PERFORMANCE-BASED ASSESSMENT "Light at the End of the Tunnel" Content Standard The learner demonstrates understanding of key concepts of antiderivatives. Performance Standard The learner formulates and solves accurately situational problems involving areas of plane regions. Learning Targets: The learner should be able to ... compute the definite integral of a function using the Fundamental Theorem of Calculus (MELCS Code: STEM_BC111-IVh-2) compute the area of a plane region using the definite integral (MELCS Code: STEM_BC111-IVij-1) solve problems involving areas of plane regions (MELCS Code: STEM_BC111-IV]-2) appreciate the use of calculus in solving areas of plane regions that could not be solved by geometry alone recognize the usefulness of calculus in solving real-life problem situations such as cost analysis. Date of Implementation: Week 7-8 (March 14-28, 2022) Engaging Scenario: The construction firm where you are working as an engineer plan to build a tunnel whose arch is in the shape of a parabola (see the illustration below). The planned tunnel is 12 meters wide. To allow safe passage for vehicles, the tunnel must be 6 meters high at a distance of 4 meters from the tunnel's edge. You have to know how many cubic meters of concrete will be used for the tunnel's side support considering that the straight tunnel is 100 meters long, First, you are to compute the area bounded by the ground and the parabola. Then, use this to compute the volume of what remains of the "prism after removing the parabolic tunnel" to know how much concrete will be needed to fill it. Your computations will also help the cost analyst to accurately compute the overall projected cost of the project and allow the construction firm to better prepare necessary materials, equipment, and manpower to finish the project on time.2 m 6 m X 4 m 2 m 12 meters 2 m Guidelines: You can use PowerPoint, Word, Google Slides or Google Docs, whichever is most convenient to you in presenting your work. . Your work will be graded using the rubric on the next page.Grading Rubric: Category Advanced Proficient Becoming Proficient Novice Mastery of conic Mastery of conic Understanding of the Partial understanding Accuracy of sections and sections and concept of conic of the concept of conic Solution antiderivatives as antiderivatives as sections and sections and applied in the area of applied in the area of antiderivatives as antiderivatives as the plane region is the plane region is applied in the plane applied in the area of shown through a shown through a region is evident as the plane region is correct, accurate, and correct and accurate shown in the solution evident as shown by well-organized computation of the which contains minor the incorrect area computation of the area bounded by the errors. bounded by the area bounded by the parabolic tunnel and parabolic tunnel and parabolic tunnel and consequently, the consequently, the consequently, the amount of concrete amount of concrete amount of concrete needed. needed. needed. Deep understanding of Full understanding of Partial understanding Little understanding of Mathematical applicable applicable of applicable applicable Understanding mathematical concepts mathematical concepts mathematical mathematical is shown through the is shown through the concepts is shown concepts is shown creative (not the usual accurate formulation through the through the but logical) solution of equations to solve formulation of some formulation of shown, accurate the required area of the equations to incorrect equations to formulation of bounded by the solve the required solve the required area equations to solve the parabolic tunnel and area bounded by the bounded by the required area bounded consequently, the parabolic tunnel and parabolic tunnel and by the parabolic tunnel amount of concrete consequently, the consequently, the and consequently, the needed. amount of concrete amount of concrete amount of concrete needed. needed. needed.Appropriate Appropriate Mathematical An attempt is made to Representation mathematical mathematical representation(s) construct representation(s) representation(s) (drawing and formula) mathematical (drawings and (drawings and are constructed to representation formulas) are formulas) are communicate strategy (drawing or formula) exceptionally constructed to and reasoning but to communicate constructed to communicate, verify, there are some strategy and communicate, verify, clarify, or extend inaccuracies in the reasoning. clarify, or extend strategy and formulas and/or strategy and reasoning. drawings made. reasoning. The solution and . The solution and . The solution and . Most parts of the Communication explanation are explanation are explanation are problem situation, and logically written in logically written in partly written in solution and Organization clear and coherent clear and coherent clear and coherent explanation are language which language. It is easy language. Some not written in clear adds clarity to the to follow and read. parts are easy to and coherent solution Organization of follow and read. language. It is a bit presented. It is thought is clear difficult or easy to follow and and consistent. confusing to read understand. and follow. . Organization of thought is clear and consistent, polished; makes the content cohesive