TEAM RELAYS MU ALPHA THETA STATE 2009 ROUND NAMES THETA

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1 TEAM RELAYS MU ALPHA THETA STATE 009 ROUND SCHOOL NAMES THETA ALPHA MU

2 What is the product of 3 ad 7? Roud ) 98 Richard s age is curretly twice Brya s age. Twelve years ago, Richard s age was three times Brya s age. How may years old is Brya ow? Evaluate: log Aswer as a commo fractio. ) 3) 3 7 What is the probability that a positive three-digit umber is divisible by both 3 ad by 6? Aswer as a commo fractio. ) 6

3 Roud What value(s) of a satisfy: 3 a 9 = a + 79? ) 6 What is the surface area, i square cetimeters, of a hemisphere with a diameter of 9 cm? Aswer as a commo fractio i terms of π. 3π ) If a agle i the third quadrat has a cosie of, what is the value of its 3 cosecat as a fractio? Aswer i simplest radical form. Give f(x) = si x + fid f '(0). 3 3) )

4 Roud 3 What is 00% of.05? Aswer as a commo fractio. Express the solutio to the system of equatios ( c, d ). c 3d = 5 c + d = 7 ) 5 as a ordered pair 009 z Evaluate: zi, give that i = z= ) (,) 3) i A triagle has side measures of, 6, ad 8. What is the area of the triagle i simplest radical form? ) 3 5

5 Roud What value(s) of b satisfy: 3b 5b = 0? 3 ) 3 ad could be i differet form What is the measure, i degrees, of a iterior agle i a regular -go? 3 I ABC, a =, b = 9, ad m C = 0, what is the value of c? ) 65 3) 33 What is the 6 th derivative of y = si(x) i simplest form? 3,07sixcosx ) 65,536si(x) or

6 Evaluate: ( + 3) ( + 3) Roud 5 ( ) ( + 3)( 3) ) 6 What is the legth, i meters, of the hypoteuse of a right triagle with legs measurig m ad 0 m? ) 9 What are the coordiates, i the form ( x, y), of the ceter of the graph of x + 9y 6x 6y =? How may of the followig series coverge? 3) (3, 3 ) a) = b) = ( ) c) = + d) = e) = 3 ) 3

7 Roud 6 Two umbers sum to 3 ad differ by 9. What is the larger umber? Evaluate ( ). Aswer as a commo fractio. = + ) 7 If si = d, evaluate si ( 3d ). Aswer as a commo fractio. ) 3) 6 If ( x 6x + 9) dx is approximated by iscribed rectagles of equal width o 0 the x-axis, what is the approximatio? ) 5

8 Roud 7 Express the umber of cubic millimeters i a cubic kilometer i scietific otatio. ) What is the area, i square meters, of a equilateral triagle with sides measurig 3 m? If w ( v ) = 3v ad u ( t ) = 7 t, evaluate w ( u ( w ( ) )). ) 3 3 3) -6 If P(A) =. ad the P(B) =.6, where A ad B are idepedet evets. Fid the P(A B) i reduced fractio form. ) 5

9 Roud 8 What is the equatio, i slope-itercept form, of the lie passig through the poits ( 3,5) ad ( 7, 3)? ) y=-x+ ± 3 The two roots of a quadratic equatio are, what is the quadratic equatio i reduced ax + bx + c = 0 form? (All coefficiets should be of smallest iteger value, where a is positive) ) 6x -6x-9=0 3π Express the polar coordiates (6, ) i Cartesia coordiates. d y If x y = 6, the dx at the poit (-, 6) is? 3) (0,-6) ) 36

10 Roud 9 Write the letters A-D i ascedig umerical order if A = 3 + 5, B = 8 07, C = 6 3, ad D = 96. ) B,D,A,C What is the largest perimeter, i meters, of a rectagle with a area of 3m whose side legths are itegers values i meters? ) 88 Fid the value(s) of x that satisfy: cos x si x = 0 i the iterval [0, π ]. Aswers must be i radias. If dy = 3x ad f(-) =, the f ( x) dx = dx 0 π 3), 3 π π 5,, π i ay order 6 6 ) 0

11 Roud 0 Whe a positive three-digit iteger has its digits reversed to form aother positive three-digit iteger, its value decreases by 95. What is the smallest possible value of the origial umber? Fid the value(s) of x that satisfy: log (x ) = 3 - log (x + ) ) 60 How may positive 3-digit umbers are palidromes? ) 3 00 Evaluate: (3 5) = 3) 90 ),650

UNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST. First Round For all Colorado Students Grades 7-12 November 3, 2007

UNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST First Roud For all Colorado Studets Grades 7- November, 7 The positive itegers are,,, 4, 5, 6, 7, 8, 9,,,,. The Pythagorea Theorem says that a + b =