Use Euler’s method with step length 0.1 to find an approximate value of y when x = 0.4.

Write down, giving a reason, whether your approximate value for y is greater than or less than the actual value of y .

use of \(y \to y + h\frac{{{\text{d}}y}}{{{\text{d}}x}}\)     (M1)

approximate value of y = 1.57     A1

Note: Accept values in the tables correct to 3 significant figures.

[7 marks]

the approximate value is less than the actual value because it is assumed that \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) remains constant throughout each interval whereas it is actually an increasing function     R1

[1 mark]

Most candidates were familiar with Euler’s method. The most common way of losing marks was either to round intermediate answers to insufficient accuracy or simply to make an arithmetic error. Many candidates were given an accuracy penalty for not rounding their answer to three significant figures. Few candidates were able to answer (b) correctly with most believing incorrectly that the step length was a relevant factor.

Most candidates were familiar with Euler’s method. The most common way of losing marks was either to round intermediate answers to insufficient accuracy or simply to make an arithmetic error. Many candidates were given an accuracy penalty for not rounding their answer to three significant figures. Few candidates were able to answer (b) correctly with most believing incorrectly that the step length was a relevant factor.