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Topic #02 - Mathematical Relationships

Word Problems

 Topic #02 Concepts and Skills Link to "Concepts and Skills"

 Vocabulary, Variables and Equations equation: an expression or a proposition, often algebraic, asserting the equality of two quantities solution: the process of determining the answer to a problem variable: a quantity or function that may assume any given value or set of values  dependent variable: a variable in an experiment that depends on the value of another variable. As in y depends on x. independent variable: a variable in an experiemnt that is not dependent on another variable, but whode value is often manipulted during the experiment. controlled variable: variables that are held constant so they do not influence the ourcome of an experiment data: values, such as observations and measurements, derived from scientific experiments data table: a table of data organized in such a way to reveal patterns among observations and measurements  graph: a series of points, discrete or continuous, as in forming a curve or surface, where each point represents a value of a given function. function: a mathematical relationship expressed as an equation that describes a relationship between or among variable variable values curve: a generic term used to mean the function / equation displayed on a graph x-axis: the horizonatal line through the origin on a cartesian coordinate system where in 2 dimensions y = 0 and in 3 dimensions y = 0 and z = 0 y-axis: the vertical line through the origin on a cartesian coordinate system where in 2 dimensions x = 0 and in 3 dimensions x = 0 and z = 0 plot: to determine and mark (points), as on plotting paper (graph paper), by means of measurements or coordinates data point: one point representing one piece of data on a graph. (On a two dimensional graph a data point is defined in terms of an x and y coordinate pair. On three dimensional graph a data point is represented by an x, y and z value.)  slope: the rate of change in a derived quantity found by dividing the change in the y value divided by the change in the x value on a two dimensional graph y-intercept: the y value in a function that has been plotted when the x value is zero relationship: the mathematical connection between to variable values as defined by a function (equation) direct variation: a realtionship that says that one variable such as the y variable varies directly with another variable such as the x variable. Mathematicians say this as "y is a function of x". direct proportion: a means of saying that the variable values in a direct variation relationship are proportional to one another. That is as one increases so does the other. inverse variation: a relationship that says that one variable such as the y variable varies inversely with another variable such as the x variable. Mathematicians say this as "y is a function of 1/x". inverse proportion: a means of saying that the variable values in an inverse variation relationship are inversely proportional to one another. That is as one increases the other decreases proportionally. linear relationship: another way of describig that a relationship between two variables is one of being a direct variation. Linear (functions) relationships always appear as straight lines when plotted on a two dimensional cartesian coordinate system. quadratic relationship: a relationship that says that one variable such as the y variable varies directly with the square of another variable. Mathematicians say this as "y varying directly with the square of x is a parabolic relationship".

 Review Questions: Chapter 2 Reviewing Concepts Questions: Section 2.1 1. Why is SI important? 2. List the common SI base units. 3. How are base units and derived units related? 4. You convert the speed limit of an expressway given in miles per hour into meters per second and obtain the value 1.5 m/s.  Is this calculation likely to be correct? Explain. 5. Give the name for each multiple of the meter. a. 1/100m b. 1/1000m c. 1000m 6. How may units be used to check on whether a conversion factor has been used correctly? Section 2.2 7. What determines the precision of a measurement? 8. Explain how a measurement can be precise but not accurate. 9. How does the last digit differ form the other digits in a measurement? 10. Your lab partner recorded a measurement as 100g. a. Why is it difficult to tell the number of significant digits in this measurement? b. How can the number of significant digits in such a number be made clear? Section 2.3 11. How do you find the slope of a linear graph? 12. A person who has recently consumed alcohol usually has longer reaction times than a person who has not.  Thus, the time between seeing a stoplight and hitting the brakes would be longer for the drinker than for the nondrinker. a. For a fixed speed, would the reaction distance for a driver who had consumed alcohol be longer or shorter than for a nondrinking driver? b. Would the slope of the graph of that reaction distance versus speed have the steeper or the more gradual slope? 13. During a laboratory experiment, the temperature of the gas in a balloon is varied and the volume of the balloon is measured.  Which quantity is the independent variable?  Which quantity is the dependent variable? 14. For a graph of the experiment in 13, a. What quantity is plotted on the horizontal axis? b. What quantity is plotted on the vertical axis? 15. A relationship between the independent variable x and the dependent variable y can e written using the equation y = ax^2, where a is a constant. a. What is the shape of the graph of this equation? b. If you define a quantity z = x^2, what would be the shape of the graph obtained by plotting y versus z? 16. Given the equation F = mv^2/R, what relationship exists between a. F and R? b. F and m? c. F and v? 17. Based on the equation in problem 16, what type of graph would be drawn for  a. F versus R? b. F versus m? c. F versus v?