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- 56+1 = - 55 AP Pre-Calculus Unit 2 Exam: Part I: Calculator inactive 45%% Name: Rehan Choudhary period y 11-1-2027 Directions: Show all work, clearly indicating what the answer is. When you complete this section, turn it in and receive part 2. All questions are worth 2 points unless otherwise specified. 1. Consider the linear function graphed below. O, S 910 a/What is the equation of the line (4pts)? Y z x - 4 b. Is the function increasing or decreasing? The function is decreasing Are the rates of change increasing, decreasing, or neither? Elks of Change "decreasing d. What are the domain and range? Domain : 00 / -00 Range : 8 3 ? ( - 8 , 0 ) "What is the equation of the line perpendicular to this one at the point (4, 0)? - 2 fox ) = 4 - 4 2. What is the slope of the line passing through the points: (a + 2, 5), (6, b-3)? (4 pts) slope = m( x ) + 5 0 1 7 3 The Slope of a line passing through those points areFind no poi 4. 3. Consider the quadratic function below xly O -1/2 21 1 1 - 1 -5 - 4 - 3 - 123 4 5 - * -2/-1 a. What is the equation of the quadratic function (in vertex form or in general form)? (6 pts) 41 - 4 2 4-41 Y - 1 = x-1 YzX2 b. What is the domain? Domain : -00, 60 What is the range? Range 1 37 - 2 7 -2 - 314 Does the function have an absolute maximum or minimum value and, if so, what is it? Absolute maximumn is - 1/2 e. Does the function have real solutions and, if so, what are they approximately? real f. Over what interval is the function increasing? (- 1/2 ) g. Over what interval is the function decreasing? ( - 21 - 1 ) h. Are the rates of change increasing or decreasing or neither? The rates of change are the decreasing . If net "neither," over what interval are the rates of change either increasing or decreasing? -2 Interval of 22- 24+27 3 - 24=-1 4. Find the point of intersection of the pair of lines by solving the system of linear equations. If there is 2- 24 21 no point of intersection, indicate no solution. (6 pts)' 01-1/7 x - 2y+2-3 -> 0-14+2-3.1/2 1/ /2 -My =1 2/ x-y=30 0-423 1/ 2 / 4 =- 3 X point of intersection is 21 - 1 5. Consider the following table of values x 2 5 8 11 14 17 20 y -3 3 9 15 21 27 33 a. What type of function is this and how do you know? (4 pts) This is a linear since the y value goes up by 6 For every single point making a straight line. b. What is the average rate of change over the interval (5, 17)? Average rate of Change, 15 6 over the interval (5 / 17 ) C. Are the rates of change increasing, decreasing, or staying the same? The rates or change are staying the Same. d. What is the equation of the function? (4 pts) equation of the function 3 Fex ) I-8 +6 +6. Consider the following table of values x -2 - 1 01 2 3 4 y 21 11 5 3 5 11 21 Vuvuy -10- 6-9 1 -4 7014 +4 e. What type of function is this and how do you know? (4 pts) This is a quadratic function, I know this becam of the way the slaph looks. I also know this since ope can see that the "value fluctuates by 4 7 and +4, f. What is the average rate of change over the interval (-1, 2)? The average rate of change over that interval is b E. Are the rates of change increasing, decreasing, or staying the same? The rate of Change They ape staying the san is increasing . Extra Credit: What is the equation of the function? (3 pts) equation of the function is X difference between x f ( x ) = 4 - 4 values is + 1 difference between y values are Unique but those numbers are all - 4 / +4AP Pre-Calculus Name: Rehan Chaud har Unit 2 Exam: Part 2: Calculator Active Directions: Show all work, clearly indicating what the answer is. If you need additional paper, just ask. When you complete this section, turn it in and work / relax silently at your seat. 1. Dr. Laske has a lot of Unit exams to grade. After 3 hours, Dr. Laske has 37 exams left to grade and after 5 hours she has 19 exams to grade. tests pra. Write a linear equation for the situation, indicating what the variables represent. (4 pts) x = hours + = x (9) 3 hours 3 7 5 hours 19 hours in will give you the amount of tests She can 37- 19 = 18 grave in x hours 2 hours = 18 b. What does the slope mean in the context of the problem? The slope would most likely be half of the 1 hour =a tests She Started off with samount of c. What does the y-intercept mean in the context of the problem? y intercept would probably be the amount of tests she started off with d. How long will it take Dr. Laske to finish grading the exams? (Round to the nearest 10th) It will take Pf, Laske approximately 64 7 hours and 10 minutes to finish Dinoing the exams. 2. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground x seconds after it is thrown is given by following quadratic function. How long after the rock is thrown will it hit the ground approximately (round to nearest 100th)? (6 pts) 6 + 0 3 2 - 4ac f(x) = -16x2 - 4x + 382 26 4 + 016 + 24498 It will take approximately ut U 156. 41 15 6,41 seconds before it hits the ground.12- 24-36 + 34 Extra Cr 6 - 20-30 (2 pts) 3. The sum of three consecutive even numbers is 34 more than the smallest of them. What are the 3 10- 16 numbers? (6 pts) consequl sy 0 26 32 Three numberscal (6/14 - X1 1 6- 20- 24 the three numbers 60 6 + 8 + 20 are 12 1 16 / 18 0 34 2 4. A parabolic shaped bowl is 15 feet deep and has a 60 feet diameter at its edge. Determine the 68 parabola's a value. (6 pts) 15+60 = ( 4 ) 34 + 17 34 5 9 = 900 feet 5. Tickets to a school dance cost $4 and the projected attendance is 300 people. For every $0.10 increase in ticket price, the dance committee projects that attendance will decrease by 5. (8 pts) a) Determine the dance committee's greatest possible revenue. b) What ticket price will produce the greatest revenue? 4 . 300 712 00 4.10 ,295 25 1209. 5 dainit of deal 4.2 - $ 1218 The greatest possible revenue 61 2 25 . 5 will be $ 12 50, 5 , 250 = $12 So The ticket price that will produce the greatest revenue is $5,Extra Credit: Consider the following table of values. What type of function is it and how do you know? (2 pts) X -2 -1 1 2 3 4 V 2 4 16 1/4 1/21 1/2 1 2 This function is exponential since none of the y values are related not quite