1. The average age of five children is 6 years old. Each child is a
different age and there is a difference of two years in the ages
of any two consecutive children. In years, how old is the oldest
child?
years old
1. _
2. For what value of n is 33
Gemini Topic Test
FAMAT State Convention 2009
NOTA means None of the Above. Assume i = 1, e is the natural base. The
determinant of matrix M is M , its transpose is M T , its adjoint is adj ( M ) , and its
inverse is M 1 . Iff means if and only if.
1. The
Gemini Solutions
FAMAT State Convention 2009
1. D On the first pass you close 2-20 even. On the second pass you close 19, 15, 11, 7,
and 3. On the third pass you close 5, 13, and 21. On the fourth you close 9. On the fifth
pass you close 17, the last lock
Theta Functions Solutions
FAMAT State Convention 2009
1. f ( 3) = 27 + 9 4 = 32 . D
2. The remainder is equal to f ( 1) = 17 23 + 12 + 9 11 = 4 . C
2
2
3. When x = 0 , ln ( x ) is undefined, so f is undefined. When x = 1 or x = 1 , ln ( x ) = 0 , so f
2
i
Theta Functions
FAMAT State Convention 2009
For all questions, E. NOTA means none of the above answers is correct.
3
1. If f ( x ) = x + 3 x 4 , then what is f ( 3) ?
A. 4
B. 14
C. 25
D. 32
E. NOTA
5
3
2
2. What is the remainder when f ( x ) = 17 x 23x +
February Regional Individual Test
The use of a calculator is not permitted!
For all questions, choice E is NOTA, meaning none of these answers.
All angles are measured in degrees
Figures are not necessarily drawn to scale
1. We begin this test by asking a
February Regional
Geometry Team
Question #1
Lines l, m, and n are parallel to each other.
Evaluate: A+B+C+D
February Regional
Geometry Team
Question #1
Lines l, m, and n are parallel to each other.
Evaluate: A+B+C+D
February Regional
Geometry Team
Questio
February Regional Solutions
Answers:
1. C
2. C
3. B
4. C
5. A
6. B
7. B
8. D
9. C
10. B
11. A
12. A
13. B
14. D
15. C
16. C
17. D
18. A
19. D
20. A
21. A
22. B
23. C
24. A
25. B
26. B
27. E
28. B
29. C
30. B
( 5 (1) ) 2 + ( n 3) 2
2
136 = 36 + ( n 3)
2
10
February Regional
Geometry Team
Question #1: Lines l, m, and n are parallel to each other.
Evaluate: A+B+C+D
Question #2: Given that the apothem of the following figures is 6 in., find the areas of the following
figures. A= area of circle B = area of equi
MAO February Regional Algebra I Team Solutions
1. -9:
The minimum value of f(x) will be at the vertex of f(x). The x -coordinate of the
vertex will be b/2a, or -1; the minimum value is therefore f(-1) or -6. The slope of the
line is 3. -12 + 3 = -9
2. -10
February Geometry Regional Answer
Key
Individual
1. C
2. C
3. B
4. C
5. A
6. B
7. B
8. D
9. C
10. B
11. A
12. A
13. B
14. D
15. C
16. C
17. D
18. A
19. D
20. A
21. A
22. B
23. C
24. A
25. B
26. B
27. E
28. B
29. C
30. B
Team
1. 377
2.
73
3
3. 25
4. 35
130
Algebra I Individual Test
MAO February Regional
No calculators allowed.
NOTA means none of these answers are correct
1. Nick decides to go on a vacation to Miami, Florida. For 4 hours, he speeds down the highway at
100 miles per hour until L isa, a police
February Regional_
Statistics Individual Test
NOTA stands for None of the Above is Correct
1. Mellican loves to bake. She has also always found psychology interesting. If she doesnt consider
any other career, which of the following is she more likely to b
Theta Equations and Inequalities Solutions
FAMAT State Convention 2009
7
.B
3
2. By examination we see that the polynomial has the root x = 1 . Synthetic division yields
( x + 1)( x 2 2 2 x + 5) . Since imaginary roots come in pairs and we already have a
Theta Equations and Inequalities
FAMAT State Convention 2009
The answer choice E. NOTA denotes None of the Above Answers is Correct. Assume least
common multiples are positive.
1. Solve for x if 4 ( x 3) 3 ( x 5 ) + 2 ( x + 1) = 12 .
7
7
A) 9
B)
C)
D) 3
3
Alpha Equations and Inequalities
FAMAT State Convention 2009
Directions: Try to answer each question to the best of your ability. The questions are in no
particular difficulty. Also, NOTA means None Of These Answers. Thus, if you obtain an
answer that is
FAMAT State Convention 2009
Errata Sheet
Reasons for changes are on following pages.
Geometry
#20 D
Theta Apps
#27 D
Theta Equations & Inequalities
#16 E
Calc Apps
#14 D
Sequences & Series Calc
#29 B
Statistics
#14 E
Number Theory
#1 B
#3 B
#12 E
#13 C
#1
Alpha Equations and Inequalities
FAMAT State Convention 2009
1) The easiest way to solve this question is to graph both equations. Notice that the
quadratic function is always positive and will never intersect the linear function on the
right hand side of
Matrices
Part II
Matrices So Far
Defined Matrices
Order of a Matrix
Matrix Addition
Zero Matrix
Matrix Subtraction
Scalar Multiplication
Multiplication
Matrices - Today
Determinants
Inverse Matrices
Multiplicative Inverse
Using the calculator
Ap
Discrete Math Answer Key
2
n
n
1) A, an = 8an 1 12an 2 x 8 x + 12 = ( x 6)( x 2) = 0 an = c1 6 + c2 2 . The initial conditions
3n1n
3 20 1 20
give an = 6 + 2 . Thus, a20 = 6 + 2 9 + 3 2 (mod10)
2
2
2
2
2) A, There exists a 3-coloring of the graph as shown
Discrete Math
FAMAT State Convention 2010
Directions: For the purposes of this test, NOTA denotes none of the above. Let Q + denote
the set of positive rationals, P* denote the set of primes, and Z denote the set of integers.
1) A sequence of numbers foll
Sequences and Series
An Introduction
Pre-Calculus
Day 75
Sequences
A sequence is an ordered list of numbers. Each number
in the sequence has a position
Mathematically, it is a function whose domain is the
set of positive integers (the position of the numb