University of Houston High School Contest Spring 2008 Algebra I Test

Transcription

1 University of Houston High School Contest Spring 008 Algebra I Test Directions: You have 50 minutes to complete this eam. Calculators are not permitted. Choose the correct answer for each question by clearly and boldly circling the answer choice. There is no penalty for guessing. In the case of a tie, students work will be used to determine the winner so show all work clearly on either your eam or on scrap paper. Write your name and school on top of each page in the blanks provided.. Give one factor of the polynomial. The variables used as eponents represent positive integers. 3m n m n 3n m 4 u v + 4u v + 48v u m n a. (u 3v ) b. This polynomial cannot be factored. 3 n c. u m 3 v 3 n d. u m 3 4 v m n e. ( u 3v ). Perform the indicated operation. Simplify completely. The variable in the eponents represents positive integers. k k k k k a. k k ( + 3) b. k + 9 k ( 3) c. k k 6 d. e. k

2 3. Replace k in the following trinomial by a number that makes the trinomial a perfect square trinomial. ks 4s + 9 a. 4 b. 3 c. 6 d. 9 e. 4. Simplify a. b c. 4 + d. e Give a real solution to the equation = 0 given that a. 3 b. 0 c. No other real solutions eist. d. e. 3 is a root.

3 6. One day you went canoeing. You learned that the current in the river was miles per hour. If it took you the same amount of time to travel 0 miles downstream as miles upstream, determine the speed at which your canoe would travel in still water. a. 3 miles per hour b. 0.5 mile per hour c. 5 miles per hour d. mile per hour e. miles per hour 7. Given c = 0, find all values of c that will result in the equation having no real number solution. a. It is not possible to find all values of c. 9 b. c < 8 c. c 9 d. c > 8 e. c < 8. Simplify y y a. y b. 3 5 y c. 5 y 5 3 y d. 3 5 y 3 5 e. y 6 3

4 9. A storeowner wants to set up a rectangular display area outside his store. He will use one side of the building (which is 5 feet long) as part of one side of the display area. He has 30 linear feet of fencing material to use to fence in the display area. Write a function which epresses the total area of the display area in terms of the length of the side of the display area opposite the building. 55 a. A ( ) = + 55 b. A( ) = 53 c. A ( ) = 53 d. A( ) = e. A ( ) = Solve for = 8 a. = -7, = b. = -7, = -3 c. = -7, = -3, = d. = -3, = e. =. Give a factor of 4 0, 000 over real numbers. a. This polynomial cannot be factored over real numbers. b. + 0 c d. 0 e

5 . Simplify. a. + b. + c. 4 d. + e. 3. Larry, a chemistry student, needs 0% acetic acid solution for a chemistry eperiment. He realizes he only has 5% and 0% acetic acid solutions available. He decides to make the 0% solution by combining the 5% and 0% solutions. How many liters of the 5% solution must he add to 8 liters of the 0% solution to get a solution that is 0% acetic acid? a. 6.5 liters b. 3 liters c. 6 liters d. 8.5 liters e. 4 liters 4. For eercise, Carrie and Amanda run from their home to a nearby park. Carrie runs 3 ½ miles per hour. Amanda runs 7 ¼ miles per hour. When Amanda arrives at the park, Carrie is 5 5 miles away. How far is the park from their house? 8 a..785 miles b miles c. 9.5 miles d..5 miles e..65 miles 5

6 5. A ball is dropped from a height of 8 feet. Its height s, in feet, at time t, in seconds, is given by s ( t) = 6t + 96t + 8. When will the ball hit the ground? a. after seconds b. after seconds c. after seconds d. after seconds e. after 4 seconds 6

7 (6) Solve the following system for and y: 7 + y = y = 3 (a) Infinitely many solutions (b) {( 5 7, 5 3 )} (c) {( 5 3, 5 7 )} (d) No solutions (e) {(, )} (7) Jim can t remember the last digit of his best friend s phone number. He plans to just dial the number and guess the last digit. What s the probability that he ll dial the correct number in the first tries? (a) 0 (b) 45 (c) 7 0 (d) 5 (e) 5 (8) Jeanini bought a ring in 990 for $00. By 995 it had lost 3% of its value. In 000 it was worth 33% more than in 995. By 005 it had lost 0% of its value from 5 years earlier. What was the ring worth in 005 (in nearest whole dollars)? (a) $3 (b) $9 (c) $7 (d) $3 (e) $

8 (9) Find the real number solutions: = 3. (a) 5 (b) 8 (c) 5,8 (d) No real number solutions. (e) 4,5,8 (0) Find the remainder of 8 + divided by. (a) (b) - (c) (d) - (e) 0 () Find the largest number that always divides the difference of the squares of two consecutive even numbers. (a) (b) (c) 3 (d) 4 (e) None of the above. () Jim buys piie sticks at 4 for 0 cents. He sells them at 4 for 5 cents. How many does he have to sell in order to make a profit of $.00? (a) 80 (b) 40 (c) 8 (d) 5 (e) 5

9 (3) Instead of walking along the adjacent sides of a rectangular field, Joe took a shortcut along the diagonal and saved a distance equal to half the length of the longer side. Find the ratio of the longer side to the shorter side of the field. (a) 5:3 (b) 3: (c) :3 (d) 5: (e) 4:3 (4) Write 5.5 in base. (a) 0.0 (b) 0.0 (c) (d) 0.00 (e) 00.0 (5) There are 500 red and blue balls in a jar. % of the balls are blue. Some red balls, but no blue balls, are withdrawn. Then % of the balls are blue. How many balls are still in the jar? (a) 490 (b) 495 (c) 485 (d) 50 (e) 45