Physics quiz question: height factor increase

Physics 205A Quiz 1, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 1.6

[3.0 points.] Hildegaard is 0.99 m tall on her eleventh birthday and 1.13 m tall on her twelfth birthday. By what factor has her height increased?
(A) 0.12.
(B) 0.14.
(C) 1.1.
(D) 14.

Correct answer: (C)

Let h_1 = initial height, and h_2 = final height, such that h_2 is some numerical factor times h_1:

h_2 = factor*h_1,

h_2/h_1 = factor,

1.1 = factor, limited to two significant figures from h_1.

Response (A) is 1 - (h_1/h_2) (which, if multiplied by 100, would give the percent increase in height); response (B) is h_2 - h_1; and response (D) is 100*((1.13/0.99) – 1).

Student responses
Sections 30880, 30881
(A) : 2 students
(B) : 30 students
(C) : 18 students
(D) : 0 students

"Difficulty level": 36%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49