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Lesson Plan 2: Curses and Re-Curses! It's Happening Again.
The questions below dealing with recursion have been selected from various state
and national assessments. Although the lesson above may not fully equip students to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.
Taken from the Michigan High School Test (Spring 2002):
During a visit to his physician, John received a single dose of medication that decays or loses its effectiveness at a rate of 20% per hour. The amounts of medication that remain in his body at the end of each hour for the first 3 hours are represented by the sequence 150, 120, 96 mg. Approximately how many milligrams of medication remained in his body after the first 6 hours?
A. 25
B. 30
C. 50 (correct answer)
D. 90
Taken from the Kentucky Core Content Test (Spring 1999):
Triangle Patterns
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The diagrams above show the first three steps of a process used to make a triangle
pattern. In Step 1, the large triangle has an area equal to 1 [square] unit. In Step 2, the large triangle is divided into 4 congruent triangles, and the middle triangle is removed.
A. What is the area of the shaded region in Step 2?
Solution: 3/4 square units
In Step 3, the dividing process continues. Each shaded triangles in Step 2 is divided into 4 congruent triangles. Each middle triangle is removed, and the shaded parts remain. The dividing process continues until the total shaded area is less than 1/2 square units.
B. How many steps does it take until the shaded area is less than 1/2 square unit? (Give a complete explanation to justify your answer.)
Solution: 4 steps, because the area for each step equals 1, 3/4, 9/16, and 27/64. A recursive formula for this sequence is Next = Now × 3/4, Start = 1.
Taken from New York Regents High School Examination, August 2002:
A used car was purchased in July 1999 for $11,900. If the car depreciates 13% of its value each year, what is the value of the car, to the nearest hundred dollars, in July 2002?
Solution: $7,800. A recursive formula for this is Next = Now - Now × 0.13 or Next = Now × 0.87, Start = 11,900. The answer is the fourth term.
Taken from the Mississippi Subject Area Practice Test, Mathematics:
The terms below belong to a famous mathematical sequence.
1, 1, 2, 3, 5, ___, 13, 21, 34, ...
Which term comes between 5 and 13?
A. 7
B. 8 (correct answer)
C. 10
D. 12
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