{"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 full test split: 5,000 problems across all seven subjects.","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":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"799a3178-e0b3-5375-a457-e2dde3368d8f","task_key":"algebra--test--799a3178-e0b3-5375-a457-e2dde3368d8f","task_revision_id":"1","upstream_id":"","short_description":"The graphs of two linear functions, $f(x)$ and $g(x)$, are shown here on one set…","config":"algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The graphs of two linear functions, $f(x)$ and $g(x)$, are shown here on one set of axes: [asy]\\nsize(150);\\nreal ticklen=3;\\nreal tickspace=2;\\n\\nreal ticklength=0.1cm;\\nreal axisarrowsize=0.14cm;\\npen axispen=black+1.3bp;\\nreal vectorarrowsize=0.2cm;\\nreal tickdown=-0.5;\\nreal tickdownlength=-0.15inch;\\nreal tickdownbase=0.3;\\nreal wholetickdown=tickdown;\\nvoid rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {\\n\\nimport graph;\\n\\nreal i;\\n\\nif(complexplane) {\\n\\nlabel(\\\"$\\\\textnormal{Re}$\\\",(xright,0),SE);\\n\\nlabel(\\\"$\\\\textnormal{Im}$\\\",(0,ytop),NW);\\n\\n} else {\\n\\nlabel(\\\"$x$\\\",(xright+0.4,-0.5));\\n\\nlabel(\\\"$y$\\\",(-0.5,ytop+0.2));\\n\\n}\\n\\nylimits(ybottom,ytop);\\n\\nxlimits( xleft, xright);\\n\\nreal[] TicksArrx,TicksArry;\\n\\nfor(i=xleft+xstep; i<xright; i+=xstep) {\\n\\nif(abs(i) >0.1) {\\n\\nTicksArrx.push(i);\\n\\n}\\n\\n}\\n\\nfor(i=ybottom+ystep; i<ytop; i+=ystep) {\\n\\nif(abs(i) >0.1) {\\n\\nTicksArry.push(i);\\n\\n}\\n\\n}\\n\\nif(usegrid) {\\n\\nxaxis(BottomTop(extend=false), Ticks(\\\"%\\\", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);//,above=true);\\n\\nyaxis(LeftRight(extend=false),Ticks(\\\"%\\\", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);//,Arrows);\\n\\n}\\n\\nif(useticks) {\\n\\nxequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks(\\\"%\\\",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));\\n\\nyequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks(\\\"%\\\",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));\\n\\n} else {\\n\\nxequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));\\n\\nyequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));\\n\\n}\\n};\\nrr_cartesian_axes(-5,5,-5,5);\\nreal f(real x) {return (4-x)/2;}\\nreal g(real x) {return 2x-4;}\\ndraw(graph(f,-5,5,operator ..), blue+1.25);\\ndraw(graph(g,-1/2,9/2,operator ..), orange+1.25);\\ndraw((-3,-6)--(-1,-6),blue+1.25); label(\\\"$y=f(x)$\\\",(-1,-6),E);\\ndraw((-3,-7)--(-1,-7),orange+1.25); label(\\\"$y=g(x)$\\\",(-1,-7),E);\\n[/asy] Each small box in the grid is $1$ unit by $1$ unit.\\n\\nEvaluate $f(g(1))\\\\cdot g(f(1))$.\",\"type\":\"Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}