PEI Math 521B case studies
PEI Math 521B · Put your knowledge to work in context.
Math 521B is a senior-level mathematics course in Prince Edward Island's high school curriculum, and the associated provincial assessment is designed for students who have completed the 521B course and want credit recognition or a benchmark of their readiness for university mathematics. It suits strong Grade 12 students, mature learners returning to mathematics, and candidates preparing for STEM programs that assume comfort with proof and abstraction rather than routine calculation. The PEI Math 521B case studies are 5 cases and about 2,885 words.
1Prime Power Divisibility in a Sum of Squares
A number theory problem asks you to determine the largest power of 3 dividing N = 5^{2024} + 7^{2024}. A classmate claims that since 5 + 7 = 12 is divisible by 3, and the exponents are even, N must be divisible by 3^2 but not by 3^3.
535 words, about 3 min2Group Action and Orbit Stabilizer on a Polyhedron
In an algebra problem, you are given the group G of rotational symmetries of a cube (orientation-preserving symmetries). You are asked to analyze the action of G on the set of faces of the cube.
569 words, about 3 min3Triangle Inequality and Locus in Coordinate Geometry
A geometry problem asks you to find the locus of points P in the plane such that the sum of distances from P to two fixed points A = (-3, 0) and B = (3, 0) is 10. A student immediately says the locus is a circle of radius 5 centered at the origin, because the midpoint of AB is the origin and the sum of distances is constant.
553 words, about 3 min4Counting Labeled Trees with Degree Constraints
A combinatorics problem asks for the number of labeled trees on vertex set {1,2,...,n} in which vertex 1 has degree 1 and vertex 2 has degree 3. A student proposes using Cayley's formula n^{n-2} and then dividing by something, but gets confused.
599 words, about 3 min5Proof by Contradiction with Irrationality and Parity
A proof problem asks you to show that if a and b are positive integers such that a^2 + b^2 is divisible by 3, then both a and b are divisible by 3. A student attempts a proof by contradiction: assume 3 divides a^2 + b^2 but 3 does not divide at least one of a or b.
629 words, about 3 min