Algebra II / Integrated Math III 2012

Transcription

1 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 Do not open this test booklet until you have been advised by the test proctor. Net year s math contest date: April 7, 0

2 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: E) 5. Write the following without radicals in the denominator: What is the reciprocal of 5? E) 0 6 Indiana State University Page of 7 4/8/0

3 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 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

4 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) 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 Let ( ) ( ) ( ) for positive a, b, and c. What is the value of? 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

5 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 Find the sum of the infinite geometric series 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

6 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 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)? 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

7 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