P3.3 Scientific Models
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The document discusses the importance of using standardized measurement units and tools when conducting scientific experiments and analyses. It describes the International System of Units (SI) as the standard system agreed upon by most scientists and countries, with all units based on multiples of ten. The document then outlines some common tools used to take measurements, such as meters, thermometers, and balances. It also identifies the SI base units for various quantities like length, mass, volume, density and temperature. Finally, safety procedures for science labs are emphasized.
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This document discusses organizing raw data from a study on employee commute distances into a grouped frequency distribution. The raw data consists of the number of miles each employee traveled to work each day. To draw useful conclusions, the data is organized into a table with class intervals, tallies of data points within each interval, and cumulative frequencies. The document provides guidelines for determining class limits and widths to properly categorize the data while maintaining mutually exclusive and exhaustive classes of equal size. Organizing data into a frequency distribution in this way facilitates analysis and presentation of the distribution's shape.
3.5 Exploratory Data Analysis
This document discusses exploratory data analysis techniques including boxplots and five-number summaries. It explains how to organize and graph data using histograms, frequency polygons, stem-and-leaf plots, and box-and-whisker plots. The five important values used in a boxplot are the minimum, first quartile, median, third quartile, and maximum. An example constructs a boxplot for a stockbroker's daily client numbers over 11 days.
3.3 Measures of Variation
This document discusses measures of variation in data, including range, variance, and standard deviation. It provides examples of calculating these measures for both individual data points and grouped data. The key measures are:
- Range is the highest value minus the lowest value.
- Variance is the average of the squared distances from the mean.
- Standard deviation is the square root of the variance, measuring average deviation from the mean.
- Coefficient of variation allows comparison of variables with different units by expressing standard deviation as a percentage of the mean.
- Chebyshev's theorem and the empirical rule specify what proportion of data falls within a given number of standard deviations of the mean.
3.4 Measures of Position
This document discusses various measures of position such as percentiles, quartiles, and standard scores. It provides examples of how to calculate percentiles, quartiles, z-scores, and identify outliers. Key points covered include how to interpret percentiles and z-scores, how to calculate quartiles and find values corresponding to specific percentiles, and the procedure for identifying outliers in a data set.
3.1-3.2 Measures of Central Tendency
This document discusses measures of central tendency including the mean, median, and mode. It provides examples of calculating the mean from raw data sets and frequency distributions. The median and mode are defined as the middle value and most frequent value, respectively. Methods for calculating each from both types of data are shown. Other measures covered include the midrange and the effects of outliers. Shapes of distributions are discussed including positively and negatively skewed and symmetric. Practice problems are provided to reinforce the concepts.
4 3 Addition Rules for Probability
This document discusses the addition rules for probability of compound events. It defines mutually exclusive events as events that cannot occur at the same time, and explains that for mutually exclusive events A and B, the probability of A or B is equal to the probability of A plus the probability of B. For events that are not mutually exclusive, the probability of A or B is equal to the probability of A plus the probability of B minus the probability of A and B occurring together. Several examples are provided to illustrate calculating probabilities using these addition rules.
4.1-4.2 Sample Spaces and Probability
The document defines key concepts in probability theory, such as probability experiments, outcomes, sample spaces, events, classical probability, empirical probability, and subjective probability. It provides examples of how to calculate probabilities of simple and compound events using classical probability methods, including determining probabilities using fractions or decimals and interpreting "and" and "or" probabilities.
2.1 Phy I - Displacement and Velocity
This document discusses displacement, velocity, and related concepts. It begins by defining displacement as the straight-line change in an object's position, measured in meters. Displacement is distinguished from distance traveled, as displacement considers only the net change in position regardless of path. Equations for calculating average velocity from displacement and time are provided. Positive and negative displacement and velocity are described based on direction of motion. Instantaneous velocity is defined as the velocity at a specific point and can be determined from the slope of a tangent line on a position-time graph. Sample problems and practice questions are included for students to calculate displacement and average velocity in various scenarios.
2.2 Phy I - Acceleration
This document discusses acceleration and kinematic equations for objects experiencing constant acceleration. It defines acceleration as the rate of change of velocity and introduces the average acceleration equation. It then derives and explains the equations for displacement given constant acceleration using the relationships between velocity, acceleration, displacement and time. Sample problems demonstrate applying the equations to calculate values when given acceleration, initial/final velocities, displacement or time. The key equations covered are for average and final velocity, and displacement given constant acceleration.
1.2 Measurements in Experiments
This document provides an overview of measurements and significant figures in physics experiments. It defines key terms like accuracy, precision, and significant figures. Accuracy refers to how close a measurement is to the true value, while precision describes the exactness of a measurement. Significant figures indicate the precision of a measuring device. The document reviews proper techniques for measurements, unit conversions using dimensional analysis, and calculating with significant figures in additions, subtractions, multiplications and divisions. Students are expected to learn the basic SI units, prefixes, and how to determine the number of significant figures in given values and calculations.
1.1 What is Physics?
Physics is the study of the physical world and how it behaves. It can be broken down into seven main categories including mechanics, thermodynamics, optics, and electromagnetism. The scientific method involves making observations, formulating hypotheses, testing with experiments, and drawing conclusions. Models are used to simplify complex physical systems and guide hypothesis building and experimental design by focusing only on relevant characteristics.
1.3 The Language of Physics
This document provides an introduction to the language of physics. It discusses how mathematical equations are used to describe physical phenomena and symbols commonly used in equations. Examples are provided on how to interpret equations and use dimensional analysis to check if equations are dimensionally consistent by evaluating the dimensions on each side. Students are assigned textbook problems evaluating physics expressions using these concepts.
AP Physics 1 - Introduction
This document provides an introduction to physics, covering several key topics:
- The main areas of physics are mechanics, thermodynamics, vibrations and waves, optics, electromagnetism, relativity, and quantum mechanics.
- Dimensional analysis is used to determine whether equations are valid by checking that quantities with the same dimensions can be combined and that both sides of an equation have the same dimensions.
- Symbols like Δ, Σ, g, x are commonly used in physics equations to represent concepts like change, sum, gravitational acceleration, and displacement.
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P3.3 Scientific Models
- 1. Warmup How would a standard system of measurements, agreed to and used around the world, make life easier? Give examples.
- 3. Objectives: 1. Identify tools used to collect and analyze data. 2. Explain the importance of the International System of Units. 3. Identify the appropriate units to use for particular measurements. 4. Identify safety symbols.
- 4. Tools in Science To get the best measurements You need the proper tools. ○ Stopwatches ○ Metersticks ○ Thermometers ○ Balances Tools are also used to: analyze data. ○ Calculators ○ Computers ○ Even pencils and paper
- 5. Making Measurements The International System of Units (SI) current name for the metric system. ○ Used by most scientists and almost all countries. All SI units are based on the number 10. Length SI unit - meter (m).
- 6. Mass Amount of matter that something is made of SI unit - kilogram (kg) Volume Amount of space that something occupies. Liquids - liters (L) or milliliters (mL) Solids - cubic meters (m3), cubic centimeters (cm3)
- 7. Density Amount of matter in a given volume SI unit – gram per milliliter (g/mL) or grams per cubic centimeter (g/cm3). ○ Derived quantity! Temperature measure of how hot (or cold) something is. ○ Scientists often use degrees Celsius (°C) as the unit. ○ SI base unit - Kelvins (K) d e n s ity m a s s v o lu m e
- 8. Safety Rules Always follow your teacher’s instructions. Read lab procedures carefully and thoroughly. Pay special attention to safety information and know the safety symbols.