FUNCTIONS
QUESTION 1 – 10 marks?Based on the definitions discussed in the course material and many other references, write your own definition of a function, the domain of a function and the range of a function. Give an example of each of the following: linear, quadratic, 3rd degree polynomial, exponential, logarithmic and periodic functions in your definitions.
QUESTION 2 – 20 marks?Investigate a life related relationship between two variables that you think may result in a periodic function. Check with your teacher as to whether this would be appropriate and ensure you are able to gather the data required reasonably easily.
. (a) Describe the relationship you have chosen to investigate and why do you believe the relationship may be periodic.
. (b) Describe what are your variables – specify dependent and independent.
. (c) Describe how you gathered your data.
. (d) Present your data in a table – computer generated screen printout.
(Note: You will not lose marks if the data turns out to be non periodic as long as you can explain in your conclusion why this model is not appropriate.)
QUESTION 3 – 10 marks?Investigate and explain in your own words and using your own examples what is the Amplitude, Frequency, Period and Average of periodic functions.
QUESTION 4 – 10 marks?Investigate and explain in your own words and using your own examples how is the inverse of one periodic function defined.
QUESTION 5 – 40 marks?Part 1: Research the invention and use of the Richter Scale. (Now adjusted and called the Moment Magnitude Scale.)?You may consult multiple websites, books, articles; however, it is highly recommended that you watch the video presentation on the Richter Scale at www.khanacademy.org as part of your research. You may present your research in “bullet points” that are complete sentences. Your presentation does NOT need to go into deep/long scientific explanations, but should demonstrate your general knowledge gained from research. Write facts as if you were presenting information to a younger brother/sister. Questions you may consider in your research and presentation might include:
What does the Richter Scale/MMS measure??How does the Richter Scale/MMS measurement compare to the actual magnitude of ground movement??What does one point higher on the scale represent, (mathematically) of the magnitude of ground movement?
Part 2: Research two past earthquakes
Present your research in a one page (2 at most) format that includes: date, location of epicenter, Richter Scale and/or Mercalli Scale measurement (may depend on date of quake).
Part 3: Mathematically Compute and Compare Earthquakes
Quantitatively compare the magnitude of ground movement (shaking) of the two past earthquakes from Part 2. The following points must be part of your research and presentation:
Write the equivalent of each Richter Scale value in logarithmic form as a basic logarithmic equation.?Write each logarithmic equation as an exponential equation.?Write a ratio of exponential expressions, which evolves from the exponential equations and then, compare the intensities of earthquakes.
QUESTION 2 – 20 marks?Investigate a life related relationship between two variables that you think may result in a periodic function. Check with your teacher as to whether this would be appropriate and ensure you are able to gather the data required reasonably easily.
. (a) Describe the relationship you have chosen to investigate and why do you believe the relationship may be periodic.
. (b) Describe what are your variables – specify dependent and independent.
. (c) Describe how you gathered your data.
. (d) Present your data in a table – computer generated screen printout.
(Note: You will not lose marks if the data turns out to be non periodic as long as you can explain in your conclusion why this model is not appropriate.)
QUESTION 3 – 10 marks?Investigate and explain in your own words and using your own examples what is the Amplitude, Frequency, Period and Average of periodic functions.
QUESTION 4 – 10 marks?Investigate and explain in your own words and using your own examples how is the inverse of one periodic function defined.
QUESTION 5 – 40 marks?Part 1: Research the invention and use of the Richter Scale. (Now adjusted and called the Moment Magnitude Scale.)?You may consult multiple websites, books, articles; however, it is highly recommended that you watch the video presentation on the Richter Scale at www.khanacademy.org as part of your research. You may present your research in “bullet points” that are complete sentences. Your presentation does NOT need to go into deep/long scientific explanations, but should demonstrate your general knowledge gained from research. Write facts as if you were presenting information to a younger brother/sister. Questions you may consider in your research and presentation might include:
What does the Richter Scale/MMS measure??How does the Richter Scale/MMS measurement compare to the actual magnitude of ground movement??What does one point higher on the scale represent, (mathematically) of the magnitude of ground movement?
Part 2: Research two past earthquakes
Present your research in a one page (2 at most) format that includes: date, location of epicenter, Richter Scale and/or Mercalli Scale measurement (may depend on date of quake).
Part 3: Mathematically Compute and Compare Earthquakes
Quantitatively compare the magnitude of ground movement (shaking) of the two past earthquakes from Part 2. The following points must be part of your research and presentation:
Write the equivalent of each Richter Scale value in logarithmic form as a basic logarithmic equation.?Write each logarithmic equation as an exponential equation.?Write a ratio of exponential expressions, which evolves from the exponential equations and then, compare the intensities of earthquakes.
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