FROM DATA TO GRAPHS AND VICE VERSA 3rd year of secondary education.

 1. PLOTTING GRAPHS AND MORE You can use the  parameter "games" in this window, to draw a graph which relates to the activities accompanying it. The plotted graph and the data given should help you to carry out the activities appropriately. 1.- Imagine that you work as a sales representative for a company that designs computer games. You earn a fixed salary of 300 euros a month plus 3 euros for each game you sell. Which magnitudes are related to each other? Are they all variables? 2.- Draw a table of values in your notebook which shows the salary you earn for different amounts of videogames sold. Give the amount of games sold in multiples of five to make it easier. 3.- Draw the graph that appears in the window. What type of graph is it? Try and write a formula which allows you to work out in advance how much you will earn in a particular month knowing the number of games sold that month. 4.- How much did you earn last month, given that you sold 347 games? How many games did you sell during a month when you earned 714 euros?

 2. MORE COMPLEX GRAPHS In this window you will see a more complex graph that in the window above. To see the graph move point A along the horizontal axis. 5.-The graph that appears in the window represents the following situation: Some secondary school students have a rope which is 24 metres long. They have to use it to form rectangles in the school playground. Draw up a table of values which shows the relationship between the base of a rectangle and its area. 6.- Draw the graph that appears in your notebook. Mark some of the values given on the axes. Give a brief description of the graph.   7.- Write a formula that allows you to work out the area of any rectangle given its base.

3. VICE VERSA: THE OTHER WAY AROUND

Use point A in the following window to obtain useful data for the following activities.

8.- The following table of values shows the cost of electricity used in a house but doesn't include VAT, the standing charge etc (the information given is just one part of an electricity bill rather than all the information which is normally included on the bill).

 consumption (Kwh) 50 100 150 200 300 450 amount (€) 4.2 8.4 12.6 16.8 25.2 37.8

Change the position of point A several times. What do you notice? Draw the graph in your notebook including the information in the table.

9.- Try and place the line that appears at the top of the window onto all the points that appear during the activity. What happens? Can you explain why?

10.- How much would the bill be if n Kwh had been used? Work out the cost for the following amounts of electricity used :280 Kwh ; 410 Kwh and 605 Kwh.

11.-If we had included the standing charge part of the electricity bill, which is always the same (it covers equipment rental etc), in the table of values what would the graph have looked like?

4.  PLOTTING ANOTHER GRAPH

The following window is similar to the previous one. The difference is that the points that appear correspond to another type of relation between two variables. There are some lines linked together by points that you also have to use in the following activities.

Esta unidad interactiva requiere la máquina virtual de Java J2RE.

12.- The following table of values shows the frequency certain radio stations are broadcast on and the wavelength of the signal. Move point A which appears in the window. When the white lines disappear, draw the graph into your notebook. Write down the information given in the table on the appropriate part of the graph.

 Wavelength (m) 6000 3000 1500 750 375 250 frequency (kHz) 75 100 200 400 800 1200

13.- Place the points joining the red lines onto the points which appeared in the window. Draw the result in your notebook. What kind of graph does it remind you of?

14.- Find an algebraic expression that relates the broadcast frequency with the wavelength. What is the wavelength of the signal if a certain station broadcasts on FM on a frequency band of 88.5 MHz (megahertz)? (1 MHz = 1000 kHz)

 Josep Mª Navarro Canut Spanish Ministry of Education. Year 2001