Sketch and grade curves with pl-sketch

Question

The examples below illustrate different drawing tools and grading criteria available in pl-sketch. For convenience, all examples allow blank submissions.

A single pl-sketch canvas can host multiple curves that are each graded independently. Each tool gets its own color, its own drawing style, and its own match-function criterion — so students get per-curve feedback, and the solution overlay reveals all three together.

For full marks, draw all three functions on the grid below:

$f(x) = \sin(x)$ — freehand
$g(x) = x^2/4$ — smooth spline
$h(x) = |x|$ — polyline

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"dashStyle": null, "fillColor": "none", "lengthConstraint": null, "directionConstraint": null, "overlay": true}, {"id": "sin-solution-overlay", "name": "freeform", "size": null, "color": "#1a3a8f", "group": null, "label": "sin(x)", "limit": null, "closed": null, "helper": false, "hollow": null, "opacity": null, "readonly": true, "arrowHead": null, "dashStyle": null, "fillColor": null, "lengthConstraint": null, "directionConstraint": null, "overlay": true}, {"id": "sin", "name": "freeform", "size": null, "color": "#1a3a8f", "group": null, "label": "sin(x)", "limit": null, "closed": null, "helper": false, "hollow": null, "opacity": null, "readonly": false, "arrowHead": null, "dashStyle": null, "fillColor": null, "lengthConstraint": null, "directionConstraint": null}, {"id": "parabola", "name": "spline", "size": null, "color": "#3b82f6", "group": null, "label": "x\u00b2/4", "limit": null, "closed": null, "helper": false, "hollow": null, "opacity": null, "readonly": false, "arrowHead": null, "dashStyle": null, "fillColor": null, "lengthConstraint": null, "directionConstraint": null}, {"id": "absval", "name": "polyline", "size": null, "color": "#f97316", "group": null, "label": "|x|", "limit": null, "closed": false, "helper": false, "hollow": null, "opacity": 1, "readonly": false, "arrowHead": null, "dashStyle": null, "fillColor": "none", "lengthConstraint": null, "directionConstraint": null}], "coordinates": "cartesian", "initialstate": {"sin-solution-overlay": [[{"x": 7.843137254901933, "y": 305.60178889762915}, {"x": 73.37707000709423, "y": 341.29000732393615}, {"x": 142.88122789324865, "y": 374.83407778395855}, {"x": 219.6078431372549, "y": 367.1345116563509}, {"x": 351.6607839231523, "y": 353.8829124988409}, {"x": 448.3392160768475, "y": 239.45042083449303}, {"x": 580.3921568627451, "y": 226.19882167698242}, {"x": 657.1187721067511, "y": 218.4992555493745}, {"x": 726.622929992906, "y": 252.0433260093974}, {"x": 792.156862745098, "y": 287.7315444357042}]], "absval-solution-overlay": [[{"x": 10.000000000000021, "y": 81.66666666666669}, {"x": 400.00000000000006, "y": 296.66666666666663}, {"x": 789.9999999999999, "y": 81.66666666666669}]], "parabola-solution-overlay": [[{"x": 7.843137254901933, "y": 133.6281751746218}, {"x": 15.686274509803923, "y": 140.08449943770682}, {"x": 23.529411764705852, "y": 146.41039290759818}, {"x": 31.372549019607845, "y": 152.60585558429585}, {"x": 39.21568627450978, "y": 158.67088746779984}, {"x": 47.05882352941177, "y": 164.60548855811038}, {"x": 54.9019607843137, "y": 170.40965885522712}, {"x": 62.74509803921569, "y": 176.0833983591503}, {"x": 70.58823529411762, "y": 181.62670706987979}, {"x": 78.43137254901961, "y": 187.0395849874157}, {"x": 86.27450980392155, "y": 192.322032111758}, {"x": 94.11764705882354, "y": 197.4740484429066}, {"x": 101.96078431372547, "y": 202.49563398086158}, {"x": 109.80392156862746, "y": 207.38678872562292}, {"x": 117.64705882352939, "y": 212.14751267719063}, {"x": 125.49019607843138, "y": 216.77780583556472}, {"x": 133.33333333333331, "y": 221.27766820074515}, {"x": 141.17647058823528, "y": 225.64709977273193}, {"x": 149.01960784313724, "y": 229.88610055152512}, {"x": 156.8627450980392, "y": 233.99467053712462}, {"x": 164.70588235294116, "y": 237.97280972953052}, {"x": 172.5490196078431, "y": 241.82051812874283}, {"x": 180.39215686274508, "y": 245.5377957347614}, {"x": 188.23529411764704, "y": 249.1246425475864}, {"x": 196.078431372549, "y": 252.58105856721775}, {"x": 203.921568627451, "y": 255.90704379365548}, {"x": 211.76470588235293, "y": 259.10259822689954}, {"x": 219.6078431372549, "y": 262.16772186695}, {"x": 227.45098039215685, "y": 265.1024147138068}, {"x": 235.2941176470588, "y": 267.90667676747}, {"x": 243.13725490196074, "y": 270.5805080279395}, {"x": 250.98039215686273, "y": 273.12390849521546}, {"x": 258.8235294117647, "y": 275.53687816929767}, {"x": 266.66666666666663, "y": 277.8194170501863}, {"x": 274.5098039215686, "y": 