AI generatedRatio, proportion and rates of changeGCSE Higher

Instantaneous rate of change in context

Interpret a tangent gradient with units.

  • Average rate: use the chord between the two specified points.
  • Instantaneous rate: use a tangent at the specified point.
  • Divide the vertical change by the horizontal change, and include the rate units.

Example 1

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph0.511.522.533.542468100P
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.

Example 2

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph0.511.522.533.5424681012140P
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.

Your turn

Question 1

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph0.511.522.533.542.557.51012.51517.50P
Check answer
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.
Question 2

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph1234524681012140P
Check answer
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.
Question 3

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph1234551015200P
Check answer
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.
Question 4

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph12345510152025300P
Check answer
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.
Question 5

The curve shows the distance of a moving object in metres against time in seconds. Estimate the speed at .

Coordinate graph12345651015200P
Check answer
Draw a tangent at P. Read two well-separated points on the tangent, not on the curve.Use the vertical change divided by the horizontal change.
← All Ratio, proportion and rates of change cardsReport a mistake