WACE ATAR Mathematics Specialist case studies
WACE ATAR Mathematics Specialist · Put your knowledge to work in context.
Mathematics Specialist is an ATAR course in the Western Australian senior secondary curriculum, administered by the School Curriculum and Standards Authority (SCSA). It is designed for students who want to build rigorous mathematical arguments and proofs and to use mathematical models more extensively than in Mathematics Methods. The WACE ATAR Mathematics Specialist case studies are 5 cases and about 2,299 words.
1Fitting a cubic through a tangent constraint
A designer models the cross-section of a skate ramp with a cubic polynomial p(x) = ax³ + bx² + cx + d defined on the interval [0, 2]. The ramp must satisfy four requirements: p(0) = 0, so the ramp meets the ground at the origin; p'(0) = 0, so the entry is smooth (horizontal tangent); p(2) = 3, so the ramp reaches a height of 3 metres at its far edge; and p'(2) = 0, so the exit is also horizontal.
456 words, about 2 min2Resolving a vector intersection ambiguity in 3D
Two straight pipes are modelled as lines in three-dimensional space. Pipe A passes through the point A(1, 2, 3) and has direction vector d A = (2, −1, 1).
474 words, about 2 min3Choosing the correct branch when solving a complex equation
A student solving z³ = 8 − 8√3 i writes the right-hand side in polar form and finds one solution, then stops, claiming 'a cube root is unique, so there is only one answer.' The teacher points out that a nonzero complex number has exactly three distinct cube roots, spaced evenly around a circle in the Argand plane, and that the student's single answer is only one of them. The student's working shows modulus 8 − 8√3 i = √(64 + 192) = √256 = 16 and argument θ = −π/3 (since the point lies in the fourth quadrant with tan θ = −√3).
472 words, about 2 min4A singular matrix in a network model
A small network of three nodes has flows x, y, z (in litres per minute) governed by the system Mx = b, where M is the 3×3 coefficient matrix with rows (1, 2, 3), (2, 4, 6), (1, 1, 1) and b = (6, 12, 3)ᵀ. A technician attempts to solve by computing the inverse of M and reports failure because 'the calculator gives an error.' A supervisor insists the system must have a solution because the physical network is running.
444 words, about 2 min5Interpreting a p-value with a small sample
A school trials a new study programme on 12 students. Their mean improvement score is 4.2 points with sample standard deviation 5.0 points.
453 words, about 2 min