A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

A generalisation is a statement or rule that applies correctly to all relevant cases.

Efficiently estimating journeys from non-linear graphs

Maths

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

Real-life graphs

To be more efficient, before calculating $${1\over2}(3+7)\times{5}+{1\over2}(7+11)\times{5}+{1\over2}(11+20)\times{5}$$ we could __________ and __________.

Use four strips of equal width to estimate the distance travelled between $$0$$ and $$8$$ seconds. Give your answer to $$1$$ d.p. {{}} metres.

What are the hidden labels on this diagram?

$$A\approx{1\over2}h(y_0+y_n+2(y_1+y_2+...+y_{n-1})$$

$$A\approx{1\over2}h(y_0+y_{n-1}+2(y_1+y_2+...+y_n)$$

$$A\approx{1\over2}h(y_0+y_n+2(y_1+y_2+...+y_{5})$$

$$A\approx{1\over2}h(y_0+y_n+2(y_1+y_{n-1})$$

Which of the below is the Trapezium Rule?

When using the Trapezium Rule which of the below calculates $$h$$, the width of the strips? $$n$$ is the number of trapezia.

Use the Trapezium Rule to estimate the area under this curve between $$t = 0$$ and $$t = 20$$ using $$5$$ trapeziums. {{}} metres.

We could estimate the distance travelled by the vehicle modelled in this speed-time graph by mapping __________ onto the graph.

breaking the shape down into a rectangle and triangle

We could improve the accuracy of this estimation by __________.

Map one polygon onto the graph to estimate the distance travelled between $$0$$ and $$4$$ seconds. {{}} metres.

Map two polygons onto the graph to estimate the distance travelled between $$0$$ and $$8$$ seconds. Give your answer to $$1$$ d.p. {{}} metres.

What are the common factors in this calculation? $${1\over4}(3+7)\times{h}+{1\over4}(7+11)\times{h}+{1\over4}(11+20)\times{h}$$

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