Home > Problem of the Week > Archive List > Detail

<< Prev 10/14/2012 Next >>

1983 Oregon Invitational Mathematics Tournament-PART B1

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 B: Number and Calculator Sense Test
Grade Levels: 7-12
Time Limit: 20 minutes for 15 questions
Directions: You can use a calculator (none-graphical at that time). Select right answer, but show your work as it will be used if a tie occurs.
NOTE: Only the first eight of fifteen questions are given below. The final seven will be printed next week.

[Q#1] Here are two situations:
A: A coin will be tossed 100 times. If it comes up heads 60 or more times, you win $1.
B: A coin will be tossed 1,000 times. If it comes up heads 600 or more times, you win $1.
Which of the following correct?
(a) Situation A is better
(b) Situation B is better
(c) Both offer the same chance of winning.

[Q#2] The largest known prime number is 286243-1. Calculate how many digits there are in the number 286243-1. (In case you need any logs here are some approximations: log 2 = .30103; log 3 = .47712; and log 5 = .69897.)

[Q#3] Each cubic centimenter contains 27,000,000,000,000,000,000 (2.7 x 1019) molecules. If the surface area of the earth is 500,000,000,000 square meters and there were as many people distributed over the face of the earth as there were molecules in a cubic centimeter, how many people would there be to each square meter?

[Q#4] What is the smallest value of n for which 12+22+32+...+n2 > 1000?

[Q#5] Given that log35 = 1.465, find the log3(5/3).

[Q#6] x varies directly as y and inversely as z2. If x = 26 when y = 8, z = 2, find value of x when y = 36 and z = 3.

[Q#7] What is the largest integer less than

[Q#8] What is the x coordinate of the right hand focus of x2/81 - y2/25 = 1?


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] (a)
[Q#2] 25962
[Q#3] 5.4x104
[Q#4] 14
[Q#5] .465
[Q#6] 52
[Q#7] 29>br> [Q#8] sqrt(106) or 10.3

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