VCE Maths Methods case studies
VCE Maths Methods · Put your knowledge to work in context.
VCE Mathematical Methods is a Victorian senior secondary mathematics study assessed by the Victorian Curriculum and Assessment Authority (VCAA). It suits students who are comfortable with algebraic manipulation and who intend to use mathematics in further study, since the course builds formal skills in functions and graphs, algebra and structure, calculus, and data analysis, probability and statistics. The VCE Maths Methods case studies are 5 cases and about 2,484 words.
1The Leaking Tank and the Ambiguous Average
A cylindrical water tank of radius 1.5 m is being drained. Engineers model the volume with V(t) = 18 - 3t + 0.25t^2 for 0 <= t <= 8, where V is in cubic metres and t is in hours.
513 words, about 3 min2Transformations and the Missing Domain
A student is asked to find the inverse of f(x) = x^2 - 4x + 7 for x = 2. They complete the square to get f(x) = (x-2)^2 + 3, then write f^{-1}(x) = 2 + sqrt(x - 3), stating the domain as all real x.
466 words, about 2 min3The Biased Survey and the Confidence Interval
A school surveys 200 students about whether they support a later start to the school day. Students are polled only in the library before school, and 130 say yes.
468 words, about 2 min4Optimising a Fenced Paddock with a Fixed Budget
A farmer has 120 m of fencing to enclose a rectangular paddock against a straight river, so only three sides need fencing (two widths and one length parallel to the river). Let the width perpendicular to the river be x metres and the length parallel to the river be y metres.
526 words, about 3 min5When the Derivative Misleads: A Piecewise Motion Problem
A particle moves along a line with position s(t) in metres given piecewise by s(t) = t^2 for 0 <= t <= 2 and s(t) = 4 + 3(t - 2) for 2 < t <= 5, where t is in seconds. A student computes the derivative at t = 2 by differentiating the first piece, getting s'(2) = 4, and concludes the particle's velocity at t = 2 is 4 m/s.
511 words, about 3 min