COMPARING GRAPHS

3rd year of secondary education

 

1. CAR JOURNEYS

The graphs in this window show the journeys made by two cars which leave and return to the same town A after a day trip.

1.- Copy both graphs, exactly as they are in the window, into your exercise book. Then, draw up a table of values, for each car, which shows the distance from town A every 30 minutes.

2.- Work out the average speed travelled by each car during each stage of the journey. Which car has the highest average speed? Which car gets caught in a big traffic jam on the way back? How do you know this?

3.- The drivers of both cars stop for lunch. How long does each car stop for? Where do the people travelling in the first car stop? What about those travelling in the second car? Which car stops so that the passengers can have a drink on the way back? How long does the car stop for?

 

2. INCOME AND EXPENDITURE

The graphs in this window show the income and expenditure of a T-shirt box factory, according to the number of T-shirts sold.

4.-Draw up a table of values for each graph in your exercise book. Write down the values for each batch of 30 T-shirts sold.

 

5.- Use each of these tables to draw up a new table in your exercise book which shows the net profit of the company according to the number of T-shirts sold.

 

6.- Answer the following questions:

a.- How much would 60 T-shirts cost? How much profit would be made on the sale?

b.- How many T-shirts need to be sold so that the income is equal to the expenditure?

c.- Work out the profit made on a sale of 75 T-shirts.

d.- Would the cost of manufacture and distribution be covered on a sale of 130 T-shirts?

7.- Work out the algebraic equations that we can use to calculate the income and expenditure generated by the sale of any number of T-shirts. Apply the equations to these cases where the following number of T-shirts are sold: 420, 600, 1300 and 2800.

3. A 1,000 METRE RACE

This window shows the performance of two athletes in a 1,000-metre race (middle-distance). Points Z and W can be moved with the mouse.

 

8.- Copy the graphs into your exercise book. Write a short description of the performance of the two athletes during the race. Draw up the corresponding tables of values too.

9.- Answer the following questions:

a.- How far had each athlete run after the first 60 seconds? Work out the average speed of each athlete.

 

b.- When athlete A catches up with athlete B how far have they both run and how long have they been running for?

c.- Work out how far behind athlete A athlete B is when athlete A crosses the finish line.

d.- Work out the average speed run by each athlete for each 40-second interval, from the start of the race until the finish line.

10.- Even though it is a bit difficult, try and find an equation that allows us to work out an approximate graph of the race for each athlete.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Josep Mª Navarro Canut

 

ProyectoDescartes.org. Year 2013

 

 

 

 

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