general mathematics pathway 2 hsc course...•another variation to simpson’s rule is to find the...

General Mathematics Pathway 2 HSC Course:

Simpson’s Rule

Introduction Simpson’s Rule

• What is Simpson’s Rule?

• Exploring the Elements of Simpson’s Rule and it’s Variations

• Simpson’s Rule Examples

• Using Simpson’s Rule to Estimate Volumes

HSC General Mathematics 2 © Adrian Kruse & Edrolo 2015

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What is Simpson’s Rule?

Source: http://www.hngn.com/articles/74316/20150304/homer-simpson-brilliant-mind-

cartoon-dad-figured-out-mass-higgs.htm



THEORY



What is Simpson’s Rule? * We use Simpson’s Rule to find an approximation for the area of a

shape that has one or more edges which are not straight.

* We can find Simpson’s Rule on your General Mathematics

Formulae Sheet:



Exploring the Elements of

Simpson’s Rule and its Variations

25 m

42 m 31 m

30 m 30 m



Exploring the Elements of

Simpson’s Rule and its Variations

• h refers to the “width of each strip”. These widths are always the

same size.

• d refers to the distance of the first offset, middle offset and the

last offset

• Notice that there are three offsets. This means that there are two

strips. So if we need to find an area containing four strips we need

to do Simpson’s Rule twice.

• Another variation to Simpson’s Rule is to find the volume of

water in a dam after finding the area of the surface of the dam.

This becomes a volume of a prism question.



Fact Check

Below is an irregular shaped piece of land. If we use Simpson’s Rule to

estimate the area of the land, h = 30 m. Is this True or False?

25 m

42 m 31 m

30 m 30 m



WORKED EXAMPLES



Simpson’s Rule Worked Examples

Find an approximation for the area of this piece of land depicted below:




2003 HSC Question 23c



Using Simpson’s Rule to Estimate

Volumes

Simpson’s Rule also has a volume variation:

The main difference is that we will be using the area of cross sections

rather than distances of offsets.




2014 HSC Specimen Paper Q9



QUESTIONS FOR

STUDENTS



Simpson’s Rule Question

2011 HSC Q13




2009 HSC Q25c



Simpson’s Rule - Challenge

Question

2008 HSC Q28b




a) 39 km3

b) 73 km3

c) 146 km3

d) 293 km3



Source: https://crystalhislop.wordpress.com/



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