Name: Date: Block: Multiple Choice Non-Calculator Quarter Summative Assessment Revision #1 1. The graph of y = x x has a relative maximum at (a) (0,0) only (b) (1,) only (c) (,4) only (d) (4, 16) only (e) (0,0) and (,4). What are all values of x for which the graph of y = (a) There are no values of x. (b) x < 4 (c) x > 4 (d) x < 4 (e) x > 4. If the graph of (a) (b) 1 (c) 0 (d) 1 (e) f ( x) k x 4 x has a point of inflection at 1 4. Piecewise functions f and g are shown to the right. If h(x) = f( x) gx, ( ) then h 8 (a) 1 (b) (c) 0 x is concave downward? x, then the value of k is (d) (e) 8 1 t 5. A particle moves along the x-axis in such a way that its position at time (t) is given by xt (). 1 t What is the acceleration of the particle at time t = 0? (a) 4 (b) (c) (d) (e) 4 5
1 6. The average rate of change of the function f ( x) cos x on the closed interval [ 4, 0] is 6 (a) 1 sin() (b) 1 4 sin() (c) 1 cos() 4 7. If 0 1 cos() (d) 4 (e) 1 sin() 4 x x dx is approximated by three inscribed rectangles of equal width on the x-axis, then the approximation is (a) 4 (b) 6 (c) 8 (d) 48 (e) 76 1 8. Let f() t for 0 t closed interval [a, b]? (a) t. For what value of t is f t ab (d) 1 ab (b) ab (e) 1 1 1 b a (c) 1 ab equal to the average rate of change of f on the 9. Let f be a function that is everywhere differentiable. The value of f x in the table below. x 10 5 0 5 10 x f 1 0 1 If f (x) is always increasing, which statement about f (x) must be true? (a) f (x) has a relative min at x = 0. (b) f (x) is concave down for all x. (c) f (x) has a point of inflection at (0, f (0)) (d) f (x) passes through the origin (e) f (x) is an odd function is given for several values of x
10. The figure above shows the graph of the derivative of a function f. How many points of inflection does f have in the interval shown? (a) None (b) One (c) Two (d) Three (e) Four 11. The graph of the derivative of a twice differentiable function is shown below. If f (1) =, which of the following must be true? (a) f () < f () < f () (b) f () < f () < f () (c) f () < f () < f () (d) f () < f () < f () (e) f () < f () < f () 1. Which graph best represents the position of a particle, s(t), as a function of time, if the particle s velocity and acceleration are both positive?
Free Response Non-Calculator 1.. The diameter and height of a paper cup in the shape of a cone are both 4 inches and water is leaking out at 1 the rate of ½ cubic inches per second. The volume V of a cone with radius r and height h is V r h. a) Write an equation for dv with respect to time. b) How fast is the water level dropping when the diameter of the surface is inches?. Let f be the function given by 4 7 f ( x) x x 5. 4 a) Find the equation of the line tangent to the graph at (, 7). b) Find the relative maxima and relative minima. Justify your answer. c) Find the coordinates of the points of inflection. Justify your answer. Multiple Choice Calculator Active 1. The amount At of a certain item produced in a factory is given by A(t) = 4000 + 48(t ) 4(t ) where t is the number of hours of production since the beginning of the workday at 8:00 a.m. At what time is the rate of the production increasing most rapidly? (a) 8:00 am (b) 10:00 am (c) 11:00 am (d) 1:00 noon (e) 1:00 pm
14. The function f x tan x has a zero in the interval [0, 1.4]. The derivative at this point is (a) 0.411 (b) 1.04 (c).451 (d).76 (e) undefined 15. A spherical balloon is inflated at the rate of 1 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is feet? (a) 1.047 ft/min (b) 0.106 ft/min (c) 0.18 ft/min (d).14 ft/min (e) 0.00 ft/min Free Response Calculator Active 4. An open top box is to be constructed with a volume of 40 inches cubed. The length of the base is four times the width of the base and if it costs two times as much to manufacture the sides as it is to manufacture the base. a) Write an equation that represents the surface area in terms of one variable x. b) Write an equation that represents the cost to manufacture the box. c) Find the dimensions that would minimize the cost to produce the box. 5.
Name: Date: Block: Quarter Summative Assessment Revision # Free Response Non-Calculator 1. Find all values of x at which all extrema and any points of inflection occur on the function f x 8x x. Justify each response. 4. Free Response Calculator Active. A right circular cylinder is to be designed to hold cubic inches of a soft drink. The cost for the material for the top and bottom if the can is twice the cost for the material of the sides. Let r represent the radius and h represent the height of the cylinder. (The surface area of a cylinder is SA r rh and the volume of a cylinder is V r h ) a) Write the equation for the surface area in terms of one variable, r. Simplify your answer. b) Write the cost function, C. Simplify your answer. c) Find the radius that minimizes the cost. 4. Two boats leave the same port at the same time with one boat traveling north at 5 knots per hour and the other boat traveling east at 40 knots per hour. How fast is the distance between the two boats changing after hours?