skillModel.json

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        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts5a": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts5b": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts6a": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts6b": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts7a": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts8a": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "aafbadeintercepts9a": [
        "find_the_x__and_y__intercepts_from_an_equation_of_a_line"
    ],
    "a18a5a6slope1a": [
        "use_geoboards_to_model_slope"
    ],
    "a18a5a6slope10a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope11a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope12a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope13a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope14a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope15a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope16a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope17a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope18a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope19a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope2a": [
        "use_geoboards_to_model_slope"
    ],
    "a18a5a6slope20a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope3a": [
        "use_geoboards_to_model_slope"
    ],
    "a18a5a6slope4a": [
        "use_geoboards_to_model_slope"
    ],
    "a18a5a6slope5a": [
        "use_geoboards_to_model_slope"
    ],
    "a18a5a6slope6a": [
        "use_geoboards_to_model_slope"
    ],
    "a18a5a6slope7a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope8a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a18a5a6slope9a": [
        "use_m=rise/run_to_find_the_slope_of_a_line_from_its_graph"
    ],
    "a28448cslope1a": [
        "recognize_the_relation_between_the_graph_and_the_slope\u2013intercept_form_of_an_equation_of_a_line"
    ],
    "a28448cslope10a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope11a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope12a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope13a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope14a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope15a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope16a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope17a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope18a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope19a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope2a": [
        "recognize_the_relation_between_the_graph_and_the_slope\u2013intercept_form_of_an_equation_of_a_line"
    ],
    "a28448cslope20a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope21a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope22a": [
        "use_slopes_to_identify_parallel_lines"
    ],
    "a28448cslope23a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope24a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope25a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope26a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope27a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope28a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope29a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope3a": [
        "recognize_the_relation_between_the_graph_and_the_slope\u2013intercept_form_of_an_equation_of_a_line"
    ],
    "a28448cslope30a": [
        "use_slopes_to_identify_perpendicular_lines"
    ],
    "a28448cslope4a": [
        "recognize_the_relation_between_the_graph_and_the_slope\u2013intercept_form_of_an_equation_of_a_line"
    ],
    "a28448cslope5a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope6a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope7a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope8a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a28448cslope9a": [
        "identify_the_slope_and_y_intercept_from_an_equation_of_a_line"
    ],
    "a08a388line1a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line10a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line11a": [
        "find_an_equation_of_the_line_given_two_points"
    ],
    "a08a388line12a": [
        "find_an_equation_of_the_line_given_two_points"
    ],
    "a08a388line13a": [
        "find_an_equation_of_the_line_given_two_points"
    ],
    "a08a388line14a": [
        "find_an_equation_of_the_line_given_two_points"
    ],
    "a08a388line15a": [
        "find_an_equation_of_the_line_given_two_points"
    ],
    "a08a388line16a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line17a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line18a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line19a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line2a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line20a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line21a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line22a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line23a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line24a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line25a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line26a": [
        "find_an_equation_of_the_line_given_two_points"
    ],
    "a08a388line27a": [
        "find_an_equation_of_a_line_parallel_to_a_given_line"
    ],
    "a08a388line28a": [
        "find_an_equation_of_a_line_perpendicular_to_a_given_line"
    ],
    "a08a388line29a": [
        "find_an_equation_of_a_line_perpendicular_to_a_given_line"
    ],
    "a08a388line3a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line30a": [
        "find_an_equation_of_a_line_perpendicular_to_a_given_line"
    ],
    "a08a388line4a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line5a": [
        "find_an_equation_of_the_line_given_the_slope_and_y_intercept"
    ],
    "a08a388line6a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line7a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line8a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "a08a388line9a": [
        "find_an_equation_of_the_line_given_the_slope_and_a_point"
    ],
    "afbeae7inequalities1a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities10a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "afbeae7inequalities11a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "afbeae7inequalities12a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "afbeae7inequalities13a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities14a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities15a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities16a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities17a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities18a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities19a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities2a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities20a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities21a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities22a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities23a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities24a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities25a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities26a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities27a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities28a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities29a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities3a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities30a": [
