AI generatedAlgebraGCSE Higher

Estimating a gradient at a point

Draw a tangent and use a large gradient triangle.

  • An average gradient uses a chord between two points.
  • A gradient at one point uses a tangent at that point.
  • Read two points on the chosen straight line, then calculate change in ÷ change in .

Example 1

Estimate the gradient 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

Estimate the gradient 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

Estimate the gradient 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

Estimate the gradient 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

Estimate the gradient 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

Estimate the gradient 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

Estimate the gradient 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.
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