January Regional
Algebra II Team Round Solutions
1.
Vertical asymptote at x=A=-­‐1 and x=B=2 (Note that A and B can be switched) Horizontal Asymptote at y=C=1/3 Removable discontinuity at (D,E)=(1,-­‐1/6) 2.
A
= =
B = C = D = 3.
A = B = C = D = Parts A and B will sum to zero making the final calculation (A+B)(C+D) equal zero as well. Note that you could immediately get 0 by recognizing the function is odd, so A+B=0. 0 4. Every 8 minutes, Kelsey paints 2 square yards, Flora paints 1 square yard, and Bobby paints 1 square yard. Thus, every 8 minutes they paint 4 square yards in total. They paint 1 square yard every 2 minutes. They paint 3 square yards every 6 minutes. A=6 In one minute, Kriti waters 12 square yards, Ina waters 8 square yards, and Reagan waters 4 square yards. In one minute, they water 24 square yards in total. Based on the January Regional
Algebra II Team Round Solutions
formula , set up the equation . 5. Gaussian elimination, substitution, and Cramer’s rule are all possible ways to determine that A=2, B=3, C=5, D=7. AD-­‐BC=(2)(7)-­‐(3)(5)=14-­‐15= -­‐1 6. A. Even function; True B. Function is neither odd nor even; False C. Letter B is a counterexample; False D. Even function; True E. Consider . . Function both even and odd; False F. . Function neither even nor odd; False True statements are A and D 7.
lies on Domain of is 8. Consider Scott as standing at the point . Apply the distance formula to find the distance from Scott to Jessica and Scott to Michelle. The distance to Jessica is minimized at an x-­‐value of Michelle is minimized at an x-­‐value of minimized at . The distance to . The distance to either girl is thus the sum of the distances is minimized at should stand at an x-­‐value of . Scott . 9.
D
= U = K = January Regional
Algebra II Team Round Solutions
E = Let 10.
has minimum at has minimum at or 11. The value of the right side of the equation is equal to yields (in base-­‐10) . Setting that . M=19 . So, A=7+4=1110 Θ = 105Θ = 45Θ = 125 Θ = Subtract the latter from the former. 12. A. False since B. True C. False since D. False since The non-­‐negative integers E. True True Statements: B,E 13.
A = -­‐4 B = 2 C = -­‐1 D = -­‐9 14.
January Regional
Algebra II Team Round Solutions
15.