        "graph_linear_inequalities"
    ],
    "afbeae7inequalities4a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities5a": [
        "verify_solutions_to_an_inequality_in_two_variables"
    ],
    "afbeae7inequalities6a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "afbeae7inequalities7a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "afbeae7inequalities8a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "afbeae7inequalities9a": [
        "recognize_the_relation_between_the_solutions_of_an_inequality_and_its_graph"
    ],
    "a3d6ae2sys1a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys1b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys10a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys10b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys11a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys11b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys12a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys12b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys13a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys13b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys14a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys14b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys15a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys15b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys16a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys16b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys17a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys17b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys18a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys18b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys19a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys19b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys2a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys2b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys20a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys20b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys21a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys21b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys22a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys22b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys23a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys23b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys24a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys24b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys25a": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys25b": [
        "determine_the_number_of_solutions_of_a_linear_system"
    ],
    "a3d6ae2sys26a": [
        "solve_a_system_of_linear_equations_by_graphing"
    ],
    "a3d6ae2sys27a": [
        "solve_a_system_of_linear_equations_by_graphing"
    ],
    "a3d6ae2sys28a": [
        "solve_a_system_of_linear_equations_by_graphing"
    ],
    "a3d6ae2sys29a": [
        "solve_a_system_of_linear_equations_by_graphing"
    ],
    "a3d6ae2sys3a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys3b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys30a": [
        "solve_a_system_of_linear_equations_by_graphing"
    ],
    "a3d6ae2sys4a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys4b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys5a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys5b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys6a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys6b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys7a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys7b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys8a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys8b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys9a": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a3d6ae2sys9b": [
        "determine_whether_an_ordered_pair_is_a_solution_of_a_system_of_equations"
    ],
    "a78ba6esubsitution1a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution10a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution11a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution12a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution13a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution14a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution15a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution15b": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution16a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution17a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution18a": [
        "solve_a_system_of_equations_by_substitution"
    ],
    "a78ba6esubsitution19a": [
        "solve_a_system_of_equations_by_substitution"
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
    "ac98d98systemMat2a": [
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    ],
    "ac98d98systemMat3a": [
        "write_the_augmented_matrix_for_a_system_of_equations"
    ],
    "ac98d98systemMat4a": [
        "write_the_augmented_matrix_for_a_system_of_equations"
    ],
    "ac98d98systemMat5a": [
        "write_the_augmented_matrix_for_a_system_of_equations"
    ],
    "ac98d98systemMat6a": [
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    ],
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    ],
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    ],
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    ],
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    ],
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        "multiply_a_binomial_by_a_binomial"
    ],
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        "multiply_a_binomial_by_a_binomial"
    ],
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        "multiply_a_binomial_by_a_binomial"
    ],
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        "multiply_a_binomial_by_a_binomial"
    ],
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        "dividing_monomials"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "dividing_monomials"
    ],
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        "dividing_monomials"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "use_the_remainder_and_factor_theorem"
    ],
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        "divide_polynomial_functions"
    ],
    "a161552dividingpoly2a": [
        "divide_polynomials_using_long_division"
    ],
    "a161552dividingpoly3a": [
        "divide_polynomials_using_long_division"
    ],
    "a161552dividingpoly4a": [
        "divide_polynomials_using_long_division"
    ],
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    ],
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        "divide_polynomials_using_long_division"
    ],
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        "divide_polynomials_using_long_division"
    ],
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        "divide_polynomial_functions"
    ],
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        "divide_polynomial_functions"
    ],
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        "dividing_monomials"
    ],