279.9715251378813}, {"x": 282.35294117647055, "y": 281.99320243238265}, {"x": 290.19607843137254, "y": 283.88444893369035}, {"x": 298.0392156862745, "y": 285.64526464180443}, {"x": 305.88235294117646, "y": 287.27564955672494}, {"x": 313.7254901960784, "y": 288.7756036784517}, {"x": 321.5686274509804, "y": 290.1451270069849}, {"x": 329.4117647058823, "y": 291.38421954232444}, {"x": 337.25490196078425, "y": 292.49288128447034}, {"x": 345.0980392156862, "y": 293.47111223342256}, {"x": 352.94117647058823, "y": 294.31891238918126}, {"x": 360.78431372549016, "y": 295.03628175174623}, {"x": 368.62745098039215, "y": 295.6232203211176}, {"x": 376.4705882352941, "y": 296.0797280972953}, {"x": 384.3137254901961, "y": 296.4058050802794}, {"x": 392.156862745098, "y": 296.6014512700699}, {"x": 400.00000000000006, "y": 296.6666666666667}, {"x": 407.843137254902, "y": 296.6014512700699}, {"x": 415.6862745098039, "y": 296.4058050802794}, {"x": 423.52941176470586, "y": 296.07972809729534}, {"x": 431.37254901960785, "y": 295.6232203211176}, {"x": 439.2156862745098, "y": 295.0362817517463}, {"x": 447.05882352941177, "y": 294.31891238918126}, {"x": 454.9019607843137, "y": 293.4711122334227}, {"x": 462.7450980392157, "y": 292.49288128447034}, {"x": 470.5882352941176, "y": 291.38421954232444}, {"x": 478.43137254901956, "y": 290.1451270069849}, {"x": 486.2745098039215, "y": 288.7756036784517}, {"x": 494.11764705882354, "y": 287.27564955672494}, {"x": 501.96078431372547, "y": 285.6452646418045}, {"x": 509.8039215686274, "y": 283.88444893369035}, {"x": 517.6470588235294, "y": 281.99320243238265}, {"x": 525.4901960784313, "y": 279.9715251378813}, {"x": 533.3333333333333, "y": 277.8194170501863}, {"x": 541.1764705882354, "y": 275.53687816929767}, {"x": 549.0196078431372, "y": 273.12390849521546}, {"x": 556.8627450980392, "y": 270.5805080279395}, {"x": 564.7058823529411, "y": 267.90667676747}, {"x": 572.5490196078431, "y": 265.1024147138068}, {"x": 580.3921568627451, "y": 262.16772186695}, {"x": 588.235294117647, "y": 259.10259822689954}, {"x": 596.078431372549, "y": 255.9070437936555}, {"x": 603.921568627451, "y": 252.58105856721775}, {"x": 611.7647058823529, "y": 249.1246425475864}, {"x": 619.6078431372549, "y": 245.53779573476143}, {"x": 627.4509803921568, "y": 241.82051812874283}, {"x": 635.2941176470588, "y": 237.97280972953052}, {"x": 643.1372549019608, "y": 233.99467053712465}, {"x": 650.9803921568626, "y": 229.88610055152515}, {"x": 658.8235294117646, "y": 225.647099772732}, {"x": 666.6666666666666, "y": 221.27766820074515}, {"x": 674.5098039215685, "y": 216.77780583556472}, {"x": 682.3529411764705, "y": 212.14751267719066}, {"x": 690.1960784313724, "y": 207.38678872562295}, {"x": 698.0392156862745, "y": 202.49563398086158}, {"x": 705.8823529411765, "y": 197.4740484429066}, {"x": 713.7254901960783, "y": 192.322032111758}, {"x": 721.5686274509803, "y": 187.03958498741576}, {"x": 729.4117647058824, "y": 181.62670706987979}, {"x": 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The match-function criterion compares a freehand sketch to a reference function. Restricting the comparison to a specific x-range lets the question grade only the relevant interval, while tolerance controls how close the sketch needs to be in pixels.

For full marks, sketch the function $f(x) = \sin(x)$ on the interval $[0, 2\pi]$.

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Multiple grading criteria can be stacked to grade open-ended questions where many curve shapes are valid answers. Here, monot-increasing, greater-than, and two match criteria at the endpoints combine to accept any positive increasing function passing through the marked points.

For full marks, draw any function that is positive and monotonically increasing on $[0, 4]$, starting at $(0, 1)$ and ending at $(4, 3)$.

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The concave-up criterion checks the shape of the drawn function rather than its exact values. Combined with a match point, the question accepts a wide range of valid answers (any U-shaped curve passing through the marked point).

For full marks, sketch any concave-up function that passes through the point $(0, 1)$.

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Loading SketchInput canvas...

Sketching is not limited to drawing curves. The point tool combined with match criteria lets students annotate specific locations on a pre-drawn graph, such as marking intersections, extrema, or roots.

Given $f(x) = x^2$ (blue) and $g(x) = x + 2$ (orange) shown below, mark the points where they intersect.

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