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# Core 3 Simpsons Rule

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Designed for OCR A Level mathematics.

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### Core 3 Simpsons Rule

1. 1. Starter Use the Trapezium Rule with four intervals to estimate the value of Have you overestimated or underestimated the true area? 3.28 (3 s.f.)
2. 2. Objective: to understand Simpson’s Rule Thomas Simpson (1710 – 1761)
3. 3. Simpson’s Rule Simpson’s Rule was actually invented by Sir Isaac Newton but Thomas Simpson published it again in 1743. It is more accurate than the Trapezium Rule because it fits a number of parabolas to the curve rather than straight lines. To use Simpson’s Rule, you must have an even number of intervals (or an odd number of ordinates).
4. 4. Example 1 Use Simpson’s Rule with five ordinates to find the approximate value of 3.24 (3 s.f.)
5. 5. Example 2 Use Simpson’s Rule with four intervals to find the approximate value of 2.87 (3 s.f.)
6. 6. Core 3 & 4 Textbook Exercise 12B Page 188