GACE Mathematics (522) case studies
GACE Mathematics (522) · Put your knowledge to work in context.
This independent study page provides practice for GACE Mathematics (522). Its editorial learning areas include Algebra and functions; Number and quantity; Geometry and measurement; Calculus foundations; Discrete mathematics and reasoning; Probability and statistics. The questions develop subject knowledge and application through worked reasoning, distinctions between competing answers, and practical scenarios. Study the relevant guide before attempting a mixed set, then explain the evidence or calculation that supports each answer. Topics on this exam: Algebra and functions, Number and quantity, Geometry and measurement, Calculus foundations, Discrete mathematics and reasoning, and Probability and statistics. The GACE Mathematics (522) case studies are 4 cases and about 2,196 words.
1Strain-Gauge Calibration: Least Squares After a Suspect Reading
A calibration technician records a strain gauge's output y (mV) at five known loads x (kN): (1, 2.10), (2, 3.95), (3, 6.10), (4, 7.85), (5, 10.20). The intended model is y = a + bx. During the run, the technician notices that the fifth reading was taken while a connector was loose and suspects a constant +1.00 mV offset on that reading only. The lab's quality procedure says a slope change of more than 8% after correcting a suspect point must trigger a full recalibration, not just a note in the log.
621 words, about 3 min2Screening Test: PPV, Repeat Testing, and a Limited Confirmation Budget
A regional clinic screens 10,000 adults, of whom 2,000 are in a high-risk subgroup with family history. The general-population prevalence is 0.80%; in the high-risk subgroup it is 6.0%. The screening test has sensitivity 92% and specificity 96%. The clinic can run a second, independent confirmatory test that costs 60 currency units per patient; treatment started on a false positive causes 250 units of avoidable harm, while a true case missed because treatment is delayed costs 400 units.
661 words, about 3 min3Auditing a Raffle's Expected Payout and Fairness Claim
A student council runs a raffle to fund a trip. Each ticket costs 5. There are 400 tickets sold. The prizes are: one grand prize of 300, two second prizes of 100 each, and ten third prizes of 20 each.
448 words, about 2 min4Interpreting a Confidence Interval from a Small Sample
Assume independent packet masses from an approximately normal population. A student measures the mass of 9 randomly selected packets of seeds from a production line and obtains a mean of 50.2 g with a sample standard deviation of 1.5 g. The student constructs a 95% confidence interval for the population mean using the normal critical value 1.96 and reports 50.2 ± 0.98, i.e., (49.22, 51.18). A classmate says the interval is wrong because the sample is small and the population standard deviation is unknown.
466 words, about 2 min