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        "use_the_remainder_and_factor_theorem"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "divide_polynomials_using_long_division"
    ],
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        "dividing_monomials"
    ],
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        "dividing_monomials"
    ],
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        "dividing_monomials"
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        "dividing_monomials"
    ],
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        "dividing_monomials"
    ],
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        "divide_a_polynomial_by_a_monomial"
    ],
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        "finding_the_greatest_common_factor_of_two_or_more_expressions"
    ],
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        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
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        "find_the_greatest_common_factor_of_two_or_more_expressions"
    ],
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        "find_the_greatest_common_factor_of_two_or_more_expressions"
    ],
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    ],
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        "find_the_greatest_common_factor_of_two_or_more_expressions"
    ],
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        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf17a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf18a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf19a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf2a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf20a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf21a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf22a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf23a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf24a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
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        "factor_by_grouping"
    ],
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        "factor_by_grouping"
    ],
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        "factor_by_grouping"
    ],
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        "factor_by_grouping"
    ],
    "a5d54dagcf29a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
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        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf30a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf4a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
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        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
    "a5d54dagcf6a": [
        "factor_the_greatest_common_factor_from_a_polynomial"
    ],
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        "factor_by_grouping"
    ],
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        "factor_by_grouping"
    ],
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        "factor_by_grouping"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
    "a7ecb8ffactoring12a": [
        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
    "a7ecb8ffactoring13a": [
        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
    "a7ecb8ffactoring15a": [
        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
    "a7ecb8ffactoring3a": [
        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
    "a7ecb8ffactoring4a": [
        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_trinomials_of_the_form_x**2+bx+c"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
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        "factor_differences_of_squares"
    ],
    "ab303f8factoring14b": [
        "factor_differences_of_squares"
    ],
    "ab303f8factoring15a": [
        "factor_sums_and_differences_of_cubes"
    ],
    "ab303f8factoring15b": [
        "factor_sums_and_differences_of_cubes"
    ],
    "ab303f8factoring2a": [
        "factor_perfect_square_trinomials"
    ],
    "ab303f8factoring2b": [
        "factor_perfect_square_trinomials"
    ],
    "ab303f8factoring3a": [
        "factor_perfect_square_trinomials"
    ],
    "ab303f8factoring3b": [
        "factor_perfect_square_trinomials"
    ],
    "ab303f8factoring4a": [
        "factor_perfect_square_trinomials"
    ],
    "ab303f8factoring4b": [
        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
    "ab303f8factoring7b": [
        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_perfect_square_trinomials"
    ],
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        "factor_differences_of_squares"
    ],
    "ab303f8factoring9b": [
        "factor_differences_of_squares"
    ],
    "a746c1bFactoring1a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring10a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring11a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring12a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring13a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring14a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring15a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring2a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring3a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring4a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring5a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring6a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring7a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring8a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bFactoring9a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly1a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly10a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly11a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly12a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly13a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly14a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly15a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly2a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly3a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly4a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly5a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly6a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly7a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly8a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a746c1bfactoringpoly9a": [
        "recognize_and_use_the_appropriate_method_to_factor_a_polynomial_completely"
    ],
    "a9ff35apoly1a": [
        "use_the_zero_product_property"
    ],
    "a9ff35apoly10a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly11a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly12a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly13a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly14a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly15a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly2a": [
        "use_the_zero_product_property"
    ],
    "a9ff35apoly3a": [
        "use_the_zero_product_property"
    ],
    "a9ff35apoly4a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly5a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly6a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly7a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly8a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "a9ff35apoly9a": [
