AP Calculus AB PRACTICE MIDTERM EXAM Read each choice carefully and find the best answer. Your midterm exam will be made up of 8 of these questions. I reserve the right to change numbers and answers on the actual exam. NO CALCULATOR 1. Find the interval or intervals on which the function whose graph is shown is increasing:. Does the graph of f( x) 6x x x x have a horizontal asymptote? If so what is it? yes, y= b. yes, y=- c. yes, y= d. yes, y= e. no. The position of a particle moving along a coordinate line is s 6t, with s in meters in t in seconds. Find the particle s velocity at t=1sec. 1/6 m/s b. -1/ m/s c. m/s d. 1 m/s e. -1/6 m/s. The graph of the original function is shown. Which of the following could be the graph of the original function? x x 5. lim x x 6x 9 - b. -1 c. 1 d. e. DNE 6. The table below gives the values of three functions f, g, and h, near x=0. Based on the values given, for which of the functions does it appear that the limit as x approaches zero is? x -0. -0. -0.1 0 0.1 0. 0. f(x).018.008.00.00.008.018 g(x) 1 1 1 h(x) 1.971 1.987 1.997 Undefined 1.997 1.987 1.971 f only b. g only c. h only d. f & h only e. f,g, & h
7. The graph of a function f whose domain is the closed interval [1,7] is shown below. Which of the following statements about f(x) is TRUE lim f( x) 1 b. x lim f( x) c. f(x) is continuous at x= x d. f(x) is continuous at x=5 e. lim f ( x) f (6) x 6 x 9 8. lim x x 7 -/9 b. /9 c. 0 d. e. DNE x 9. lim x x b. -1 c. 0 d. 1 e. 10. lim x b b x x b b b. b c. b d. b e. b 11. ( x) lim x ( x ) 0 b. - c. 1 d. -1 e. DNE x x 6 1. lim x 7 x 7 DNE b. 16 c. d. 0 e. 1. Find the equation of the line tangent to the graph of y x b. y x c. x y 1, at the point (,). y x d. y x e. none of these 1. The graph of y f ( x) is shown below. At what values of x does f(x) appear to be nondifferentiable? x=1, x= b. x=-1, x=1, x= c. x=-1, x=1 d. x=-1, x=1, x=- e. none of these
15. Find the value or values of c that satisfy the mean value theorem for the function interval [,16]. 0, b.,16 c. d., e. none of these x 1 16. Find the relative/local extrema for hx ( ). x 5x 10 rel min at x=-, rel max at x=5 b. rel min at x=-, rel max at x=5 c. rel min at x=-, no rel max d. no rel extrema f ( x) 8 x, on the x 17. On the interval (1,), the curve y x 6x 9x 1 is, increasing and CCU b. increasing and CCD c. decreasing and CCU d. decreasing and CCD e. horizontal 18. Find the intervals where the graph of the function is concave up if y x x 9x (1, ) b. (,1)(1, ) c. (,1) d. (, ) e. none 19. A sphere is increasing in volume at the rate of cm / s. At what rate is its radius changing when the radius is ½ cm? ( V r ) cm / s b. cm/s c. cm/s d. 1cm/s e. ½ cm/s 6x 5, x 0. Find a value of a so that the function f( x) ax, x is continuous. 6/ b. a=16 c. a=19/16 d. a=19/ e. 16/19 x x 1. lim x x 6x 1 b. c. d. 0 e.. Let lim f( x) 1 and x 10 lim gx ( ) 5. Find lim[ f ( x) ( )] x 10 x 10 g x. 6 b. 6 c. 6 d. - e. 1 X f(x) g(x) f (x) g (x) - 6-5 1 0-9 5-5. Using the table above find h '(5), if h( x) f ( x) g( x) b. 7 c. 1 d. 0 e. 6
. Using values from the table above find h '(), if h( x) f ( g( x)) -5 b. -7 c. -15 d. 0 e. 5 6 x 5. Find the derivative of f( x), for x=. 1 x -7 b. 1 c. 7 d. 10 e. 7 1 7 6. Find dy dx by implicit differentiation for 5 5 cos( xy) x y 5x y sin xy 5x y sin xy b. c. none of these d. 5y xsin xy 5y 5 sin 5 sin x y xy y x xy e. 5 sin x x xy 5y 7. Find the horizontal tangents of the curve y x x 1 x=1,-1 b. x=0, 1 c. x=0, 1, -1 d. x=0 e. x=0,-1 8. Find dy dx if y (1 5 x )(9x 180) 180x 1818 b. 180x 1818x c. 5x 909 x d. 180x 1818x e. 5x 909 9. Find dy dx if 7x 8 y 8x (8x ) 56x 107x 5 b. (8x ) 56x 18x 1 56x 11x 19x c. d. (8x ) 168x 18x 1 (8x ) e. none of these 0. For the function f ( x) x, at the point (,8), find: i) the slope of the curve ii) the equation of the tangent line iii) the equation of the normal line. m y x 8 y x 8 b. m y x 8 c. 1 1 y x 8 6 1 m 1 1 y x 8 6 y x 8 d. 1 m 1 1 y x 8 y x 8 e. none of these 1. Use a right-hand Riemann sum with equal subdivisions to approximate the integral x dx 1 1 b. 10 c. 8.5 d. 8 e. 6.. An equation of the line tangent to the graph of y = x + x + at its point of inflection is y = x + 1 b. y = x 7 c. y = x + 5 d. y = x + 1 e. y = x + 7
. cos( x)dx = sin( x) + C b. sin( x) + C c. 1 sin( x) + C d. 1 sin( x) + C e. 1 sin( x) + C 5. What is lim x ( 9x + x+ )? b. c. d. 1 e. The limit does not exist. 5. Suppose F(x) = x 0 1 +t dt for all real x. Then, F (-1) = b. 1 c. 1 d. - e. 6. What is the average value of x x + over the interval 1 x 1? 0 b. 7 c. d. e. 6 7. lim x 1 ( x 1 x 1 )? 0 b. 1 8. If y = cos x sin x, then y = c. 1 d. e. The limit does not exist. -1 b. 0 c. (cos x + sin x) d. (cos x + sin x) e. (cos x)(sin x) 9. 0 and 5 b. 5 and 10 c. 10 and 15 d. 15 and 0 e. 0 and 5 0. The acceleration at time t > 0 of a particle moving along the x-axis is a(t) = t + ft/sec. If at t = 1 seconds the velocity is ft/sec and the position is x = 6 feet, then at t = seconds, the position x(t) is 8 ft. b. 11 ft. c. 1 ft. d. 1 ft. e. 15 ft.
1. A leaf falls from a tree into a swirling wind. The graph below shows the vertical distance in feet above the ground plotted against time in seconds. According to the graph, in what time interval is the speed of the leaf the greatest? 1 < t < b. < t < 5 c. 5 < t < 7 d. 7 < t < 9 e. none of these... 5.
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