Utah State Mathematics Contest
Junior Exam Solutions
March 14, 2012
1. What is the units digit of
?
Solution: (c) The units digit is determined by the power of the last digit 2 alone modulo 4:
1 mod 4
State Math Contest 2015 - Senior Exam Solutions
1. If 4x 2x 6 = 0, then x =
a)
log2 3
b)
-2
c)
log4 3
d)
3
e)
log3 2
Solution: Let y = 2x . Then the equation is y 2 y 6 = 0, or (y 3)(y + 2) = 0, which
State Math Contest 2015- Junior Exam Solutions
1. Find the slope of the line containing the two points (2, 4) and (5, 3).
a)
7
3
b)
3
7
c)
3
7
d)
7
3
e)
4
3
3 (4)
7
= .
52
3
The answer is a.
Solution:
Name:
State Math Contest - Junior Exam
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Name:
State Math Contest - Senior Exam
Instructions:
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Enter your name, grade, and school information following the instructions given by your proct
Utah State Mathematics Contest
Junior Exam
March 14, 2012
1. What is the units digit of ?
(a) 2
(b) 0
(c) 6
(d) 4
(e) 8
2. A train, traveling at a constant speed, takes 20 seconds from the time it ent
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