Algebra II / Integrated Math III 0 Sponsored by the Indiana Council of Teachers of Mathematics Indiana State Mathematics Contest This test was prepared by faculty at Indiana State University ICTM Website http://www.indianamath.org/ Do not open this test booklet until you have been advised by the test proctor. Net year s math contest date: April 7, 0
0 State Mathematics Contest Algebra II/Integrated Math III ICTM. Solve for : 0 or or. Find P( i) given that P( ). E). ( y z) y z y z yz y z y z yz y z y z yz y z 4. Evaluate: 8 6 8. 8 E) 5. Write the following without radicals in the denominator: 7 7 7 7 7 7 7 7 9 6. What is the reciprocal of 5? 5 0 5 0 6 5 0 5 E) 0 6 Indiana State University Page of 7 4/8/0
0 State Mathematics Contest Algebra II/Integrated Math III ICTM 7. Find a quadratic function f ( ) a b c having minimum value -9 and zeros and 5. The coefficients a, b, c are relatively prime integers. Find the sum a b c. 7-9 7 8. Which inequality is false for every real number? r 4r 5 (z)( z ) 6 t 9t 0 s E) 9u 49 4u 9. Solve t t 7 8. E) 0. Which epression below is equivalent to log8 4? 5 4 ln e 4 log log 0.0 E) log5 5 log55 5. An ellipse with equation y has which point as a focus? 6 6 (0, ) (0, 5) ( 5,0) (,0) E) (0,6). How many real number solutions are there to the equation 4? 4 5 E) 6 Indiana State University Page of 7 4/8/0
0 State Mathematics Contest Algebra II/Integrated Math III ICTM. The domain of the function f( ) 5 is and and 4. If f 4 if possible. ( ), find f (7) 0.5 7 4 0 E) does not eist 5. Solve for u in terms of v if u v u 5. v u v 5 u v v 5 v 5 u v 5v u E) v 5v u v 6. If 40 mg of a radioactive substance decays to 5 mg in minutes, find the half-life, in minutes, of the substance. 4 6 E) 8 7. Solve 5 e 7. ln 7 5 ln 7 5 ln7 5 ln 7 5 8. Let ( ) ( ) ( ) for positive a, b, and c. What is the value of? 49 7 6807 9. To measure the speed of the jet stream, a weather plane left its base at noon and flew 800 km directly against the stream with an airplane speed of 750 km/h. It then returned directly to its base, arriving at :4 p.m. What was the speed of the jet stream? 00 km/h 50 km/h 00 km/h 50 km/h E) 00 km/h Indiana State University Page 4 of 7 4/8/0
0 State Mathematics Contest Algebra II/Integrated Math III ICTM 0. If log z log log y, write z in terms of and y. b b b y y ( ) ( ) y y. Suppose z varies directly as and inversely as the square of y. If when and, find z when and. 6. What is the sum of all the coefficients of the terms of the epansion of 9 4y - 44-78. Find the sum of the infinite geometric series 64 48 6 7 if it has one. no sum 4. Find the roots of y y 0 i i i i 5. Find the number of real solutions of this system: y 6 5 y 0 0 E) 4 6. At :00 p.m. Sue left her home and began walking at 6 km/h toward Sandy s house. Fifteen minutes later, Sandy left her home and walked at 8 km/h toward Sue s house. If they live 5 km apart, at what time did they meet? :0 p.m. :5 p.m. :40 p.m. :45 p.m. Indiana State University Page 5 of 7 4/8/0
0 State Mathematics Contest Algebra II/Integrated Math III ICTM h 7. Solve A ( b b ) for b. A b h A b h hb A b A h E) A hb 8. Three of the vertices of square ABCD have coordinates A(, ), B(,4) and C (4,). The product of the - and y-coordinate of the fourth verte is -6-4 4 6 9. Suppose f ( ) e and f ( g( )) g( f ( )) for appropriate values of. Then g ( ) ln ln( ) ln( ) ln( ) 0. What is the distance from (,) to the midpoint of the segment from (,4) to (5,6)? 4 5 4. Suppose that 0t s. For what value(s) of t is s > t? t 6 t 4 t 6 0t 4 t 4 E) 0 t 4 or t 6. If and y are real numbers with y, which of the following must be true? I. y y II. y 0 III. y I only I and II III only I and III E) I, II, and III Indiana State University Page 6 of 7 4/8/0
0 State Mathematics Contest Algebra II/Integrated Math III ICTM. If f ( ), then f ( f ( )) ( ) E) 4. The graph of ( a) 4( y a) intersects the -ais at = r and = s. Find s + r. 8a 8a a a E) 8a 5. Solve for : 0 0. ln ln 4 ln ln 0 ln 0 ln ln 4 ln 6. Cassandra set her watch to the correct time at p.m. At the actual time of 4:00 p.m., she noticed that her watch read :57:6 p.m. Assuming that her watch loses time at a constant rate, what will be the actual time when her watch first reads a.m.? ::4 a.m. :4 a.m. :5 a.m. :7 a.m. E) :0 a.m. Indiana State University Page 7 of 7 4/8/0