FTCE Mathematics 6-12 case studies
FTCE Mathematics 6-12 · Put your knowledge to work in context.
The FTCE Mathematics 6–12 examination, identified in the Florida test catalog as Mathematics 6–12 (026), is one of the subject-area certification tests in the Florida Teacher Certification Examinations program. It is intended for candidates seeking certification to teach mathematics at the secondary level in Florida public schools, and it is one of many tests listed alongside Middle Grades Mathematics 5–9 (025), Elementary Education K–6 (060), and other subject fields in the FTCE/FELE catalog. The FTCE Mathematics 6-12 case studies are 5 cases and about 3,244 words.
1The Fence Problem: Maximizing Area with Limited Resources
A homeowner wants to enclose a rectangular garden using 40 meters of fencing. One side of the garden will be against a barn and requires no fencing.
622 words, about 3 min2The Case of the Missing Probability: Conditional Probability and Independence
In a certain school, 60% of students play sports, 40% play a musical instrument, and 30% do both. A student is selected at random.
510 words, about 3 min3The Limits of Average Rate of Change: A Calculus Conundrum
A car's position along a straight road is given by the function s(t) = t^3 - 6t^2 + 9t + 5, where s is in meters and t is in seconds, for 0 ≤ t ≤ 5. A student computes the average rate of change of s over the interval [0,5] and gets (s(5)-s(0))/5 = (125-150+45+5 - 5)/5 = (25-5)/5 = 20/5 = 4 m/s.
468 words, about 2 min4The Trigonometric Identity Trap: Solving an Equation with Extraneous Solutions
A student is solving the equation 2 sin^2(x) - 3 sin(x) + 1 = 0 for x in [0, 2π). They factor it as (2 sin(x) - 1)(sin(x) - 1) = 0, giving sin(x) = 1/2 or sin(x) = 1.
481 words, about 2 min5The Geometry of a Kite: Applying the Law of Cosines and Area Formulas
A kite is being designed with two sides of length 5 cm and two sides of length 8 cm. The angle between the two 5 cm sides is 60°.
1,163 words, about 6 min