{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the algebra / test selection.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"96e957e6-1935-538b-9094-37098af42129","task_key":"algebra--test--96e957e6-1935-538b-9094-37098af42129","task_revision_id":"2","upstream_id":"","short_description":"Below is a portion of the graph of a function, $y=h(x)$:","config":"algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Below is a portion of the graph of a function, $y=h(x)$:\\n\\n[asy]\\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-0.75,xmax=8.25,ymin=-1.25,ymax=10.25;\\n\\npen cqcqcq=rgb(0.75,0.75,0.75);\\n\\n/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype(\\\"2 2\\\"); real gx=1,gy=1;\\nfor(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);\\n\\nLabel laxis; laxis.p=fontsize(10);\\n\\nxaxis(\\\"\\\",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis(\\\"\\\",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true);\\nreal f1(real x){return (x-0.5)*(x-2.5)*(x-6.5)*(x-7.5)/16+x;}\\ndraw(graph(f1,-0.25,8.25),linewidth(1));\\nclip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);\\nlabel(\\\"$y=h(x)$\\\",(8.5,8),E);\\n[/asy]\\n\\nWhat is the sum of all integers $x$ in the interval shown ($0\\\\le x\\\\le 8$) such that $h(x)>x$ ?\",\"type\":\"Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}