Nagasaki High School Entrance Exam - Mathematics

It is a written, constructed-response paper: you write answers as numbers or expressions and, in some parts, write a short explanation of your reasoning. There is no multiple-choice section. The current number of questions, marks, and time allowed are set by Nagasaki Prefecture and published in its official selection guidelines.

Most items test standard junior high content and are reachable with solid fundamentals. Difficulty comes from the later parts of multi-part questions, which ask you to justify a result or use a result from an earlier part. Losing marks through incomplete reasoning is more common than failing to know the method.

Retake and re-application rules depend on the selection system in force for that year, and different schools and courses may have different provisions. Nagasaki Prefecture publishes the current rules in its admission guidelines. Check the official documents for your year and confirm with your school before assuming a retake is possible.

The total time allowed is set by the prefecture, so build your own plan from past papers. A workable habit is to sweep the paper once for items you can do immediately, then return to the multi-part questions. Never leave a justification blank because the final value is uncertain; partial reasoning can earn credit.

Start with numbers, algebraic expressions, and equations, because every other topic depends on fluent manipulation. Then work on functions and graphs, followed by geometry, where you must also practise writing reasons. Add data handling and probability in short regular sessions, and finish with timed mixed practice.

The usual causes are an unjustified step, such as assuming two lines are parallel or two angles equal without stating why, and using a theorem in a form that does not match the figure. Practise writing each proof as a chain in which every line cites a known property or an earlier result.

Do them timed and without notes, then mark them by cause: misread question, calculation slip, missing condition, or incomplete reasoning. Keep a list of the causes and redo the same paper a few weeks later. Comparing the two attempts shows whether the weakness was knowledge or execution.

Follow the instructions printed on the paper. Where a question asks for a value or expression only, the answer is what is marked. Where it asks you to explain or show, the reasoning is marked, so write the steps in order and state the property or result you are using at each step.

Nagasaki Prefecture publishes the current selection schedule, guidelines, and examination information on its official website, and your school can also supply the documents. Use those sources for dates, time limits, and any changes to the format, since secondary summaries may be out of date.