        "solve_quadratic_equations_by_factoring"
    ],
    "af04890Rational1a": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational1b": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational1c": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational10a": [
        "multiply_rational_expressions"
    ],
    "af04890Rational11a": [
        "multiply_rational_expressions"
    ],
    "af04890Rational12a": [
        "multiply_rational_expressions"
    ],
    "af04890Rational13a": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational14a": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational15a": [
        "multiply_and_divide_rational_functions"
    ],
    "af04890Rational2a": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational2b": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational2c": [
        "determine_the_values_for_which_a_rational_expression_is_undefined"
    ],
    "af04890Rational3a": [
        "simplify_rational_expressions"
    ],
    "af04890Rational4a": [
        "simplify_rational_expressions"
    ],
    "af04890Rational5a": [
        "simplify_rational_expressions"
    ],
    "af04890Rational6a": [
        "simplify_rational_expressions"
    ],
    "af04890Rational7a": [
        "simplify_rational_expressions"
    ],
    "af04890Rational8a": [
        "simplify_rational_expressions"
    ],
    "af04890Rational9a": [
        "multiply_rational_expressions"
    ],
    "a3abd22AddRational1a": [
        "add_and_subtract_rational_expressions_with_a_common_denominator"
    ],
    "a3abd22AddRational10a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational11a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational12a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational13a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational14a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational15a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational2a": [
        "add_and_subtract_rational_expressions_with_a_common_denominator"
    ],
    "a3abd22AddRational3a": [
        "add_and_subtract_rational_expressions_with_a_common_denominator"
    ],
    "a3abd22AddRational4a": [
        "add_and_subtract_rational_expressions_with_a_common_denominator"
    ],
    "a3abd22AddRational5a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational6a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational7a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational8a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22AddRational9a": [
        "add_and_subtract_rational_expressions_whose_denominators_are_opposites"
    ],
    "a3abd22addsubrational1a": [
        "add_and_subtract_rational_expressions_with_a_common_denominator"
    ],
    "a3abd22addsubrational10a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational11a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational12a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational13a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational14a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational15a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational2a": [
        "add_and_subtract_rational_expressions_with_a_common_denominator"
    ],
    "a3abd22addsubrational3a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational4a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational5a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational6a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational7a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational8a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a3abd22addsubrational9a": [
        "add_and_subtract_rational_expressions_with_unlike_denominators"
    ],
    "a1c9712Sim1a": [
        "simplify_a_complex_rational_expression_by_writing_it_as_division"
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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        "determine_whether_a_function_is_one_to_one"
    ],
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        "determine_whether_a_function_is_one_to_one"
    ],
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    ],
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    ],
    "a9e42b3CompInv18a": [
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    ],
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        "find_the_inverse_of_a_function"
    ],
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    ],
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    ],
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    ],
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    ],
    "a9e42b3CompInv23a": [
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    ],
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    ],
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    ],
    "a9e42b3CompInv26a": [
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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    ],
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        "section_5.2_exercises"
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        "section_5.2_exercises"
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        "section_5.2_exercises"
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        "area_and_the_definite_integral"
    ],
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        "area_and_the_definite_integral"
    ],
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        "properties_of_the_definite_integral"
    ],
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        "properties_of_the_definite_integral"
    ],
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        "properties_of_the_definite_integral"
    ],
    "a961302definite8a": [
        "average_value_of_a_function"
    ],
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        "section_5.2_exercises"
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    ],
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        "the_fundamental_theorem_of_calculus"
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        "the_fundamental_theorem_of_calculus"
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        "the_fundamental_theorem_of_calculus"
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    "a06269afundamental3a": [
        "the_fundamental_theorem_of_calculus"
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        "the_fundamental_theorem_of_calculus"
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        "the_fundamental_theorem_of_calculus"
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        "basic_integration_formulas"
    ],
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        "section_5.4_exercises"
    ],
    "a526a0cintegration11a": [
        "section_5.4_exercises"
    ],
    "a526a0cintegration12a": [
        "section_5.4_exercises"
    ],
    "a526a0cintegration13a": [
        "section_5.4_exercises"
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    "a526a0cintegration14a": [
        "section_5.4_exercises"
    ],
    "a526a0cintegration15a": [
        "section_5.4_exercises"
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        "the_net_change_theorem"
    ],
    "a526a0cintegration16b": [
        "the_net_change_theorem"
