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Mathematics (09) Practice TestANALYSIS FOR FIRST STRONG RESPONSE TO OPEN-RESPONSEITEM ASSIGNMENT #2This is an example of a strong response because it is characterized by the following:Purpose: The purpose of the assignment is fully achieved. The volume of a single ball, V b(d), in cubic inches isfound and used to calculate the volume of three balls. The volume of a foot-long piece of stock is found using theformula for the volume of a cylinder. The speed of stock feed required to produce balls of various diameters isexpressed as a function of the diameter. The speed function is then graphed.Subject Matter Knowledge: By correctly converting the formulas to be expressed in terms of diameter, thecandidate demonstrates understanding that the formulas for the volume of a sphere and the volume of a cylinderare needed to solve this problem. The explanation, "The speed per second to produce the balls is the ratio of thevolume of the 3 balls produced compared to the volume of one linear foot of stock," shows a sophisticatedunderstanding, relating the concepts of volume and speed.Support: The response provides a detailed step-by-step approach showing formulas (e.g., V = 4 3 πr3 ), substitutionfor given data (e.g., V b(d) = 4 3 π ⎝ ⎛ d⎠ ⎞3 42 ), calculations (e.g., 3 π ⎝ ⎛ d⎠ ⎞32 ), and final results (e.g., Vb (d) = π 6 d 3 ). The responsecontains verbal explanations of reasoning involved, although it does not substantially contribute to making this astrong response because each step is fully explained numerically. The graph is correctly labeled with anorganized supporting chart of data points.Rationale: Each step is fully explained and justified, which makes the candidate's reasoning process clear. Thedata table and resulting graph allow for a broad interpretation of the problem beyond producing three balls of aspecific size. This demonstrates the candidate's depth of understanding of the underlying concepts.94