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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QUICK REFERENCE

Look up a term, grammar form, or method

Showing 12 items

Solving methodsEssential

Chapter 13

reading the answer frame

解答欄の形から逆算する

What this method solves

EJU mathematics answers go into lettered boxes, so the number and position of boxes constrain the form of the answer.

How to use it

01
Count the boxes first: two boxes usually mean a two-digit number or a signed single digit.
02
Fraction bars and radical signs tell you which form the answer must be reduced to.
03
Match your answer against the boxes digit by digit before filling in the sheet.

While answering

When your result does not fit the boxes, the error is almost always in your calculation, not in the printed frame.

Solving methodsEssential

Chapter 13

following the guided sequence

誘導に乗る

What this method solves

Each large question is split into steps whose later parts reuse earlier results; the examiner has already laid the path.

How to use it

01
Before each step, check whether it refers to symbols defined earlier.
02
Copy the previous answer somewhere visible in your scratch work to avoid recomputing it.
03
Use the final step to sanity-check the earlier results.

While answering

If one step stalls, assume its result and continue; the later steps often let you work backwards.

Solving methodsEssential

Chapter 13

substitution checking

代入検算

What this method solves

After solving an equation or finding a range, substituting one concrete value is the cheapest possible check.

How to use it

01
Pick the integer that makes the arithmetic lightest and substitute it into the original expression.
02
Confirm it satisfies every stated condition, not just the final equation.
03
If it fails, check signs and transposition first, then your recall of the formula.

While answering

For range problems test values near the endpoints, where the inclusion or exclusion of equality most often goes wrong.

Solving methodsEssential

Chapter 13

redrawing the figure

図を描き直す

What this method solves

Figures in geometry questions are rarely to scale; redrawing them to the stated conditions prevents false inferences.

How to use it

01
Write the known lengths and angles directly onto the figure.
02
Add auxiliary lines: perpendiculars, medians, tangents, or the circumcircle.
03
Mark the target quantity and identify which triangle puts it together with known values.

While answering

Never conclude an angle is right because it looks right; use only the conditions actually stated.

Solving methodsEssential

Chapter 13

allocating the 80 minutes

80分の時間配分

What this method solves

Course 1 runs 80 minutes with a heavy, fully compulsory paper, so deciding when to move on matters more than raw calculation speed.

How to use it

01
Scan the whole paper first and mark the large questions you can start immediately.
02
Budget by large question and write each deadline in your scratch work.
03
Reserve the final five minutes to verify that no answers were marked one row off.

While answering

Skip after three minutes stuck on one step; later steps do not always depend on the one blocking you.

Solving methodsEssential

Chapter 13

normalizing the answer form

答えの形をそろえる

What this method solves

Reduce fractions, simplify radicals, and clear radicals from denominators — the fixed routine before marking.

How to use it

01
Reduce the fraction first, then handle the radical.
02
Move any radical out of the denominator.
03
Match digit count and sign against the boxes before marking.

While answering

A sign box means the answer may be negative; getting a negative without one means you must recompute.

Solving methodsEssential

Chapter 14

Japanese mathematical vocabulary

数学用語の日本語

What this method solves

The concepts are already familiar from school at home; what blocks students is the naming — 判別式, 素因数分解, 余事象 and the like.

How to use it

01
Work through the readings of the 72 concept terms in this index.
02
For each term write the matching symbol or formula rather than a translation.
03
Add any unfamiliar term you meet during practice back into the same table.

While answering

Record terms in three columns — Japanese, your language, and the symbol — so that in the exam the Japanese jumps straight to the symbol.

Solving methodsEssential

Chapter 14

standard question phrasing

設問文の定型表現

What this method solves

Patterns such as 〜を求めよ, 〜とする, and ただし〜 recur constantly; reading them is reading the structure of the question.

How to use it

01
Read the sentence ending first: 求めよ asks you to compute, 示せ to justify.
02
Circle the conditions introduced by ただし, のとき, and に対して.
03
Translate each condition into a formula before starting to solve.

While answering

What follows ただし is a restriction, and skipping it is a leading cause of lost marks — circle it every time.

Solving methodsEssential

Chapter 14

wording that carries the condition

条件を表す言い回し

What this method solves

少なくとも, ちょうど, いずれか, and すべて decide directly whether you add, multiply, or take a complement.

How to use it

01
Mark every such quantifying expression in the question text.
02
Restate it in the language of sets or inequalities.
03
After choosing the counting method, check that no boundary case was dropped.

While answering

Map 少なくとも1つ to the complement, and ちょうど to excluding both more and fewer.

Solving methodsEssential

Chapter 14

reading numbers and units

数と単位の読み方

What this method solves

You need Japanese number readings: the decimal point is てん, fractions are read denominator first, and ratios use たい.

How to use it

01
Remember 通り counts ways and 個 counts objects.
02
Copy the required unit next to your answer in the scratch work.
03
Before marking, confirm the dimension of your answer matches what was asked.

While answering

When the question fixes the unit — cm², degrees, 通り — omitting it costs marks wherever written form is required.

Solving methodsEssential

Chapter 14

answer-sheet instructions

マークシートの指示文

What this method solves

The notes at the head of the paper and between question groups define the symbols, sign boxes, and which items may be left blank.

How to use it

01
Read past instruction texts before exam day.
02
Memorize the conventions for sign boxes and fraction boxes.
03
On the day, check only what differs from previous years.

While answering

The wording is stable year to year, so reading it in advance lets you skip it in the exam and save time.

Solving methodsEssential

Chapter 14

Japanese labels on figures and tables

図表の日本語ラベル

What this method solves

Phrases like 右図, 斜線部, and 点Pが動く define what is being asked and carry as much weight as the formulas.

How to use it

01
Shade the region actually being asked about on the figure.
02
Check the range of any moving point and whether endpoints are included.
03
Match each label on the figure to a condition in the text.

While answering

For 斜線部の面積 confirm the shaded region on the figure first; guessing loses the whole question.