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        "the_net_change_theorem"
    ],
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        "applying_the_net_change_theorem"
    ],
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        "integrating_an_even_function"
    ],
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        "integrating_an_even_function"
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        "basic_integration_formulas"
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        "basic_integration_formulas"
    ],
    "a526a0cintegration9a": [
        "section_5.4_exercises"
    ],
    "a82ea5csubstitution1a": [
        "proof"
    ],
    "a82ea5csubstitution10a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution11a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution12a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution13a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution14a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution15a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution16a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution17a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution18a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution19a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution2a": [
        "proof"
    ],
    "a82ea5csubstitution20a": [
        "section_5.5_exercises"
    ],
    "a82ea5csubstitution3a": [
        "proof"
    ],
    "a82ea5csubstitution4a": [
        "proof"
    ],
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        "substitution_for_definite_integrals"
    ],
    "a82ea5csubstitution6a": [
        "substitution_for_definite_integrals"
    ],
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        "substitution_for_definite_integrals"
    ],
    "a82ea5csubstitution8a": [
        "section_5.5_exercises"
    ],
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        "section_5.5_exercises"
    ],
    "a046eedintegrals1a": [
        "integrals_of_exponential_functions"
    ],
    "a046eedintegrals10a": [
        "integrals_involving_logarithmic_functions"
    ],
    "a046eedintegrals11a": [
        "integrals_involving_logarithmic_functions"
    ],
    "a046eedintegrals12a": [
        "integrals_involving_logarithmic_functions"
    ],
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        "section_5.6_exercises"
    ],
    "a046eedintegrals14a": [
        "section_5.6_exercises"
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    "a046eedintegrals15a": [
        "section_5.6_exercises"
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        "integrals_of_exponential_functions"
    ],
    "a046eedintegrals3a": [
        "integrals_of_exponential_functions"
    ],
    "a046eedintegrals4a": [
        "integrals_of_exponential_functions"
    ],
    "a046eedintegrals5a": [
        "integrals_of_exponential_functions"
    ],
    "a046eedintegrals6a": [
        "integrals_involving_logarithmic_functions"
    ],
    "a046eedintegrals7a": [
        "integrals_involving_logarithmic_functions"
    ],
    "a046eedintegrals8a": [
        "integrals_involving_logarithmic_functions"
    ],
    "a046eedintegrals9a": [
        "integrals_involving_logarithmic_functions"
    ],
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        "integrals_that_result_in_inverse_sine_functions"
    ],
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        "section_5.7_exercises"
    ],
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        "section_5.7_exercises"
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        "section_5.7_exercises"
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        "section_5.7_exercises"
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        "section_5.7_exercises"
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        "section_5.7_exercises"
    ],
    "aed93bainv16a": [
        "section_5.7_exercises"
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        "section_5.7_exercises"
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    "aed93bainv18a": [
        "section_5.7_exercises"
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        "section_5.7_exercises"
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        "integrals_that_result_in_inverse_sine_functions"
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        "section_5.7_exercises"
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    "aed93bainv21a": [
        "section_5.7_exercises"
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        "section_5.7_exercises"
    ],
    "aed93bainv3a": [
        "integrals_that_result_in_inverse_sine_functions"
    ],
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        "integrals_resulting_in_other_inverse_trigonometric_functions"
    ],
    "aed93bainv5a": [
        "integrals_resulting_in_other_inverse_trigonometric_functions"
    ],
    "aed93bainv6a": [
        "integrals_resulting_in_other_inverse_trigonometric_functions"
    ],
    "aed93bainv7a": [
        "section_5.7_exercises"
    ],
    "aed93bainv8a": [
        "section_5.7_exercises"
    ],
    "aed93bainv9a": [
        "section_5.7_exercises"
    ],
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        "area_of_a_region_between_two_curves"
    ],
    "a1cc0dcareas10a": [
        "section_2.1_exercises"
    ],
    "a1cc0dcareas11a": [
        "section_2.1_exercises"
    ],
    "a1cc0dcareas2a": [
        "area_of_a_region_between_two_curves"
    ],
    "a1cc0dcareas3a": [
        "areas_of_compound_regions"
    ],
    "a1cc0dcareas4a": [
        "areas_of_compound_regions"
    ],
    "a1cc0dcareas5a": [
        "regions_defined_with_respect_to_y"
    ],
    "a1cc0dcareas6a": [
        "section_2.1_exercises"
    ],
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        "section_2.1_exercises"
    ],
    "a1cc0dcareas8a": [
        "section_2.1_exercises"
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    "a1cc0dcareas9a": [
        "section_2.1_exercises"
    ],
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        "volume_and_the_slicing_method"
    ],
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        "section_6.2_exercises"
    ],
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        "section_6.2_exercises"
    ],
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        "section_6.2_exercises"
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        "section_6.2_exercises"
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        "section_6.2_exercises"
    ],
    "a9ef311slicing15a": [
        "section_6.2_exercises"
    ],
    "a9ef311slicing16a": [
        "section_6.2_exercises"
    ],
    "a9ef311slicing17a": [
        "section_6.2_exercises"
    ],
    "a9ef311slicing18a": [
        "section_6.2_exercises"
    ],
    "a9ef311slicing19a": [
        "section_6.2_exercises"
    ],
    "a9ef311slicing2a": [
        "solids_of_revolution"
    ],
    "a9ef311slicing20a": [
        "section_6.2_exercises"
    ],
    "a9ef311slicing3a": [
        "the_disk_method"
    ],
    "a9ef311slicing4a": [
        "the_disk_method"
    ],
    "a9ef311slicing5a": [
        "the_washer_method"
    ],
    "a9ef311slicing6a": [
        "the_washer_method"
    ],
    "a9ef311slicing7a": [
        "section_6.2_exercises"
    ],
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        "section_6.2_exercises"
