Tackling the Calculator Multiple Choice Section (AB) The approach to attacking the calculator multiple choice problems on the AP exam can be very different than the non-calculator multiple choice. If thought out correctly, you can be efficient and let your calculator do a lot of the dirty work but you MUST HAVE A PLAN!!! (1) A particle moves along the x-axis so that its position at any time t > 0 is given by x( t) = t + t+ 6cos( πt). For what value of t is the velocity negative? (a) 1 t = (b) t = 1 (c) t = (d) t = (e) Velocity is never negative We are given a position function. In order to find when the velocity is negative, you would need to the of the position function and see where it lies the. () Which statement is true for the function f ( x) = ln(tan x) on the open interval 5π π < x <? 4 (a) f ( x) is increasing at an increasing rate. (b) f ( x ) is increasing at a decreasing rate. (c) f ( x) has an absolute maximum in the open interval. (d) f ( x) has a point of inflection in the open interval. (e) f ( x) has a point of symmetry in the open interval. In this question, it seems like the answers hold a clue to the approach. By looking at choices (a) and (b), we see that we would need to analyze the and to determine whether a function is increasing, decreasing, or doing so at an increasing or decreasing rate. In doing this, we would then be able to see if the other choices fit. () How many extrema (maximum and minimum) does the function on the open interval < x < 6? f( x) ( x ) ( x 5) = + have (a) None (b) One (c) Two (d) Three (e) Four We don t want to do anything by hand here so let s.
dv (4) The rate at which ice is melting in a pond is given by = 1+ t, where V is the volume of dt ice in cubic feet and t is the time in minutes. What amount of ice has melted in the first 5 minutes? (a) 14.49 (b) 14.51 (c) 14.5 (d) 14.55 (e) 14.57 The question gives us a. The phrase What amount of ice has melted indicates the need to find the. Using calculus, we must from to. (5) An object moves along the x-axis so that at time t > 0 its position is given by 4 xt () = t t t +. At the instant when the acceleration becomes zero, the velocity of the object is approximately (a) 1.04 (b) 4.15 (c) 0.178 (d) 1.46 (e) 1.985 This question asks us to find the velocity of an object. But when? First, we need to find the and the function. Once we do this, we can use the calculator to find when the is. Finally, we will plug this value into our equation. (6) If xy = 0, and x is decreasing at the rate of units per second, the rate at which y is changing when y = is nearest to (a) 0.6 (b) 0. (c) 0. (d) 0.6 (e) 1.0 It s best to rewrite this problem using calculus notation. x is decreasing at the rate of can be written as. The rate at which y is changing.. can be written as. Now, in order to find, we must the given function using the process of. Finally, we will substitute all of our known values. It should be noted that if they told me y =, I might want to find the of this function at this time. 4 (ln x) (7) Let F( x ) be an antiderivative of. If F () = 0, then F (8) = x (a) 5.16 (b) 0.860 (c) 0.184 (d) 0.180 (e) 0.004 In times where we are dealing with integration, and we have some information about a point on the function, it would help to look at a number line. This will always be helpful, especially since the process of and the geometric concept of are synonymous.
π π (8) If 0 k and the area under the curve y = sin xfrom x = k to x = is 0.75, then k = (a) 1.18 (b) 0.848 (c) 0.7 (d) 0.5 (e) 0.5 Let s treat this split in area as if we were splitting a line segment. For instance, If we knew that line segment AC was split into two adjacent segments at point B, then we could say AB + BC = AC. Likewise, we can do the same with the interval given, and the value k in that interval. Alright, time for the bird to fly from the nest attack these the same way THINK FIRST, THEN DO THE PROBLEM! 1 1 (9) The position of an object attached to a spring is given by yt () = sin(4) t cos(4) t 8 where t is time in seconds. How many times does the acceleration of the object change from negative to positive in the first 5 seconds? (a) Three (b) Four (c) Five (d) Six (e) Seven (10) A company manufactures x calculators weekly that can be sold for 75 0.01x dollars each. The cost of manufacturing x calculators is given by 1850 + 8x x + 0.001x. The number of calculators the company should manufacture weekly in order to maximize its weekly profit is (a) 611 (b) 65 (c) 68 (d) 749 (e) 754 (11) The number of inflection points for the graph of y x x 0 x 5is (a) 6 (b) 7 (c) 8 (d) 9 (e) 10 = + cos( ) in the interval
(1) Let R be the first quadrant region bounded by the graph of f ( x) 1 x = to = + x from 1 x = 4. Use the Trapezoid Rule with equal subdivisions to approximate the area of the region R. (a) 8.15 (b) 8.17 (c) 8.19 (d) 8.1 (e) 8. (1) Two particles move along the x-axis and their positions at time 0 t π are given by ( t ) x1 = cos( t) and x = e 0.75. For how many values of t do the two particles have the same velocity? (a) 0 (b) 1 (c) (d) (e) 4 (14) The sale of lumber S (in millions of square feet) for the years 1980 to 1990 is modeled by the function St ( ) = 0.46cos(0.45t+.15) +.4 where t is time in years with t = 0 corresponding to the beginning of 1980. Determine the year when lumber sales were increasing at the greatest rate. (a) 198 (b) 198 (c) 1984 (d) 1985 (e) 1986 (15) An approximation for nearest to sin(1.5x 1) e dx using three circumscribed rectangles of equal width is 1 (a) 4.5 (b) 4.7 (c) 4.9 (d) 5.1 (e) 5. (16) Let f ( x) = e x and gx ( ) = 5x. At what value of x does the graphs of f and g have parallel tangents? (a) 0.445 (b) 0.66 (c) 0.44 (d) 0.51 (e) 0.165 (17) Which of the following is an equation of the line tangent to the graph of at the point where f ( x) = 1? (a) y = x 1.01 (b) y = x 0.86 (c) y = x+ 0.86 (d) y = x+ 0.94 (e) y = x+ 1.01 f ( x) = x x 6 4
(18) Let f be the function given by f ( x) = 5e x. For what positive value of a is the slope of the line tangent to the graph of f at ( a, f( a)) equal to 6? (a) 0.14 (b) 0.44 (c) 0.9 (d) 0.595 (e) 0.714 (19) Two roads cross at right angles, one running north/south and the other east/west. Eighty feet south of the intersection is an old radio tower. A car traveling at 50 feet per second passes through the intersection heading east. At how many feet per second is the car moving away from the radio tower seconds after it passes through the intersection? (a) 4.65 (b) 44.1 (c) 44.59 (d) 56.67 (e) 81.76 (0) If y = x+ 6, what is the minimum value of x y? (a) 10.15 (b) 5.065 (c) 1.5 (d) 0 (e) 1.5