EJU Mathematics Course 2 case studies
EJU Mathematics Course 2 · Put your knowledge to work in context.
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. The EJU Mathematics Course 2 case studies are 5 cases and about 3,222 words.
1Check Characters on Eight-Character Borrower Codes
A regional library network issues eight-character borrower codes. The first seven characters are digits d1…d7 chosen by the branch; the eighth is a check character c computed by c ≡ d1 + 2d2 + 3d3 + 4d4 + 5d5 + 6d6 + 7d7 (mod 11), where a residue of 10 is printed as the letter X.
633 words, about 3 min2Fencing a Plot Against a Wall of Limited Length
A neighbourhood association has 30 metres of fencing and wants to enclose a rectangular vegetable plot against an existing straight stone wall, using the wall as one full side so that only three sides need fencing. The section of wall the council will allow them to use is 7 metres long, and the plot's side along the wall may not exceed that length.
668 words, about 3 min3Two Boxes, a Die and a Transferred Ball
Two boxes stand on a table in a school mathematics club demonstration. Box A contains 2 red balls and 1 blue ball; Box B contains 1 red ball and 3 blue balls.
600 words, about 3 min4Average Cost, Marginal Cost and an Area Under the Curve
A small workshop produces a single product in batches of one hundred units. The manager models the total cost of producing x hundred units per day as C(x) = x³ − 12x² + 60x, measured in hundreds of yen, for 0 < x ≤ 10; the factory cannot run above 1000 units per day.
685 words, about 3 min5Triangular Plot: Shortest Path, Perpendicular Post and Median
A land surveyor is mapping a triangular plot OAB. From the survey data, OA = 2 units, OB = 3 units, and the angle AOB is 60°.
636 words, about 3 min