Kyoto Entrance Mathematics case studies
Kyoto Entrance Mathematics · Put your knowledge to work in context.
Kyoto University's general entrance examination in mathematics is the university-set written paper that follows the National Center for University Entrance Examinations (Daigaku Nyūshi Center Shiken) stage. It is intended for high-school graduates and equivalent applicants seeking undergraduate admission to Kyoto University, and it is a constructed-response paper: candidates write full solutions, including reasoning and proofs, rather than selecting answers. The Kyoto Entrance Mathematics case studies are 5 cases and about 3,312 words.
1Parabolic Gateway Arch: Fitting a Banner and Sizing a Steel Beam
A parent-teacher committee is building a decorative gateway arch for a school festival. On a coordinate grid where the ground is the x-axis and 1 unit equals 1 metre, the arch is specified as a parabola y = ax² + bx + c that must pass through A(−4, 0) and B(6, 0), with a = −0.25 fixed by the design software.
722 words, about 4 min2Ambiguous Triangular Flower Bed with a Fixed Budget
A landscaping class is laying out a triangular flower bed ABC on flat ground. They measure AB = 9.0 m and AC = 7.0 m, and the angle at B is 40°.
628 words, about 3 min3Open-Top Box from 30 cm by 20 cm Cardboard with a Volume Promise
A technology club is making open-top storage boxes from rectangular cardboard sheets measuring 30 cm by 20 cm. From each corner they cut out a square of side x cm, then fold up the four flaps.
670 words, about 3 min4Transport Survey: Independence Claim, At-Least-One Percentage and a Subgroup Claim
A student council surveys 200 of the school's 1200 students about how they travel to school. Of the 200 surveyed, 120 say they use a bicycle at least once a week, 90 say they use the train at least once a week, and 50 say they use both.
605 words, about 3 min5Canteen Snack Count: Remainders, Pack Sizes and a Check-Digit Condition
The school canteen receives a delivery of wrapped snack bars. When the staff count them into bags of 5, 3 bars are left over; into boxes of 7, 4 are left over; into trays of 9, 6 are left over.
687 words, about 3 min