Gradients of Curves

Gradients

• You can estimate the gradient of a curve at a given point by drawing a tangent to the curve at that point

• This distance-time graph shows a runner accelerating at the start of a race

  

• Always draw a large triangle to make your estimate as accurate as possible

• Pay attention to the scale when you calculate the gradient

Problem solved

• To work the average rate of change between two points draw a straight line between these points on the graph and find its gradient
• This is the same as working out
  • Change in voltage / change in time
• You need to find the point on the curve with the same gradient
• That means you need to find a tangent to the curve that is parallel to the first line
• Slide a transparent ruler across the graph until it just touches the curve
• You can show how you got your answer by drawing the tangent to the curve at this point

Examiners report

• Read scales carefully
• On the horizontal axis squares can represent different amount

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