Download Math 2303 Summer 2008 Test 4 Version A and more Exams Algebra in PDF only on Docsity! Math 2303 Summer 2008 Test 4 Version A 1. (10 points) Given the line 2 4 12− =x y , answer the following: a. What is the x-intercept? 6 b. What is the y-intercept? -3 c. What is the slope of the line? 1/2 d. Graph the line, be sure to label the scale for your axes and plot the intercepts. 2. (10 points) Given the graph: a. What is the x-intercept? 3 b. What is the y-intercept? -2 c. What is the slope of the line? 2/3 d. Give the equation of the line in slope-intercept form. 2 2 3 = −y x 3. (10 points) Kevin recorded the following data on his recent trip from Houston to El Paso. He noticed that this data could be represented by a linear equation, where x represents the time since he left in hours, and y represents the distance traveled in miles. Time (hours) Distance (miles) 3 180 5 300 9 540 13 780 a. The slope of the line connecting these data points is the average speed at which Kevin traveled. What are the appropriate units for his speed? i. Feet per second ii. Miles per minute iii. Miles per hour CORRECT since the same units as the points plotted. iv. Feet per hour b. Find the slope of the line. Slope = 60 c. Find the equation of the line and put it into slope intercept form. 60=y x d. The y-intercept represents: i. The distance at time 0 CORRECT since the time 0 is x = 0 and y is distance ii. The time at distance equal to 0 iii. The average speed at time equal to 0. 4. (20 points) Consider the system consisting of the set of integers with the operations of addition and multiplication, ( , , )+ × . Answer the following questions: a. Is addition closed on this set? yes b. Is addition associative? yes c. Does a identity element for addition exist in this set? If so, what is it? Yes, it’s 0. d. Does every integer have an additive inverse? What is the inverse of –3? Yes, the inverse of -3 is 3. e. Is the system consisting of integers under addition a group? yes f. Is addition commutative? yes g. Is the multiplication closed on the set of integers? yes h. Is multiplication associative? yes i. Does multiplication distribute over addition? yes j. Is the system ( , , )+ × a ring? yes 5. (20 points) Consider the finite mathematical system defined by the following operation table: ^ P Q T P P T Q Q T P Q T Q T P a. What the operation symbol? It is ^. b. What are the elements in the set? P, Q, T c. Is the operation closed? yes d. Is (P^P)^Q=P^(P^Q)? no e. Is the operation associative? no f. Is the operation commutative? no g. Is there an identity element in this set? If so, what is it? no h. If there is an identity, does every element have an inverse? If there is not an identity, state no inverses. No inverses i. Is this system a group? no j. Is this system a commutative group? no
