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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

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More Parabolic Patterns

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

 

The diagram shows a simple circuit: the cell provides energy, V volts, which causes a current, I amps, to flow around the circuit. There is also a resistance, R ohms.
 circuit diagram
 
This circuit provides a simple model for what happens in an electric kettle: a resistance converts electrical energy into heat energy by impeding the flow of electrons around the circuit.

The table shows data collected from a circuit like this.
 

Resistance (ohms) Temperature (degrees Celsius)
5 44.9
6 50
7 55.1
8 59.9
9 65
10 70.1


  • Draw a graph of this data, with the resistance on the horizontal axis, putting a straight line through the points.
  • Find the gradient of the line.
  • Find the equation of the line.


Once you have found the equation, discuss these questions:
 

  • What resistance would you need to heat water to 100 C°?
  • What would the temperature be if the resistance was zero?
  • Do you think that in practice, any circuit can have zero resistance?