Home > Problem of the Week > Archive List > Detail

<< Prev 9/16/2012 Next >>

1983 Oregon Invitational Mathematics Tournament-PART A1

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
Grade Levels: 7-12
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 first six of eleven questions are given below. The final five will be printed next week.

[Q#1] For what values of x is the following statement true? log3x+logx9+3 = 0.
(a) 1/3, -1/3 (b) 1/3, 3 (c) 1/9, 3 (d) 1/9, 1/3 (e) 9, 1/3

[Q#2] If one root of the following equation is twice the other root, find the value of k: x2+(8+k)x+18 = 0.
(a) k is between -7 and -5
(b) k is between -4 and -1
(c) k is between 0 and 3
(d) k is between 4 and 7
(e) k is greater than 8

[Q#3] For what numerical value of q will the coefficients of x3 and x4 in the expansion of (1+qx)8 be equal?
(a) 1/5 (b) 1/4 (c) 3/5 (d) 4/5 (e) 5/4

[Q#4] Consider the line y = 3x-1 and the point (2,7). What is the shortest distance between this point and the line?
(a) sqrt(10)/5 (b) (4/9)sqrt(10) (c) (2)sqrt(2) (d) sqrt(10) (e) sqrt(13)

[Q#5] A right pyramid (with apex B) has a square base AEDC of side length 1 cm. Its height BP is 1 cm. Find Tan(ABC).
(a) (-1/2)sqrt(5) (b) (1/2)sqrt(5) (c) (-1/5)sqrt(5) (d) (2/5)sqrt(5) (e) sqrt(2)

[Q#6] Suppose the roots of a 10th degree polynomial, x10+a9x9+a8x8+...+x+a0, are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. What is the coefficient of the x9 term, a 9 in this polynomial?
(a) -10 (b) 15 (c) -35 (d) 45 (e) -55


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#1] (d)
[Q#2] (c)
[Q#3] (d)
[Q#4] (a)
[Q#5] (b)
[Q#6] (e)

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