Practice Round
Theta Ciphering
Mu Alpha Theta National Convention 2004
If 2x – y = -6 and 4x – 3y = -16,find the sum of x and y.
Question #1
Theta Ciphering
Mu Alpha Theta National Convention 2004
Let A = the slope of the graph of 2x – 5y = 2004
Let B = the slope of the line containing the points (12, 1) and (-6, 7)
Let C = the x-intercept of the graph of 2x + 7y = 10
Let D = the y-intercept of the graph of 6x – 5y = 30
Find:
ABCD
Question #2
Theta Ciphering
Mu Alpha Theta National Convention 2004
Find the area of the region determined by the intersection of the graphs of the given
system of inequalities:
5  y  9

y  2x  9
 x  7

Question #3
Theta Ciphering
Mu Alpha Theta National Convention 2004
Consider the following compound function:
 x, if x  2

g(x) =  x2 , if - 5 < x < 2
 x, if x  -5

Find: g(-2004) – g(-5) + g(-1) + g(25)
Question #4
Theta Ciphering
Mu Alpha Theta National Convention 2004
Let A = the perimeter of a rectangle whose width is log62 and whose length is log63
Let B = the value of x that satisfies logx100 – logx4 = log x x
Find:
A+B
Question #5
Theta Ciphering
Mu Alpha Theta National Convention 2004
Find:
the sum of a and b when
i 2004  (1 3i)2  (2  i)(3  i) 
1  2i
3  4i
is written in the form a + bi
a, b ; i =
-1
Question #6
Theta Ciphering
Mu Alpha Theta National Convention 2004
One side of an equilateral triangle is the hypotenuse of an isosceles right triangle. If the
altitude of the equilateral triangle is 8 3 , find the length of a leg of the right triangle.
Question #7
Theta Ciphering
Mu Alpha Theta National Convention 2004
A polynomial P(x) has zeros 1, -1, and 2, each with multiplicity 1, and no other complex
zeros. If P(0) = 8, find P(4).
Question #8
Theta Ciphering
Mu Alpha Theta National Convention 2004
Let A = the length of the major axis of an ellipse whose equation is 4x2 + 25y2 – 100 = 0
Let B = h + k + r, given that (h, k) is the center and r is the length of the radius of the
circle defined by the equation x2 + y2 + 6x – 4y – 12 = 0
Find: AB
Question #9
Theta Ciphering
Mu Alpha Theta National Convention 2004
Evaluate:
50

k1
k1
k1
1
 2k  3   2 
3
Question #10
Theta Ciphering
Mu Alpha Theta National Convention 2004
Let x = the units digit of the sum 1! + 2! + 3! + 4! + . . . + n! + . . . + 2004!
x
Evaluate: 4 
4 x
 C
2 5 5 x
Question #11
Theta Ciphering
Mu Alpha Theta National Convention 2004
A parabola with a vertical axis of symmetry has vertex (3, -2) and a x-intercept of 4. If the
equation of the parabola is written in the form y = ax2 + bx + c, find the sum a + b + c.
Question #12
Theta Ciphering
Mu Alpha Theta National Convention 2004
A pair of fair, six-sided dice is thrown. What is the probability that the numbers on the
top faces match or the sum of the numbers shown on the dice is at most 6?
Mu Alpha Theta National Convention 2004
Theta Ciphering
Answers
#
Practice
1
2
3
4
5
6
7
8
9
10
11 - TB
12 - TB
Answer
3
4
49
-1993
627
1
26
5 or
or 5.2
5
5
8 2
120
40
2703
Thrown out
6
1
or 0.5 or 50%
2