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## 1983 Oregon Invitational Mathematics Tournament-PART A2

Have times (e.g. goals, content focus, etc.) changed in mathematics education? One measure is obtained by examining exams from the past.

For example, the following questions are from the "1983 Oregon Invitational Mathematics Tournament." I do not know who produced, coordinated, or scored the exam....as it is one of thousands of items stored in my "MISC" files.

Version: Part A: Paper and Pencil Test
Time Limit: 20 minutes for 11 questions
Directions: Select right answer, but show your work as it will be used if a tie occurs.
NOTE: Only the final five of eleven questions are given below. The first six were printed last week.

[Q#7] Below there are five graphs. Which one could be the sketch of a graph for y = (x+1)2(x-3)(x-5)?

[Q#8] Below are shown five graphs. which one could be a sketch for the graph of y = log3x?

[Q#9] The cube has side length of 10 cm. M is the midpoint of AB. N is the midpoint of CD. Find the area of MENF.
(a) (125/2)sqrt(3) (b) (50)sqrt(5) (c) (50)sqrt(6) (d) 125 (e) (100)sqrt(6)

[Q#10] How many solutions does the equation cos x = x/(3π) have?
(a) 2 (b) 4 (c) 6 (d) 8 (e) infinitely many

[Q#11] Assume a model for the population of a species as a function of time is
where a, N0, and k are certain constants. If initially the population of a species is 5,000, then after 10 days it is 8,000, and after a very long time the population stabalizes at 15,000, how should the formula read?

Hint: No hints, as this is a test!

Solution Commentary: An answer key was found with this same test in my files. It claims the answers are as follows:

[Q#7] (b)
[Q#8] (c)
[Q#9] (c)
[Q#10] (c)
[Q#11] (b)

Do you agree with all of these answers?...think and work carefully....