SACE Stage 2 Specialist Mathematics case studies
SACE Stage 2 Specialist Mathematics · Put your knowledge to work in context.
Specialist Mathematics is a Stage 2 SACE subject (code 2MSC20) worth 20 credits. It draws on and deepens students' mathematical knowledge, skills, and understanding, giving them opportunities to develop rigorous mathematical arguments and proofs and to work with mathematical models; its content includes the study of functions and calculus. The SACE Stage 2 Specialist Mathematics case studies are 5 cases and about 2,271 words.
1Projectile Range with a Fence Constraint
A ball is launched from ground level at 18 m/s at an angle of 35° above the horizontal. A vertical fence of height 4.2 m stands 14 m from the launch point, measured horizontally.
473 words, about 2 min2Complex Roots and Loci in an Argand Diagram
A complex number z satisfies z − 3 − 4i = 5. A student is asked to describe the locus, find the greatest and least values of z , and determine whether z = 8i lies on the locus.
452 words, about 2 min3Differential Equation Model of Cooling with a Changed Ambient
A cup of coffee cools in a room. Newton's law of cooling gives dT/dt = −k(T − Tₐ), where T is the coffee temperature in °C, t is in minutes, and Tₐ is the ambient temperature.
431 words, about 2 min4Hypothesis Test on a Mean with Unknown Variance
A manufacturer claims that the mean mass of its cereal boxes is at least 500 g. A consumer group samples 16 boxes and obtains a sample mean of 494 g with sample standard deviation 9 g.
393 words, about 2 min5Vector Equation of a Line and Shortest Distance
In three-dimensional space, line L₁ passes through A(1, 2, −1) with direction d₁ = (2, −1, 3). Line L₂ passes through B(4, 0, 2) with direction d₂ = (1, 1, −2).
522 words, about 3 min