WYSE Academic Challenge Math Test (Regional) m x

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1 WYSE Academic Challenge Math Test (Regional) Correct Answer: C For the height of the Loki kite we have = 7 sin For the height of the Thor kite we have = 50 sin The Thor kite is higher by. meter. See the diagrams below: Loki Thor 7m 50m o 8 o 45. Correct Answer: C The car is moving 0 mph to the east and 40 mph to the south. Using the Pythagorean Theorem, that means it s moving 50 mph in total.. Correct Answer: B Using cosθ = and r we have r = +, r = 4 cosθ r = 4 r = 4. Substituting for r y + y = y = 0. Completing the square we have y 4 what we need to find the linear feet for the border. π + =. The garden is circular with a radius of feet. The circumference is 4. Correct Answer: B r = 4π = An identity matri is its own transpose. An identity matri is its own inverse. An identity matri multiplied by itself is the same identity matri. 5. Correct Answer: C Let be the leg length of the triangle. =, =. The hypotenuse/ diameter is therefore 6. Correct Answer: D + =, the radius =, and area = π. This describes an arithmetic series with a = 40, d =, and n = 4 4 4( ) a = = 5. k k =. Then 06 Regional

2 Math - 7. Correct Answer: E The magnitude of.5 + is.5 i = 45. By DeMoivre s Theorem, the magnitude of a comple number raised to the nth power is the magnitude of that comple number, r, raised to the nth power. 45 cubed is 9,5. 8. Correct Answer: E ( 4) ( y + ) 9( 4) + 5( y + ) = 45 + =. The semi-major ais is a =. The 5 9 semi-minor ais is b = 5 and the distance from the center to the foci is c = 9 5 =. c The eccentricity is e = =. a 9. Correct Answer: C The domain is dependent upon where is positive. That is equivalent to the positive real numbers. 0. Correct Answer: B 0 Using = years after 000, the population can be modeled by y = , or the equivalent y = 0000 e. Solving 0000 = gives 7... Correct Answer: A θ 5 π ω = ; The angular speed. ω = = 5π. The linear speed t ν = r ω = 8 5π = Correct Answer: C There are letters in illegibility, one of which is repeated four times and one of which is repeated thrice. So the number of distinguishable strings is!,6,400 4!! =.. Correct Answer: B Converse of states that if two angles are vertical angles then the angles are congruent (true). Converse of states that if two angles have the same verte then the two angles are adjacent. This is false. The angles could be vertical. Converse of states if alternate interior angles are congruent then the two lines are parallel. This is true (Postulate 4.). Only the Converse of is false. 06 Regional

3 Math - 4. Correct Answer: B Bob does of the job every hour and Nate does of the job every hour. That means 6 that together, they do + = 7 of the job each hour. This means that it will take the 6 48 two of them = 48 = 6 6 hours to finish the job Correct Answer: C Let the starting amounts be A, B, and C. A =, so A =.5, B =, so B = 4, and 4 C =, so C =.5. The eaten amounts are A = 0.5, B =, and C =.5, for a total amount eaten of = Correct Answer: C The jog represents a right triangle with the legs of the triangle represented by 5 and. The shortest distance then would be the hypotenuse side to get back home. This is the 5 + =. typical 5,, right triangle 7. Correct Answer: A This is easiest to solve when we set f() to be equal to 5 and then solve for. = 5,so = 5 ( ). So = and then -7 = Correct Answer: E Since there are factors of ( ) and ( + ) there are no vertical asymptotes. in both the numerator and denominator, 9. Correct Answer: D Even functions are functions for which f(-) = f() is an identity. cos and sec are the two basic trig functions which are even. This makes both I and II even. Odd functions are functions for which f(-) = -f() is an identity. The other four basic trig functions are odd. This makes III odd, and since tan is odd, cos (tan ) would be even. 0. Correct Answer: A Kite, by definition. 06 Regional

4 Math - 4. Correct Answer: A ( + 5) ( ) ( + 5) + ( ) ( + 5) ( ) Correct Answer: D The eponential portion goes to infinity much, much faster than the linear portion goes to negative infinity, so the answer is infinity.. Correct Answer: D ln 0.6 ln 0.5 5r 0.065t 0.6p = pe r = = 0.065, 0.5 = e t = The half-life of a new married couple in the city is approimately 7 years. 4. Correct Answer: A The period of tan is π, so the period of tan would be A. The other transformations of the function are merely shifts, so the period does not change. 5. Correct Answer: E The overall number of possible draws is given by C(0,) = 0. The ways we can get all three the same color is all three blue C(,)= or all three green C(6,)=0. This makes the overall probability /0=7/ Correct Answer: B Solving the system of equations we have 7 + y 5 = 0 + 5y + 0 y = = = 5 =. Then y = 8. + ( 8) = 5. Then 7. Correct Answer: D f( ) = ( ) + = = Correct Answer: E log 4 b = b = 4 b = 4 9. Correct Answer: A The average rate of change of a function is the slope of the secant line between the two described points. In this case, the points are (0, 8) and (, 6) and the slope is thus A. 06 Regional

5 Math Correct Answer: E We can start by filling out the AM deliveries as Amy to Hamms (since Carol follows), Carol to Flower s R Us (to follow Amy), and Beth to Embry s (so she doesn t repeat). We then fill out the PM as none to Embry s (to satisfy I), Carol to GrowLots (to follow Anne), Beth to Hamm s (so she doesn t repeat) and Amy to Flowers R Us (by default). We can now list deliveries by person. Amy: F-H-G-F, Beth: G-E-F-H, and Carol: E-F-H-G. Beth and Carol went to all four. 06 Regional