Question 6 - A-Level Maths

Exam Board	OCR MEI
Module	Further Numerical Methods (Further Numerical Methods)
Year	2023
Session	June
Topic	Sign Change & Interval Methods
Type	Error Analysis in Approximations

1. Calculate the relative error when $\pi$ is chopped to $\mathbf { 2 }$ decimal places in approximating $$\pi ^ { 2 } + 2 .$$
2. Without doing any calculation, explain whether the relative error would be the same when $\pi$ is chopped to 2 decimal places when approximating $( \pi + 2 ) ^ { 2 }$. The table shows some spreadsheet output. The values of $x$ in column A are exact.
  A B C
  1 $x$ $10 ^ { x }$ $\log _ { 10 } 10 ^ { x }$
  2 $1 \mathrm { E } - 12$ 1 $1.00001 \mathrm { E } - 12$
  3 $1 \mathrm { E } - 11$ 1 $9.99998 \mathrm { E } - 12$
  The formula in cell B2 is $= 10 ^ { \wedge } \mathrm { A } 2$.
  This has been copied down to cell B3.
  The formula in cell C2 is $\quad =$ LOG(B2) .
  This formula has been copied down to cell C3.
1. Write the value displayed in cell C 2 in standard mathematical notation.
2. Explain why the values in cells C 2 and C 3 are neither zero nor the same as the values in cells A2 and A3 respectively.