Assignment: Practice Exam Big Losers AB Calculus - Hardtke Name Due Date: Tuesday, 4/30 Show all work and circle your answer. 1. A water tank contains 100 gallons of water at time t = 3 hours. Water is pumped into the tank at a rate R(t), where R(t) is measured in gallons per hour and t is measured in hours. Selected values of R(t) are shown in the table below. Using left Riemann sum with three subintervals and data from the table, what is the approximation of the number of gallons in the tank at time t = 13 hours. t 3 8 10 13 (hours) R(t) 5 2 7 4 gallons/hour 2. What is the area of the region in the first quadrant bounded by the graph of y = and the line x = 4? 3. The graph of a differentiable function f is shown at the right. If ( ) ( ), write the following values from smallest to largest: h(2), h (2) and h (2) 4. A particle moves along the x-axis with its position at time t given by x(t) = (t + p)(t + q), where p and q are constants and p q. For which of the following values of t is the particle at rest? (A) t = pq (B) t = ½ q (C) t = -½ (p + q) (D) t = 2p + 2q (E) t = -2(p q) 5. Let f(x) = (3x 1) 4 and let g(x) be the inverse function of f. Given that f(0) = 1, find g (1).
6. The line y = 2 is an asymptote of which graph(s) below? The line x = 2 is an asymptote of which graph(s) below? (A) y = 2sin x (B) y = 2x (C) y = (D) y = (E) y = 7. Does f(x) = have an absolute maximum? If yes, what is the absolute maximum? 8. If N(t) is the total number of concert tickets that have been sold at time t, which of the following equations describes linear growth in the number of tickets sold? (A) = 300N (B) = 300N 2 (C) = 300t 2 (D) = 300 (E) = 300t 9. Let f(x) = x 3 e kx, where k is a constant. For what value of k does f have a critical point at x = 2? 10. Which of the following is the solution of = -3 sin x with the initial condition y(π) = 1? (A) y = 3cos x (B) y = 3cos x + 1 (C) y = 3cos x 1 (D) y = 3cos x + 4 (E) y = 3cos x + 4 11. Let h be a function with first derivative given by h (t) =. Which of the following must Be true on the interval 0 < x < 12? (A) h has one inflection point on 0 < x < 12 (B) h is decreasing and the graph of h is concave down (C) h is increasing and the graph of h is concave down (D) h is decreasing and the graph of h is concave up (E) h is increasing and the graph of h is concave up 12. If (2x y)( ) = x + 2y, what is the value of at the point (2, 0)?
13. For t 0, the position of a particle moving along the x-axis is given by x(t) = cos t sin t. What is the acceleration of the particle at the point where the velocity is first equal to 0? You may use your calculator for these three problems. 14. A student 5 feet tall is 10 feet away from a lamppost 15 feet tall. She is walking away from the lamppost at 2 feet per second. How fast is the tip of her shadow moving away from the foot of the lamppost? 15. A particle moves along a line so that its acceleration for t 0 is given by a(t) =. If the particle s velocity at t = 0 is 2, what is the velocity of the particle at t = 3? (A) 3.539 (B) 3.124 (C) 4.070 (D) 5.124 (E) 6.070 16. Let f be a function such that ( ) = 4. Find ( ).
AB Calculus - Hardtke Assignment: Practice Exam Big Losers SOLUTION KEY Due Date: Tuesday, 4/30 Show all work and circle your answer. 1. (8) A water tank contains 100 gallons of water at time t = 3 hours. Water is pumped into the tank at a rate R(t), where R(t) is measured in gallons per hour and t is measured in hours. Selected values of R(t) are shown in the table below. Using left Riemann sum with three subintervals and data from the table, what is the approximation of the number of gallons in the tank at time t = 13 hours. t 3 8 10 13 (hours) R(t) 5 2 7 4 gallons/hour 2. (10) What is the area of the region in the first quadrant bounded by the graph of y = and the line x = 4? 3. (15) The graph of a differentiable function f is shown at the right. If ( ) ( ), write the following values from smallest to largest: h(2), h (2) and h (2) 4. (16) A particle moves along the x-axis with its position at time t given by x(t) = (t + p)(t + q), where p and q are constants and p q. For which of the following values of t is the particle at rest? (A) t = pq (B) t = ½ q (C) t = -½ (p + q) (D) t = 2p + 2q (E) t = -2(p q) 5. (20) Let f(x) = (3x 1)4 and let g(x) be the inverse function of f. Given that f(0) = 1, find g (1).
6. (21) The line y = 2 is an asymptote of which graph(s) below? The line x = 2 is an asymptote of which graph(s) below? (A) y = 2sin x (B) y = 2x 7. (22) Does f(x) = (C) y = (D) y = (E) y = have an absolute maximum? If yes, what is the absolute maximum? 8. (23) If N(t) is the total number of concert tickets that have been sold at time t, which of the following equations describes linear growth in the number of tickets sold? 2 2 (A) = 300N (B) = 300N (C) = 300t (D) = 300 (E) = 300t 3 kx 9. (24) Let f(x) = x e, where k is a constant. For what value of k does f have a critical point at x = 2? 10. (25) Which of the following is the solution of = -3 sin x with the initial condition y(π) = 1? (A) y = 3cos x (B) y = 3cos x + 1 (C) y = 3cos x 1 (D) y = 3cos x + 4 (E) y = 3cos x + 4 11. (26) Let h be a function with first derivative given by h (t) = Be true on the interval 0 < x < 12? (A) h has one inflection point on 0 < x < 12 (B) h is decreasing and the graph of h is concave down (C) h is increasing and the graph of h is concave down (D) h is decreasing and the graph of h is concave up (E) h is increasing and the graph of h is concave up 12. (27) If (2x y)( ) = x + 2y, what is the value of. Which of the following must at the point (2, 0)? 13. (28) For t 0, the position of a particle moving along the x-axis is given by x(t) = cos t sin t. What is the acceleration of the particle at the point where the velocity is first equal to 0?
You may use your calculator these three problems. 14. (88) A student 5 feet tall is 10 feet away from a lamppost 15 feet tall. She is walking away from the lamppost at 2 feet per second. How fast is the tip of her shadow moving away from the foot of the lamppost? 15. (89) A particle moves along a line so that its acceleration for t 0 is given by a(t) =. If the particle s velocity at t = 0 is 2, what is the velocity of the particle at t = 3? (A) 3.539 (B) 3.124 (C) 4.070 (D) 5.124 (E) 6.070 16. (90) Let f be a function such that ( ) = 4. Find ( ).