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
2 mod 4
3 mod 4
0 mod 4
1
2
3
2 = 2,
2 = 4,
2 = 8,
24
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 means that
y = 3, 2. It is not possible for 2 = 2x , s
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:
2. Given a point P inside of a square, the distances f
Name:
State Math Contest - Junior Exam
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State Math Contest - Senior Exam
Instructions:
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Enter your name, grade, and school information following the instructions given by your proctor.
This is a multiple choice test with 40 questions.
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 enters a tunnel
that is 300 meters long until it emerges f
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Exercise 6
MA407
This set of exercises will make you more familiar with the object oriented programming features
of Java. You will practise to implement APIs and design and use own data types. We start
with a simple data type implementation for a given AP
Exercise 5
MA407
This exercise set concerns sorting algorithms and their running times. It should make you
familiar with the type of questions that you will encounter in the exam. (In fact Exercise 2(a),
2(c), 2(d) appeared in a very similar form in last
Exercise 2
MA407
One subject where two dimensional arrays prove particularly useful are calculations with matrices - which has a multitude of applications, as you know. The following exercises ask you
to implement matrices and some common matrix operation
Exercise 3
MA407
This set of exercises will introduce you to a particularly ecient method to search for an entry
in a sorted array, which is called binary search. The basic idea of binary search is that the
section of the array where the entry is searched
Exercise 1
MA407
Since the times of the Ancient Greeks prime numbers have held much fascination for mathematicians. Although today we know quite a lot about them, many questions remain open
and they are still a topic under intensive study. (For example, o
Exercise 4
MA407
In this exercise we to consider a sorting strategy that is dierent from the strategies we saw
in the lecture: we want to sort by switching elements that are not in the right order. More
precisely we want to sort an array x of type int[] b
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 7: More improper integrals and the manipulation of proper integrals
For these and all other exercises on this course, you must show all your working.
1.
Determine whether each of the followin
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 8: Leibnizs rule, the manipulation of improper integrals and LTs
For these and all other exercises on this course, you must show all your working.
1.
For x > 0, a function, f , is dened by
x2
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 5: FTC (again), transformations and more double integrals
For these and all other exercises on this course, you must show all your working.
1.
The function, p(x, y ), of two variables is dene