    ],
    "a9ef311slicing9a": [
        "section_6.2_exercises"
    ],
    "a33da99volumes1a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes10a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes11a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes12a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes13a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes14a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes15a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes2a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes3a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes4a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes5a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes6a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes7a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes8a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a33da99volumes9a": [
        "the_volume_of_revolution:_cylindrical_shells"
    ],
    "a3e1067arc1a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc10a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc11a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc12a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc13a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc14a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc15a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc2a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc3a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc4a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc5a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc6a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc7a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc8a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "a3e1067arc9a": [
        "arc_length_of_a_curve_and_surface_area"
    ],
    "af9dcc3physical1a": [
        "physics_application"
    ],
    "af9dcc3physical10a": [
        "physics_application"
    ],
    "af9dcc3physical11a": [
        "physics_application"
    ],
    "af9dcc3physical12a": [
        "physics_application"
    ],
    "af9dcc3physical13a": [
        "physics_application"
    ],
    "af9dcc3physical14a": [
        "physics_application"
    ],
    "af9dcc3physical15a": [
        "physics_application"
    ],
    "af9dcc3physical2a": [
        "physics_application"
    ],
    "af9dcc3physical3a": [
        "physics_application"
    ],
    "af9dcc3physical4a": [
        "physics_application"
    ],
    "af9dcc3physical5a": [
        "physics_application"
    ],
    "af9dcc3physical6a": [
        "physics_application"
    ],
    "af9dcc3physical7a": [
        "physics_application"
    ],
    "af9dcc3physical8a": [
        "physics_application"
    ],
    "af9dcc3physical9a": [
        "physics_application"
    ],
    "ad4fd60center1a": [
        "arc_length_of_the_curve"
    ],
    "ad4fd60center10a": [
        "arc_length_of_the_curve"
    ],
    "ad4fd60center2a": [
        "arc_length_of_the_curve"
    ],
    "ad4fd60center3a": [
        "arc_length_of_the_curve"
    ],
    "ad4fd60center4a": [
        "arc_length_of_the_curve"
    ],
    "ad4fd60center5a": [
        "arc_length_of_the_curve"
    ],
    "ad4fd60center6a": [
        "the_symmetry_principle"
    ],
    "ad4fd60center7a": [
        "using_the_theorem_of_pappus_for_volume"
    ],
    "ad4fd60center8a": [
        "finding_the_centroid_of_a_region_bounded_by_two_functions"
    ],
    "ad4fd60center9a": [
        "arc_length_of_the_curve"
    ],
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        "kedjeregeln"
    ],
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        "deriveringsregler"
    ],
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        "deriveringsregler"
    ],
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        "Areor"
    ],
    "swedish_a2d77b8chainrule6a": [
        "kedjeregeln"
    ],
    "swedish_aca1a7dderivative3a": [
        "deriveringsregler"
    ],
    "swedish_a2d77b8chainrule11a": [
        "kedjeregeln"
    ],
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        "deriveringsregler"
    ],
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        "derivator_av_trigonometriska_funktioner"
    ],
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        "kedjeregeln"
    ],
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        "derivator_av_trigonometriska_funktioner"
    ],
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        "deriveringsregler"
    ],
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        "deriveringsregler"
    ],
    "swedish_a394625deriv20a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_aca1a7dderivative10a": [
        "deriveringsregler"
    ],
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        "deriveringsregler"
    ],
    "swedish_aca1a7dtangentline7a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dderivative12a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dtangentline6a": [
        "deriveringsregler"
    ],
    "swedish_a394625deriv15a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_aca1a7dderivativetangent1a": [
        "deriveringsregler"
    ],
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        "kedjeregeln"
    ],
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        "områden_av_sammansatta_regioner"
    ],
    "swedish_a1cc0dcareas1a": [
        "area_av_ett_område_mellan_två_kurvor"
    ],
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        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_aca1a7dtangentline2a": [
        "deriveringsregler"
    ],
    "swedish_a1cc0dcareas11a": [
        "Areor"
    ],
    "swedish_aca1a7dderivative5a": [
        "deriveringsregler"
    ],
    "swedish_a1cc0dcareas3a": [
        "områden_av_sammansatta_regioner"
    ],
    "swedish_aca1a7dderivativetangent3a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dvelocity1a": [
        "deriveringsregler"
    ],
    "swedish_a394625deriv11a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_a394625deriv23a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_a2d77b8chainrule8a": [
        "kedjeregeln"
    ],
    "swedish_a394625deriv21a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_aca1a7dderivative9a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dtangentline8a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dderivativetangent2a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dderivative7a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dderivative1a": [
        "deriveringsregler"
    ],
    "swedish_aca1a7dderivative8a": [
        "deriveringsregler"
    ],
    "swedish_a2d77b8chainrule4a": [
        "kedjeregeln"
    ],
    "swedish_aca1a7dderivative11a": [
        "deriveringsregler"
    ],
    "swedish_a1cc0dcareas6a": [
        "Areor"
    ],
    "swedish_aca1a7dderivative6a": [
        "deriveringsregler"
    ],
    "swedish_a394625deriv25a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_a2d77b8chainrule3a": [
        "kedjeregeln"
    ],
    "swedish_a394625deriv13a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_a394625deriv24a": [
        "derivator_av_trigonometriska_funktioner"
    ],
    "swedish_a2d77b8chainrule12a": [
        "kedjeregeln"
    ],
    "swedish_aca1a7dtangentline5a": [
        "deriveringsregler"
    ],
    "swedish_a2d77b8chainrule14a": [
        "kedjeregeln"
    ]
}