GCSE Maths (AQA)

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Algebra Graphs

Gradient of a Tangent

4:44 calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts
Spec A15
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  • The tangent to a curve at a point is a straight line that just touches the curve at that point
  • Tangent lines are similar to tangent lines of a circle, as they both just touch without crossing
  • The gradient of the curve at a point is equal to the gradient of the tangent at that point
  • The tangent is parallel to the curve at the highlighted point and has the same gradient
  • The gradient of a straight line can be calculated using the formula: gradient = (y2 - y1) / (x2 - x1)
  • The phrase "rise over run" can be used to remember how to calculate the gradient
  • Drawing a perfect tangent by hand is difficult, so there is a range of acceptable gradients
  • An example is given to demonstrate how to calculate the gradient of a curve using the tangent line method

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310

questions for Algebra

95

questions for Graphs