SACE Stage 2 Mathematical Methods case studies
SACE Stage 2 Mathematical Methods · Put your knowledge to work in context.
Mathematical Methods is a Stage 2 SACE subject worth 20 credits, listed under subject code 2MHS20. It is designed for Year 12 students in South Australia who want a mathematically rigorous pathway into university study, and it develops an increasingly complex and sophisticated understanding of calculus and statistics. The SACE Stage 2 Mathematical Methods case studies are 5 cases and about 2,640 words.
1Optimising a School Fundraiser: Profit Maximisation with Constraints
A school committee is planning a fundraiser selling two types of items: small and large. Each small item costs 2 to produce and sells for 5.
682 words, about 3 min2Analysing a Sinusoidal Model for Temperature Data
The temperature T(t) in degrees Celsius in a town over a 24-hour period is modelled by T(t) = 10 + 8 ( /12(t-4) ) , where t is the time in hours after midnight, 0 t 24 . A student claims that the maximum temperature occurs at 4 pm ( t=16 ) and the minimum at 4 am ( t=4 ).
358 words, about 2 min3Evaluating a Definite Integral in a Real-World Context
A car's velocity v(t) in metres per second over a 10-second interval is measured at discrete times: t=0,2,4,6,8,10 with velocities 0, 5, 12, 20, 25, 30 respectively. The car's acceleration is not constant.
563 words, about 3 min4Solving a Trigonometric Equation with Domain Restrictions
A mechanical arm's vertical position is given by h(t) = 3 (2t) + 4 (2t) for t [0, ] , where t is in seconds and h is in metres. An engineer needs to find all times when the arm is exactly 2 metres above the ground.
572 words, about 3 min5Hypothesis Testing with Sample Data: Interpreting p-values and Errors
A company claims that the mean weight of its cereal boxes is 500 grams. A consumer group takes a random sample of 40 boxes and finds a sample mean of 495 grams with a sample standard deviation of 12 grams.
465 words, about 2 min