Algebra I / Integrated Math I 2012

Transcription

1 Algebra I / Integrated Math I 0 Sponsored by the Indiana Council of Teachers of Mathematics Indiana State Mathematics Contest This test was prepared by faculty at University of Southern Indiana 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 I/Integrated Math I ICTM. The point 4, 8 is on the graph of which of the following equations? y 8 y= 4 y Both a and c e. Both b and c. Which is the equation of a line with the same y-intercept but half the slope of the line y0 6? y5 6 y0 y 0 y 6 5 e. y 0. Solve the inequality: z z + < 0 8,4 4,, 4 4, 4. Solve the compound absolute value inequality: w 7 or w 0 4, 0 4, 5 5, 0 5, 0 5. Larry, Curly, and Moe love jelly beans. Larry opens a new jar and eats one-third of them. Later, Moe eats three-fifths of the original number of beans. There are then twenty-five left for Curly. What fraction of the original amount does Curly get? Which of the following does NOT define a function? 5 y 5 (,),(0,),(, ) y ( 5,),(,0),(, 5),(,7) e. y 7. Solve the equation: University of Southern Indiana Page of 8 4/8/0

3 0 State Mathematics Contest Algebra I/Integrated Math I ICTM 8. Solve the equation: Both a and b e. 9. A gardener wishes to line the 96 cm front of a rock garden with miniature bricks. He has si cm bricks and five 6 cm bricks available. Assuming he uses some of each size of brick, lines the entire front of the garden eactly, and does not cut any of the bricks, how many 6 cm bricks will he use? 4 e Joe has a cell phone plan where he pays $ per month plus $0.0 per minute of talk time. Let represent the number of minutes of talk time and y represent the cost of his cell phone bill. What equation represents his cell phone bill at the end of each month? y 0. 0.y y 0. y0 e. y0.. What is the equation of a vertical line passing through the point 4,? y y 4 4 e. y. Find the range of f ( ) if the domain is,,0,,.,, 9, 5,,, 5,,,,,,5 e. 9.,,. Simplify the epression: 9y y e y 4. Write the equation of the line in standard form that passes through the points 5, and,. 4y 8y 7 8y 7 5 y 5 e. 8y 7 University of Southern Indiana Page of 8 4/8/0

4 0 State Mathematics Contest Algebra I/Integrated Math I ICTM 5. Determine the domain of the function: f( ) 4 0 5,,, 5,, 5,,, e Solve the equation: ,4,8 e. 7. Solve the equation: e. 8. Which of the following numbers is greater than 4 and less than 5? Find a non-zero value for k such that k k 0 has one unique real solution. 4 e For three consecutive positive integers, the product of the first and second integer is five times the sum of the first and third integers. What is the sum of the three consecutive integers? University of Southern Indiana Page 4 of 8 4/8/0

5 0 State Mathematics Contest Algebra I/Integrated Math I ICTM. Which two ordered pairs are part of the solution set of the system of inequalities? 57 y 4 6, 6,,,. Dan D. Lyon is growing like a wee Last year he grew inches. At what rate in cm per month did he grow last year? ( inch =.54 centimeters) e. 4.7,,6 0,, e., 4 6, 0. Which system of equations below has no solution? y 5 y5 y5 y5 y6 5 y0 y 5 6 y0 e. y Which of the following statements is NOT true? All negative integers are irrational numbers. All negative rational numbers are real numbers. All even integers are rational numbers. All positive integers are rational numbers. e. All irrational numbers are real numbers. y 7 5. In the solution to the system, 5 the sum of and y is what? y University of Southern Indiana Page 5 of 8 4/8/0

6 0 State Mathematics Contest Algebra I/Integrated Math I ICTM 6. Simplify the epression: e A Boeing 747 flies the 000-mile distance from Los Angeles to New York City with the wind in 5 hours. The return trip, against wind of the same speed, takes 6 hours to complete. Assuming the wind speed doesn t change find the correct wind speed from the choices below e For the equation 8, which of the following is/are true? I. The sum of the solutions is negative II. The product of the solutions is negative III. Eactly one of the solutions is a fraction I only II only III only I and II only e. II and III only 9. Find all values of k that will result in the equation k 0 having no real number solution. 9 k k 8 9 k > k < e. 8 It is not possible to find all values for k 0. The epression is equivalent to which of the following? 4 4 (4 4 5) (4 5 4) 4 ( 4 5) ( 5 4) 4 4 (4 8 4 ) ( ) Both a and b. A ball is thrown from a height of 8 feet. The height of the ball t seconds after it has been thrown is given by the function s( t) 6t 96t 8. After how many seconds will the ball hit the ground? e. 4 University of Southern Indiana Page 6 of 8 4/8/0

7 0 State Mathematics Contest Algebra I/Integrated Math I ICTM. For which of the following equations does the graph have -intercepts at 5,0 and,0? y y 6 5 y 6 0 y 6 5 e. All of the these 4 7. Factor 44 y z z completely. z( y z )( y z ) 7 ( yz )( y z ) 4 (44 yz z )( y z ) z( y z )( y z ) e. 7 z y y ( )( ) 4. A seed farm has two separated square test plots. The side length of the larger plot is times the side length of the smaller plot. If the total area contained in both plots is 50 ft, how many feet of fencing is needed to enclose both plots? (If necessary, round answer to the nearest foot.) 40 feet 87 feet 84 feet 56 feet e. 75 feet For the remainder of the test, assume all denominators to be non-zero. C 5. Solve the formula for C: A = 0 C + B A + B AB AB A B 6. Divide : e University of Southern Indiana Page 7 of 8 4/8/0

8 0 State Mathematics Contest Algebra I/Integrated Math I ICTM 7. Simplify the epression: a 5b a 5b a 50b 50b a( a 5 b)( a 5 b) 50b a( a 5 b)( a 5 b) 4a 50b a( a 5 b)( a 5 b) 8. Multiply and divide, writing the answer in simplest terms ( ) 9. Simplify the epression: 9 4 y z 96 y z 9 5 y 4 4 y y e The epression 9 64 y z is equivalent to what? y z ( y z ) y z 7 9 y z 4 7 (4 y z ) Both a and c e. All of the these University of Southern Indiana Page 8 of 8 4/8/0