Designed for OCR A Level mathematics.

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. Objective: to understand Simpson’s Rule Thomas Simpson (1710 – 1761)

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. Example 1 Use Simpson’s Rule with five ordinates to find the approximate value of 3.24 (3 s.f.)

5. Example 2 Use Simpson’s Rule with four intervals to find the approximate value of 2.87 (3 s.f.)

6. Core 3 & 4 Textbook Exercise 12B Page 188