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EJU Mathematics Course 2

Examination for Japanese University Admission for International Students (EJU) - Mathematics Course 2

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Cheat sheet

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Key terms

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Study plan

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Common mistakes

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Case studies

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Exam-day guide

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About this exam

EJU Mathematics Course 2 is the more demanding of the two mathematics papers in the Examination for Japanese University Admission for International Students, the standardized test used by Japanese universities to assess international applicants whose schooling was largely outside Japan. Course 2 is aimed at students heading into science, engineering, or mathematics-heavy programmes, and it assumes a fuller high-school mathematics background than Course 1, including calculus, vectors, and the wider treatment of probability. Universities set their own score requirements, so the paper is a component of an application rather than a pass/fail certificate. The syllabus is published by JASSO, and the current official outline on its site is the authoritative description of scope. Preparation rewards depth over breadth: rebuild fluency in algebra and functions first, then work through calculus and vectors, since those carry the most weight in practice. Past-published questions are the best calibration tool, but time yourself, because the paper is long and rewards accuracy under pressure. Expect to write clean, fast working rather than rely on intuition. Verify all administrative details, including dates and fees, on the official JASSO site, as these change each year.

What you'll study

Numbers and Expressions (real numbers, powers and roots, polynomials, factoring, rational expressions)5% Quadratic Functions (graphs, maxima/minima, quadratic equations and inequalities, relationship to the number of real roots)10% Sets, Logic and Counting (sets, propositions, permutations and combinations, binomial theorem)10% Probability (classical probability, independent and dependent events, conditional probability, expected value)15% Number of Integers and Integer Properties (divisibility, Euclidean algorithm, integer solutions, base representation)5% Plane Geometry (triangles, circles, angles, lengths, areas, similarity, the power of a point, inscribed figures)10% Trigonometry (trigonometric ratios, trigonometric identities, graphs, equations and inequalities)10% Exponential and Logarithmic Functions (exponents, logarithms, exponential/logarithmic equations and inequalities, common and natural logarithms)5% Differentiation and Integration (limits, derivatives, tangents, monotonicity, extrema, indefinite and definite integrals, areas)20% Sequences (arithmetic and geometric sequences, sums, recurrence relations, mathematical induction)5% Vectors (vector operations, position vectors, inner products, equations of lines and planes, applications to figures)5%
Common questions

About EJU Mathematics Course 2 preparation

How is the paper structured?

It is a written paper-based test. Most items are multiple choice answered on a mark sheet, and some are constructed items where you fill in numbered blanks with numeric answers. The official JASSO syllabus describes the exact format and permitted materials; check the current version before test day.

How difficult is Course 2 compared with Course 1?

Course 2 extends into differentiation, integration, vectors, and fuller probability and sequences, which Course 1 does not cover. If your target faculty is science or engineering, you almost certainly need Course 2. Confirm the requirement for each university and department, because it varies.

What score do I need?

There is no universal passing score. Each university and faculty sets its own requirement or uses the score as one element among many. Look up the admission guidelines for your specific programme and check the official JASSO site for how scores are reported.

Can I retake the exam?

The exam is offered more than once a year, and most candidates can sit it again at a later administration. Retake rules, eligibility, and which score universities accept are set by JASSO and by each university. Verify the current policy on the official JASSO site before planning.

How should I manage time during the paper?

The paper is long relative to the time allowed, so speed matters. Practise with a timer and aim to bank the straightforward algebra and function items quickly, leaving room for multi-step calculus and geometry. If an item stalls, mark it and move on rather than losing several minutes.

In what order should I study the topics?

Start with numbers and expressions, quadratics, and functions, since everything else depends on them. Then take trigonometry and exponential/logarithmic functions, followed by differentiation and integration. Add probability, sequences, and vectors once the core is solid. This order matches how the topics build on each other.

What are the most common mistakes candidates make?

Weak algebra undermines calculus work: sign errors, careless factoring, and mishandled fractions cost more marks than unfamiliar topics. Others misread constructed items and fill the wrong blank, or run out of time because they never practised under exam conditions. Accuracy on routine manipulation is where most marks are won or lost.

Where do I find official dates, fees, and syllabus details?

JASSO publishes the syllabus, application periods, fees, and test-day rules on its official site. Those figures change between administrations, so do not rely on second-hand summaries. Confirm everything there, and check the individual university's admission page for how it uses the score.