Download Document

32nd Annual
Armstrong Atlantic State University
High School Math Tournament
Ciphering Round
Question 1
Make the statement true by filling in the boxes
using each of the four symbols exactly once:
,,,
5
3
12
4
2 = 5
Question 2
Suppose that the 4×4 array below is completed so
that each row and each column is a permutation of
the numbers: 1, 2, 3, 4. What is a – b?
1
2
3
2
1
a
3
4
4
b
Question 3
Let a, b, and c be the lengths of the three
sides of a right tria ngle. Suppose that
a  b  c  30 and a  b  c  392.
What is the area of the triangle?
2
2
2
Question 4
Two distinct numbers (a and b) are randomly
selected from the set {2, 3, 4, 5, 6, 7, 8, 9}.
a
What is the probabilit y that the fraction is less than 1
b
and can be expressed as a terminati ng decimal?
(express answer as a fraction in simplest terms)
Question 5
A robot is programmed to do the following in a
coordinate system:
Its first move -- Start at the origin facing in the positive y
direction and move one unit.
Each subsequent move -- it is to turn 90 degrees clockwise
and go forward 1 unit further than
it went in the previous move.
What is the sum of the coordinates of the robot after it
completes its 10th move?
Question 6
Each circle has a radius of 6 units.
Consider the triangle formed by joining
the three centers of the tangent circles.
What is the area inside the triangle but outside the circles?
Question 7
What is the 110th term of the sequence given below,
where the terms are found by adding consecutive
odd integers to previous terms?
0, 3, 8, 15, 24, 35, 48, 63, …
Question 8
A five digit number is created by using each
of the digits 3, 4, 5, 7, and 8 exactly once.
What is the probability that the number
created will be a multiple of 4?
(express answer as a fraction in simplest terms)
Question 9
A plane passes through a sphere,
and the area of the circle formed
by that intersection is 25π cm2.
The perpendicular distance from the center
of the sphere to the plane is 12 cm.
What is the length of the radius of the sphere?
Question 10
(As heard on NPR-Weekend Edition Sunday, December 13, 2009)
“Name five two-digit numbers that are evenly spaced out
— like 32, 34, 36, 38 and 40 — in which all 10 digits
from 0 to 9 are used once each. What numbers are these?”
List 2 out of the 4 possible solutions.