Gradients and areas under graphs

What this chapter teaches

The gradient of a curve at a point is the gradient of the tangent there. A chord gives only an average gradient. The area under a graph is estimated with trapeziums, one for each strip between two readings. On a distance time graph the gradient is the speed. On a speed time graph the gradient is the acceleration and the area is the distance.

Three questions to ask

There is no one right wording. Listen for the idea.

1. How do you estimate the speed at one moment from a distance time curve?
2. Why is a chord not the same as a tangent?
3. If a graph is cut into 6 strips, how many heights do you read, and what does the area mean on a speed time graph?

After the chapter, the learner can

• Estimate the gradient of a curve by drawing a tangent
• Estimate the area under a curve using trapeziums
• Explain what gradient and area mean on a speed time graph