Computing one randomly-selected element from the Hessian for a given quadratic function with two arguments. The coefficients of the function are drawn randomly and the correct answer has to be selected from five choice items. The latter are generated through
num_to_schoice()by providing the other three elements of the Hessian as typical errors. Further random answers are taken from a prespecified range, assuring only integer solutions. Although the Hessian of a quadratic function has only constant elements, an argument vector is given in the exercise because other types of functions might have non-constant Hessians.
Random numbers and text blocks
Verbatim R input/output:
(Note that the HTML output contains mathematical equations in MathML, rendered by MathJax using ‘mathjax = TRUE’. Instead it is also possible to use ‘converter = “pandoc-mathjax”’ so that LaTeX equations are rendered by MathJax directly.)
library("exams") set.seed(403) exams2html("hessian.Rmd", mathjax = TRUE) set.seed(403) exams2pdf("hessian.Rmd") set.seed(403) exams2html("hessian.Rnw", mathjax = TRUE) set.seed(403) exams2pdf("hessian.Rnw")