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March Regional Algebra II Team Question 1

A = the sum of the following finite sequence {3, 6, 9, 12, . . . , 30}.B = the sum of the following infinite sequence {1, 1/2, 1/4, . . . }.C = the number of terms in part A.D = the sum of the following finite sequence {10,9, . . . ,3,2,1, 0, 1, 2, 3, . . . , 9, 10}.

Find ABCD.


Joe can do a job in 5 hours. John can do the same job in 2 hours. Jake can do the same job in 1hour. How long will it take Joe, John, and Jake to do 1 job? (Give your answer in HOURS.)


2 trains are both on the same track, traveling directly at each other. At the beginning, they are 100yards apart. Each train travels at a constant speed of 5 feet per second. Patrick starts running at thesame time starting from one train running to the other and back and forth. Patrick runs at a speed of 100feet per second. How far will Patrick run until the trains crash? (Give your answer in FEET.)


f(x) = x3 6x2 + 11x 6.A = the sum of the roots.B = the sum of the squares of the roots.C = the product of the roots.D = the sum of the reciprocals of the roots.

Find ABCD.


Point A is the vertex of y = x2 6x + 15.Points B and C are the 2 vertices of the major axis of 9x2 + 4y2 18x 8y 23 = 0.

Find the area of the triangle with vertices A, B, and C.


A = 1035 in base 10.B = 101012 in base 10.C = 304 in base 10.D = 739 in base 10.

Find A + B + C + D in base 10.

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A = the number of distinguishable permutations of the letters of the word MARCHB = the number of distinguishable permutations of the letters of the word REGIONALC = the number of distinguishable permutations of the letters of the word ALGEBRAD = the number of distinguishable permutations of the letters of the word ALGEBRATWOTEAM-QUESTIONSEVEN

List the letters ABCD in ASCENDING order based on their numerical value. (From least to great-est)


x 1 2 3 4

f(x) -1 3 -2 -9

g(x) 4 5 1 0

Note: f(x) is an even function and g(x) is an odd function. Also, f(x) and g(x) both have domains of allreal numbers.

A = f(1).B = g(3).C = g(3).D = f(4).E = g(2).F = g(2).

Find ABCDEF .


The lines y = 3x + 4 and y = 3x 4 intersect at the point (a, b).The lines 2y = 2x + 1 and 3y = 5x 4 intersect at the point (c, d).

Find the distance between the points (a, b) and (c, d).


How many of the following are ALWAYS true for x and y real numbers and a and b real positive constants?

1. axay = axy

2. log(a) + log(b) = log(ab)3. y = x and y = x2 intersect exactly twice.4. ax + bx = (a + b)x

5. A graph can cross its horizontal asymptote.6. A graph can cross its vertical asymptote.

7. The horizontal asymptote of y =1

xdoes not exist.

8. A parabola has an eccentricity of 1.9. A singular matrix has an inverse.

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3x + 4y 5 x 0 y 0Find the maximum value of x + y for every ordered pair (x, y) which is in the solution set to the abovesystem of inequalities.


A =

[3 51 4

]B =

2 1 10 1 01 1 2

C = B1.D = BT .E = BCD.x = |A|.y = |E|.

Find x + y.


f(x) =2x3 + 3x2 2x 3

x2 3x + 2 .

x = C is the vertical asymptote of f(x).Point (D,E) is the removable discontinuity of f(x).Find CDE.


Simplify

(3xy2

z

)4(z2y3

5x

)2(4z3

x3

)4for xyz 6= 0.


What is the sum of the first 12 terms of the Fibonacci sequence with first two terms f1 = f2 = 1?

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