Mathematics Specialised Level 4 case studies
Mathematics Specialised Level 4 · Put your knowledge to work in context.
Mathematics Specialised Level 4 is a rigorous, post-foundational mathematics credential for candidates who already handle single-variable calculus, basic vectors and elementary probability comfortably and want to demonstrate depth across pure and applied topics. It suits students preparing for mathematically demanding university programmes, teachers refreshing subject knowledge, and professionals who need a verifiable signal of advanced technique. The Mathematics Specialised Level 4 case studies are 5 cases and about 2,574 words.
1The Fence That Doubled Back
A landscape architect is fencing a rectangular garden against a straight wall. The wall forms one full side, so fencing is needed on only three sides: two equal ends of length x metres and one side parallel to the wall.
503 words, about 3 min2The Recurring Deposit That Never Settles
A student is analysing a savings scheme. A deposit of 1000 dollars is made at the start of each year, and the account earns 5 percent interest compounded annually, credited at the end of each year.
463 words, about 2 min3The Vector That Would Not Normalise
A graphics programmer is rotating a triangle in the plane. The vertices are A(1, 2), B(4, 6) and C(-1, 5).
457 words, about 2 min4The Integral That Was Split Too Soon
A student evaluates the definite integral of sin x - 0.5 from 0 to pi. She writes the integrand as sin x - 0.5 and integrates directly, obtaining [-cos x - 0.5x] from 0 to pi = (1 - 0.5pi) - (-1) = 2 - 0.5pi, approximately 0.429.
553 words, about 3 min5The Proof That Assumed Its Conclusion
A student is asked to prove that for all positive integers n, n^3 - n is divisible by 6. She writes: 'Assume n^3 - n = 6k for some integer k.
598 words, about 3 min