OCR MEI Further Numerical Methods 2023 June — Question 1

Exam BoardOCR MEI
ModuleFurther Numerical Methods (Further Numerical Methods)
Year2023
SessionJune
TopicSign Change & Interval Methods
TypeError Analysis in Approximations

1 You are given that \(\left( x _ { 1 } , y _ { 1 } \right) = ( 0.9,2.3 )\) and \(\left( x _ { 2 } , y _ { 2 } \right) = ( 1.1,2.7 )\).
The values of \(x _ { 1 }\) and \(x _ { 2 }\) have been rounded to \(\mathbf { 1 }\) decimal place.
  1. Determine the range of possible values of \(x _ { 2 } - x _ { 1 }\). The values of \(y _ { 1 }\) and \(y _ { 2 }\) have been chopped to \(\mathbf { 1 }\) decimal place.
  2. Determine the range of possible values of \(y _ { 2 } - y _ { 1 }\). You are given that \(m = \frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } }\).
  3. Determine the range of possible values of \(m\).
  4. Explain why your answer to part (c) is much larger than your answer to part (a) and your answer to part (b).