EXAM QUICK REFERENCE

EJU Mathematics Course 1 exam quick reference

Course 1 serves humanities and some science applicants, and its scope is strictly the first seven syllabus domains. Chapters 1–12 open those domains, chapter 13 handles the mechanics of a guided mark-sheet paper, and chapter 14 addresses the difficulty international students actually face: the mathematics is familiar, the Japanese is not.

Strictly follows domains 1–7 of JASSO's 2026 Course 1 syllabus; domains 8 and later belong to Course 2 and are out of scope here.

Exam time: 80 minutes
Domains: 7 domains
Answer language: Japanese or English
Questions: 70

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Quadratic functions I: graphs and extrema

001平方完成completing the squareEssential

Core note: Rewriting y=ax²+bx+c as y=a(x−p)²+q makes the vertex and the extreme value readable at a glance.
Exam area: Quadratic functions I: graphs and extrema
Decision focus: Fix the opening direction, then check whether the vertex lies inside the interval.

002頂点と軸vertex and axis of symmetryEssential

Core note: The vertex (p, q) is the highest or lowest point of the parabola, and the line x=p is its axis of symmetry.
Exam area: Quadratic functions I: graphs and extrema
Decision focus: Fix the opening direction, then check whether the vertex lies inside the interval.

003平行移動と対称移動translation and reflection of graphsFrequent

Core note: Shifting right by p replaces x with x−p and shifting up by q adds q; reflecting in the x-axis negates the function and reflecting in the y-axis replaces x with −x.
Exam area: Quadratic functions I: graphs and extrema
Decision focus: Fix the opening direction, then check whether the vertex lies inside the interval.

004最大値・最小値maximum and minimum valuesEssential

Core note: An upward parabola takes its minimum at the vertex and a downward one its maximum, so decide the opening direction first.
Exam area: Quadratic functions I: graphs and extrema
Decision focus: Fix the opening direction, then check whether the vertex lies inside the interval.

005定義域の制限extrema on a restricted domainEssential

Core note: When the vertex lies outside the interval the extremes occur at the endpoints, so compare the vertex against both endpoints.
Exam area: Quadratic functions I: graphs and extrema
Decision focus: Fix the opening direction, then check whether the vertex lies inside the interval.

0062次関数の決定determining a quadratic functionFrequent

Core note: Use a(x−p)²+q given the vertex, a(x−α)(x−β) given the x-intercepts, and the general form with simultaneous equations given three points.
Exam area: Quadratic functions I: graphs and extrema
Decision focus: Fix the opening direction, then check whether the vertex lies inside the interval.