Gradients and areas under curves
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The gradient of a curve at a point
Drawing a tangent and taking its gradient, since a curve’s gradient varies.
Average and instantaneous rates of change
The chord for the average rate, and the tangent for the rate at an instant.
Estimating the area under a graph
Splitting the region into strips and trapeziums to estimate the area.
Gradients and areas in context
On a velocity–time graph the gradient is acceleration and the area distance.