Ehime Entrance Mathematics study guide
Ehime Entrance Mathematics · Work through your exam, one topic at a time.
愛媛大学の一般選抜で課される数学の筆記試験は、数学を必須または選択科目とする学部・学科の合否を大きく左右する記述式の試験です。本ページは愛媛大学とは関係のない独立した学習用の解説で、試験の性格と対策の組み立て方をまとめたものです。 主な対象は、高等学校を卒業（見込み）の人、または高等専門学校などから志願する人で、数学I・A・II・B、現行課程では数学III・Cまで含めて一通り学習を終えた受験生です。出題は教科書の範囲全体におよび、単独の分野をきれいに切り分けた問題よりも、複数の分野を組み合わせたり誘導を付けたりした設問が中心になります。したがって、公式を暗記して当てはめる力よりも、定義に戻って考え、日本語で筋道を立てて書き切る力が問われます。答案は結論だけでなく、場合分けの条件や定理を用いた理由まで読み取って評価されるため、日頃から「人に読ませる答案」を意識して練習することが近道です。 準備は三段階で考えると進めやすくなります。第一に、教科書の例題と定理の証明を自分の手で再現する。第二に、過去問を時間を計って解き、解けなかった原因を「知識」「方針」「計算」「記述」に分類する。第三に、答案を第三者に読ませ、論理の飛躍や書き漏れを潰す。この順序なら、伸びしろの大きい記述力から先に固められます。試験時間・大問数・配点・選択の有無は年度や学部で変わるため、必ず受験する年度の募集要項と学生募集要項で確認してください。. The Ehime Entrance Mathematics study guide has 9 sections and about 2,586 words.
01Differentiation and its applications
Differentiation is the Ehime entrance domain that links limits, local behaviour, and curve shape. Expect questions that ask for a derivative from first principles, a tangent or normal, intervals of increase and decrease, extrema, or a sketch justified by signs of f' and f''.
276 words, about 1 min02Integration and its applications
Integration in this exam tests the definite integral as accumulation, the fundamental theorem, and geometric applications such as area between curves and volumes of revolution. Questions often combine an algebraic curve with a line and ask for the bounded region.
319 words, about 2 min03Sequences, series and limits
Sequences and series questions at this level mix algebra with limiting behaviour. You should recognise arithmetic and geometric patterns, solve first-order recurrences, prove statements by induction, and decide whether an infinite series converges.
291 words, about 1 min04Vectors in the plane and in space
Vector questions test both calculation and interpretation: dot products encode angles and projections, while vector equations describe lines and planes in the plane or in space. Expect intersections, perpendicularity, distance, and configurations of points.
289 words, about 1 min05Trigonometric, exponential and logarithmic functions
Trigonometric, exponential, and logarithmic functions are examined through equations, inequalities, graph transformations, and rates of change. The key is to respect domains and periods before manipulating expressions.
293 words, about 1 min06Probability and counting
Probability and counting questions reward a clear sample-space decision. Decide whether order matters, whether selection is with or without replacement, and whether the question asks for a count or a probability.
246 words, about 1 min07Complex numbers and the complex plane
Complex-number questions combine algebra with geometry. Expect polar form, modulus and argument, loci, De Moivre's theorem, and polynomial equations over the complex numbers.
278 words, about 1 min08Polynomials, equations and integer properties
Polynomial and integer questions test exact algebra: factor and remainder theorems, rational-root candidates, divisibility, the Euclidean algorithm, and base representations. Neat bookkeeping is as important as the main theorem.
285 words, about 1 min09Plane and solid geometry
Plane and solid geometry questions ask you to combine standard theorems with a diagram you construct yourself. The exam favours triangle calculations, circle properties, similarity and congruence arguments, and coordinate methods for loci and distances.
309 words, about 2 min