March Regional Algebra 2 Team: Question 1 For this question i is the imaginary number 1. Let A = the remainder when 3x4 5x3 3( ) is divided by x 2( ) . Let B = the remainder when x2010 2ix + 5( ) is divided by x i( ) Let C = the quotient produced when x4 6x2 5x 12( ) is divided by x 3( ) Let D = the sum of the coefficients of the polynomial produced in part C (included the constant term). Evaluate A + B + D March Regional Algebra 2 Team: Question 2 How many of the following functions are neither odd nor even? f a( ) = a3 j u( ) =100u3 + 56u v x( ) = x4 + 5x2 +10 g x( ) = x4 + 5x + 6 f x( ) = 0 p x( ) = x7 +10x2

h x( ) = x2 + 7x2 r x( ) = x + 5x

March Regional Algebra 2 Team: Question 3 Given a + b = 6 and a2 + b2 = 28. Let A = the value of a b Let B = the value of a2 + ab + b2( ) Let C = the value of a3 + b3( ) Let D = the value of a3 b3

Evaluate A2 +C + DB

2

March Regional Algebra 2 Team: Question 4

If f x( ) = 5x2 8x 4

3x2 7x + 2 Let x = A be the vertical asymptote of f(x) Let y = B be the horizontal asymptote of f(x)

Let C = the value of the x intercept of f(x) Let D = the y value of the removable discontinuity Evaluate 3(A + B) + 5(C + D) March Regional Algebra 2 Team: Question 5 Let A = the units digit of 32010. Let B = the length of the major axis of the ellipse described by 25x2 50x + 4y2 + 24y = 39 Let C = 1+ 23 +

49 +

827 + ...

Evaluate A + B C March Regional Algebra 2 Team: Question 6 Let A = the second term of a harmonic sequence if: the first term of the harmonic

sequence is 12 the third term is 18 and the fourth term is

111

Let B = the numerical value of 7log21 2( ) 3log213( ) 3log218( ) 7log2112( )

Evaluate 2A + B March Regional Algebra 2 Team: Question 7

Let A = the value of 37 a + b( ) if 4 + 9i7+ 5i is written in the form a + bi Let B = the sum of the squares of the roots of the following function: f x( ) = x2 + 6x + 7 Let C = the number of distinguishable ways the letters of stanfordrocks can be arranged Let D = the number of distinguishable ways twelve different people can sit around a perfectly circular table.

Evaluate A B + 2CD March Regional Algebra 2 Team: Question 8 In Facetiousland, the world is flat and everything can be mapped perfectly with a Cartesian coordinate system. Dianne and Richard are fleeing from the FBI in Facetiousland; in order to avoid detection, they must make stops at (1, 0), (-1, 16), and (2, 1). After carefully examining a secret map, Richard discovers PharmaExpress, a parabolic road that passes through all three points.

What is the parabolic function that passes through all three these points? Express your answer in the following form: y = Ax2 + Bx +C March Regional Algebra 2 Team: Question 9

Let A = the solution set to: x + 4x 2 5 Let B = the solution set to: x3 4x2 4x + 5 3x 5 For your final answer, evaluate the sum of the greatest integer in A with the smallest negative integer in B March Regional Algebra 2 Team: Question 10 The expression 12 + 4 8 can be written in the form A + B C where everything is in simplest radical form and A, B, and C are whole numbers.

Let D = 6 0 03 2 15 4 1

Evaluate A + B + C D March Regional Algebra 2 Team: Question 11 f x( ) = 3x3 4x2 +1 g x( ) = x2 5, where x > 0 h x( ) log2 x Let A = f h 16( )( ) Let B = f g 3( )( ) Let C = g h1 2( )( ) Let D = f g1 20( )( ) Evaluate D C2 B A March Regional Algebra 2 Team: Question 12 In an effort to increase his presidential powers, Grant intends to trap Ms. Herron and Mr. Rohan in an enchanted garden. Grant has 200 feet of magic fencing to build a boundary for the garden; furthermore, he intends to use an infinite strip of the Everglades as one side of the gardens boundary. By the laws and regulations of magic, Grant must use all

of his fencing, the garden must be a rectangle, and the area of the garden must be as large as possible. Given these conditions, what will be the area of Grants enchanted garden in square feet? March Regional Algebra 2 Team: Question 13 Let A = the base ten representation of 7618 Let B = the base ten representation of 2145 + 3025 Evaluate the sum of the digits of (A + B) March Regional Algebra 2 Team: Question 14

Simplify the expression 11( ) 2( ) +12( ) 3( ) + ... +

198( ) 99( ) +

199( ) 100( ) into the form

AB

where A and B are relatively prime whole numbers. Evaluate A + B March Regional Algebra 2 Team: Question 15 To test whether or not Ari is psychic, Grant sets up two tests: a coin test and a dice test. Let A = the probability that Ari correctly predicts exactly seven out of ten tosses of a fair coin. Let B = the probability that Ari correctly predicts exactly two out of three rolls of a standard six sided die Let C = the denominator of A, if A is expressed as a simplified fraction Let D = the numerator of B, if B is expressed as a simplified fraction Evaluate C + D