########################### # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGML.pl", "PGbasicmacros.pl", "parserRadioButtons.pl", "draggableProof.pl", "PGcourse.pl" ); TEXT(beginproblem()); ########################### # Setup Context("Numeric"); $CorrectProof = DraggableProof([ "Let $$n$$ be even.", "By the definition of even, $$n = 2k$$ for some integer $$k$$.", "It follows that $$\\n^2 + 3n + 5 = (2k)^2 + 3(2k) + 5$$ $$\\ \hspace{38mm}= 4k^2 + 6k + 5$$ $$\\ \hspace{37mm} = 2(2k^2 + 3k+ 2) + 1$$", "Since $$k$$ is an integer,", "$$2k^2 + 3k+ 2$$ is an integer.", "Since $$n^2 + 3n + 5$$ equals $$2$$ times an integer plus one,", "$$n^2 + 3n + 5$$ is odd."], # The lines below are extras and will be listed as options but not # needed for the correct answer in$Proof. ["$$2k^2 + 3k+ 2$$ is even.", "By the definition of odd, $$n = 2k + 1$$ for some integer $$k$$.", "Let $$n$$ be odd."] , SourceLabel => "Choose from this list of sentences", TargetLabel => "Direct proof of the statement (in order):", ); ################################### # Main text BEGIN_PGML Order *[$CorrectProof->numNeeded] of* the following sentences so that they form a direct proof of the statement: If [n] is even, then [n^2 + 3n + 5] is odd. [@$CorrectProof->Print @]* END_PGML ############################ # Answer evaluation $showPartialCorrectAnswers = 0; install_problem_grader(~~&std_problem_grader); ANS($CorrectProof->cmp); ENDDOCUMENT();