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"course": "Algebra 2", "coverage": "most" }, { "course": "Precalculus", "coverage": "some", "note": "二項定理は Precalculus" } ], "term_refs": [ "am-gm-inequality", "find-a-common-denominator", "compare", "prove", "remainder", "expansion", "completing-the-square", "compare-coefficients", "triangle-inequality", "polynomial-division", "division-algorithm", "synthetic-division", "rational-expression", "complex-fraction", "identity", "substituting-values", "proving-an-identity", "arithmetic-mean", "geometric-mean", "equality-holds", "multinomial-theorem", "general-term", "cauchy-schwarz-inequality", "reduce", "numerator", "denominator", "partial-fraction-decomposition", "binomial-theorem", "binomial-coefficient", "pascals-triangle" ], "sources": [ { "type": "mext-translation", "doc": "高等学校学習指導要領（平成30年告示）英訳版（仮訳）" } ], "updated": "2026-09-27" }, { "id": "jp-suugaku-2-shisuu-taisuu", "system": "jp", "subject": "数学II", "unit": "指数関数と対数関数", "topics": [ "指数の拡張", "指数関数", "対数とその性質", "対数関数", "常用対数" ], 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"limit", "rational-function", "radical-function", "composite-function", "convergence", "divergence", "diverge-to-positive-infinity", "diverge-to-negative-infinity", "oscillate", "infinity", "comparison-for-divergence", "infinite-geometric-sequence", "infinite-series", "sum-of-the-series", "right-hand-limit", "left-hand-limit", "one-sided-limit", "as-x-approaches-infinity", "as-x-approaches-a", "the-limit-does-not-exist", "indeterminate-form", "continuous", "discontinuous", "continuous-function", "intermediate-value-theorem", "extreme-value-theorem", "limit-of-sine-x-over-x", "base-of-the-natural-logarithm", "find-the-limit", "approaches", "limit-laws", "find-the-domain", "find-the-asymptotes", "find-the-inverse", "compose", "one-to-one", "bounded", "monotonic", "squeeze", "inverse-function", "converge", "diverge", "limit-of-a-sequence" ], "sources": [ { "type": "mext-translation", "doc": "高等学校学習指導要領（平成30年告示）英訳版（仮訳）" } ], "updated": "2026-09-27" }, { "id": "jp-suugaku-3-sekibun", 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"variable-of-integration", "let-u-equal", "write-dx-in-terms-of-du", "change-the-limits-of-integration", "integrate-by-parts", "which-one-to-differentiate", "decompose-into-partial-fractions", "evaluate-the-integral", "revolve-around-the-x-axis", "revolve-around-the-y-axis", "disk", "cylindrical-shell", "find-the-arc-length", "as-n-approaches-infinity", "can-be-integrated", "find-an-antiderivative", "integrals-giving-inverse-trig-functions", "integral", "arc-length-of-a-curve", "substitute-new-variable" ], "sources": [ { "type": "mext-translation", "doc": "高等学校学習指導要領（平成30年告示）英訳版（仮訳）" } ], "updated": "2026-09-24" }, { "id": "jp-suugaku-a-baai-no-kazu-to-kakuritsu", "system": "jp", "subject": "数学A", "unit": "場合の数と確率", "topics": [ "集合の要素の個数", "場合の数", "順列", "組合せ", "事象と確率", "独立な試行と確率", "反復試行", "条件付き確率", "期待値" ], "us_equivalents": [ { "course": "Algebra 2", "coverage": "most" }, { "course": "Precalculus", "coverage": "some" }, { "course": "AP Statistics", "coverage": "some" }, { "course": "Discrete Math", "coverage": "most" } ], "term_refs": [ "sample-space", "expected-value", "basic-properties-of-probability", "general-addition-rule", "general-multiplication-rule", "independence-of-events", "split-into-cases", "at-least-one", "counting", "enumeration", "permutation", "circular-permutation", "permutation-with-repetition", "combination", "combination-with-repetition", "factorial", "binomial-coefficient", "shortest-path", "permutation-of-a-multiset", "lexicographic-order", "partitioning-into-groups", "trial", "elementary-event", "mutually-exclusive-events", "union-of-events", "intersection-of-events", "repeated-trials", "binomial-probability", "conditional-probability", "sampling-with-replacement", "sampling-without-replacement", "arrange", "choose", "distinguish", "double-count", "undercount", "order-matters", "occur", "complementary-event", "addition-principle", "multiplication-principle", "number-of-elements", "law-of-large-numbers" ], "sources": [ { "type": "mext-translation", "doc": "高等学校学習指導要領（平成30年告示）英訳版（仮訳）" } ], "updated": "2026-09-27" }, { "id": "jp-suugaku-a-suugaku-to-ningen-no-katsudou", "system": "jp", "subject": "数学A", "unit": "数学と人間の活動", "topics": [ "約数と倍数", "ユークリッドの互除法", "一次不定方程式", "n 進法", "合同式", "座標と経路", "ゲームやパズルの中の数学" ], "us_equivalents": [ { "course": "Discrete Math", "coverage": "most", "note": "整数論の基礎は大学の Discrete Math / Number Theory" }, { "course": "Pre-Algebra", "coverage": "some", "note": "約数・倍数・素因数分解のみ" } ], "term_refs": [ "prime-factorization", "coordinates", "multiple", "repeating-decimal", "proof-by-contradiction", "composite-number", "greatest-common-divisor", "least-common-multiple", "relatively-prime", "number-of-divisors", "divisibility-rules", "classification-by-remainder", "modulus", "euclidean-algorithm", "linear-diophantine-equation", "diophantine-equation", "integer-solution", "base-n", "binary", "hexadecimal", "numeral-system", "digit", "place", "parity", "remainder", "divisibility", 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"Precalculus", "coverage": "some", "note": "行列の基礎" }, { "course": "Linear Algebra", "coverage": "some" }, { "course": "Discrete Math", "coverage": "some", "note": "グラフ" } ], "term_refs": [ "matrix", "row", "column", "entry", "square-matrix", "identity-matrix", "zero-matrix", "inverse-matrix", "matrix-multiplication", "determinant", "linear-transformation", "statistical-graph", "vertex-graph", "eulerian-path", "adjacency-matrix", "tree", "line-graph", "pie-chart", "stacked-bar-chart", "system-of-linear-equations", "edge-of-a-graph", "path-in-a-graph", "graph-network" ], "sources": [ { "type": "mext-translation", "doc": "高等学校学習指導要領（平成30年告示）英訳版（仮訳）" } ], "updated": "2026-09-25" }, { "id": "jp-suugaku-c-kyokusen-to-fukuso-heimen", "system": "jp", "subject": "数学C", "unit": "平面上の曲線と複素数平面", "topics": [ "二次曲線（放物線・楕円・双曲線）", "媒介変数表示", "極座標と極方程式", "複素数平面", "極形式とド・モアブルの定理", "複素数と図形" ], "us_equivalents": [ { "course": "Precalculus", "coverage": "most", "note": "円錐曲線・極座標・複素数の極形式" }, { "course": "Algebra 2", "coverage": "some", "note": "複素数の演算" }, { "course": "AP Calculus BC", "coverage": "some", "note": "媒介変数・極座標の微積" } ], "term_refs": [ "sketch-the-graph", "rotation", "rotate", "pure-imaginary-number", "complex-conjugate", "locus", "nth-root", "ellipse", "conic-section", "focus", "directrix", "major-axis", "minor-axis", "transverse-axis", "eccentricity", "standard-form-of-a-conic", "cycloid", "polar-coordinates", "pole", "polar-angle", "polar-equation", "rectangular-coordinates", "complex-plane", "real-axis", "imaginary-axis", "polar-form", "de-moivres-theorem", "nth-roots-of-unity", "eulers-formula", "raise-to-the-nth-power", "modulus-of-a-complex-number", "argument-of-a-complex-number" ], "sources": [ { "type": "mext-translation", "doc": "高等学校学習指導要領（平成30年告示）英訳版（仮訳）" } ], "updated": "2026-09-11" }, { "id": "jp-suugaku-c-vector", "system": "jp", "subject": "数学C", "unit": "ベクトル", "topics": [ "平面上のベクトル", "ベクトルの演算", "ベクトルの成分", "ベクトルの内積", "位置ベクトル", "ベクトル方程式", "空間のベクトル" ], 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