MEXT scholarship · Undergraduate applicants
Mathematics A · 2016–2019
Worked solutions in English
English worked solutions to four MEXT undergraduate Mathematics A papers. Follow the intermediate calculations, check the conditions and match each result to its answer field. One purchase includes one four-year PDF, used alongside the free official questions.
2016–2019 · Four official public papers
12 major problems · 68 questions · 141 answer fields · 44 pages
English / A4 PDF
See included papersSample worked solutions
Open the 8-page sampleThe free 8-page sample contains the actual cover and three complete major problems: 2016 problem 3 on statistics, 2018 problem 3 on cross-sections, and 2019 problem 3 on an integral-defined cubic. Extracts retain the book's printed page numbers. These are actual pages from the book. Select an image to read it at full size.
Included years and mathematical topics
| Paper | Topics | Pages |
|---|---|---|
| 2016 | Counting, rotations, constrained extrema, normal-line areas, boxplots and correlation | 2–11 |
| 2017 | Telescoping sums, distinct-ball arrangements, trigonometric inequalities, variance ratios and function reconstruction | 12–21 |
| 2018 | Digit counts, reflected paths, lattice-point extrema, cubic monotonicity and elliptical sections | 22–32 |
| 2019 | Reset probabilities, graph intersections, divisor sums, binomial identities, exact geometry and normalized cubics | 33–43 |
All three major problems in each of four papers. The 2016 paper has 17 questions and 29 answer fields; 2017 has 16 and 41; 2018 has 17 and 36; 2019 has 18 and 35. Answer-field numbers are retained beside each result. The 44-page total includes covers, reading notes and contents. Page ranges use the printed numbering within each volume.
Who this is for
Applicants practising the undergraduate Mathematics A paper for Social Sciences and Humanities. The book assumes secondary-school algebra, trigonometry, probability and basic calculus. Attempt the official paper first; use the solution to trace a missing transformation, condition or answer-field value. It is not an introductory course covering every prerequisite.
Not included
No Mathematics B, Physics, Chemistry, Japanese or English language-test solutions. No college-of-technology or specialized-training-college papers, papers after 2019, question translations, personal tutoring or scholarship guarantee. Check current application rules with your Japanese embassy or consulate.
Three places where the condition changes the calculation
2017: variance, not just the common mean
Two three-value data sets have the same mean, but their deviations from that mean differ. Write the deviations before squaring: the common denominator in the two variances then cancels, leaving the ratio 3/4. The explanation checks that the reference variance is nonzero and distinguishes a variance ratio from a standard-deviation ratio.
2018: check the order along the reflected path
The two intermediate points lie on specified lines, not necessarily on the original finite segments. After reflecting the endpoints, check that the straight path meets those lines in the required order. The parameters satisfy 0 < 1/4 < 3/5 < 1, so the lower bound is attainable. Restricting the points to the original finite segments would impose a condition absent from the question.
2019: count from the last reset
For the random walk, the last reset separates paths into disjoint cases. After that reset, every remaining step must avoid another reset; a terminal position of zero also requires an even number of moves with equal left and right counts. The derivation keeps those probabilities separate instead of using an ordinary binomial walk for the whole experiment.
2017 answer field [1-10]: 576 or 648?
The official answer table prints 648. Under the printed condition that the six balls are individually distinguishable, count all 6! = 720 orders and subtract the orders with white balls at both ends: 3 × 2 × 4! = 144. The result is 576. A separate count gives 432 orders with exactly one red end and 144 with two red ends, again totalling 576.
The book explicitly shows both the derived value and the published key, including the counting argument. It does not claim that MEXT has issued a correction. All other answer fields have been compared with the published keys; this discrepancy is not silently replaced with the official number.
Mathematics A is not Natural Sciences A
In the linked 2027 undergraduate guidelines, both Social Sciences and Humanities courses take Japanese(A), English(A) and Mathematics(A). Natural Sciences A instead includes Mathematics(B), Physics and Chemistry, as well as language tests. This book covers only Mathematics A, not every written test required of a humanities applicant. Calculators are prohibited in the written examinations, so practise exact arithmetic and check signs without one.
Preparing for the science papers instead? See the separate Mathematics B, Physics and Chemistry worked-solution set. The two products explain different papers; one is not a translated or shortened version of the other.
Free official Mathematics A papers and answer keys
Select 2016, 2017, 2018 or 2019, then Undergraduate Students and Mathematics(A) on the official page. The 2017 combined undergraduate answer PDF has Mathematics A on physical page 2; Mathematics B is the following page. This book gives original worked explanations, not copies of the official questions or keys.
Independently written by InshiHub, not an official MEXT / Study in Japan publication and not affiliated with MEXT / Study in Japan. For corrections, email the subject, year, question number and issue to inshihub.com@gmail.com. About InshiHub (Japanese)
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