asks the reader to write equations representing translations of sine graphs based on given functions. It also asks the reader to write one function in terms of another after a translation. Homework assigned is to complete exercise 7 and encourages studying.
Slides February 23rd
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
AM40SFeb19
In a family with 3 children, the probability that 2 of the children will be girls can be calculated as follows:
There are 3 children and each child can be either a boy or a girl. So there are 2 possible outcomes for each child. Using the fundamental principle of counting, there are 2 * 2 * 2 = 8 possible combinations of boys and girls. Out of these 8 combinations, 3 combinations will have exactly 2 girls. Therefore, the probability that 2 of the 3 children will be girls is 3/8.
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Pre-Cal 20S September 29th
The problem asks to find the length of DC given that AB is 3 units long, BC is 4 units long, and DE is 10 units long. The midpoint formula is used to find the coordinates of point B given that the midpoint M of AB is (1/2, 6) and the coordinates of A are (3, 7).
Applied Math 20S October 8th, 2008
This document provides instructions for students to transition from Investigation 1 to Investigation 2 in their science class, suggests making graph paper if none is available, and assigns homework of questions 1 through 6 on pages 207 to 209 for their teacher, Mrs. Karras, which is due tomorrow.
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The document discusses finding the derivative of a function f(x) = x^2 at x = a in multiple ways. It lists methods such as the slope program, difference quotient, symmetric difference quotient, drawing the tangent line, using a numerical derivative program, and the limit definition of the derivative. The document provides instructions on deriving a derivative through various mathematical techniques.
AP Calculus October 6th, 2008
This document lists homework problems assigned from a textbook or class. The homework problems that were assigned are problems 1, 7, 9, 11, 15, 19, 22, 23, and 25.
Completing the Square
La ecuación original es y = x2 - 4x + 3, luego se agregan términos constantes para obtener y = x2 - 4x + 3 + 16x + 8 = x2 + 12x + 11. Finalmente, se factoriza como y = (x - 2)(x - 5) = 2x2 - 12x + 13.
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The document discusses homework assignments involving using experiments and simulations to determine probabilities. The first assignment involves simulating a 6 question multiple choice test by guessing answers. The second asks to simulate a 10 question true/false test using coins to find the probability of scoring at least 70% by guessing. The third asks to find the probability of flipping 3 pennies and getting at least 1 head. Guidance is provided on using the calculator's randBin function and the Random.org website to perform the simulations.
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The document discusses volumes of revolution and provides formulas to calculate volumes. It mentions volumes can be found by rotating a function about the x-axis and using a function that represents the changing cross-sectional areas. The document also references homework problems and calculating the volume of a cone but provides minimal details or explanations.
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The document contains several math and probability word problems and examples presented as homework assignments. It provides the questions, working, and answers for problems involving Pascal's triangle, counting paths, probability, coin flipping, and spinners. The document is a collection of homework questions and solutions on topics of combinatorics, probability, and experimental vs theoretical probability.
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This document provides instructions for calculating the volumes of various 3D shapes using integrals. It discusses finding the volume of a revolving cube, calculating the area between curves, and using a function for the changing radii to determine the volume of a cone.
Transformations02
The document discusses translations and stretches of graphs, with sections on the role of parameters a and b in shifting graphs right or left (parameter a) and up or down (parameter b). It also covers stretches and compressions along the x and y axes depending on whether parameters a or b are greater than, less than, or between 0 and 1.
Ch8 Lesson01
A car leaves Winnipeg traveling east or west on a highway at 35 miles per hour. The document discusses using integrals to calculate how far the car is from Winnipeg after 4 hours, taking into account the car's average speed and time traveled. It provides some examples of potential velocity functions that could model the car's motion and notes the driver's poor driving abilities may impact the results.
Slides February 24th
The document discusses translations of graphs and functions. It provides examples of translating graphs by sliding them along the x-axis. It asks the reader to write equations representing translations of sine graphs based on given functions. It also asks the reader to write one function in terms of another after a translation. Homework assigned is to complete exercise 7 and encourages studying.
Slides February 23rd
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
AM40SFeb19
In a family with 3 children, the probability that 2 of the children will be girls can be calculated as follows:
There are 3 children and each child can be either a boy or a girl. So there are 2 possible outcomes for each child. Using the fundamental principle of counting, there are 2 * 2 * 2 = 8 possible combinations of boys and girls. Out of these 8 combinations, 3 combinations will have exactly 2 girls. Therefore, the probability that 2 of the 3 children will be girls is 3/8.
PreCal 20S October 30
This document contains answers to a pre-test, including: the time in minutes taken to complete a task; an equation for height h in terms of meters m; the values for variables A, B, and C; the lengths of sides of triangles ABC and BCD; and ratios of sides for triangles ABC and BCD.
AM20S Oct29
This document contains 10 multiple choice questions testing math skills. The questions cover topics like fractions, square roots, averages, profit calculations, and repeating decimals. The document is assessing understanding of basic mathematical operations and concepts.
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The document discusses that if the discriminant of a quadratic function is negative, then the roots of the quadratic function are imaginary numbers rather than real numbers.
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The document contains 5 math problems involving geometry, calculating distances, finding equations of lines, and writing equations in slope-intercept form. It gives the questions and worked out solutions. The problems cover topics like finding coordinates of a point given other information, calculating distances between points, finding the equation of a line passing through two points, writing an equation in slope-intercept form, and finding the equation of a line perpendicular to another line with a given x-intercept.
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The document contains math word problems asking to find equations of lines from points and slopes, find intercepts of lines, and homework assignments for the week including exercises due today and Thursday, a pre-test on Friday, and a unit test on Monday.
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