. CALCULUS AB. Name: Class: Date:

Size: px
Start display at page:

Download ". CALCULUS AB. Name: Class: Date:"

Transcription

1 Class: _ Date: _. CALCULUS AB SECTION I, Part A Time- 55 Minutes Number of questions -8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each of the following problems, using available space for scratchwork. After examining the form of the choices, decide which is the best of the choices given and fill corresponding oval on the answer sheet. No credit will be given for anything written in the test book. Do not spend too much time on any one problem. In this test: Unless otherwise specified, the domain of the function f is assumed to be the set of all real numbers x for which f(x) is a real number.. If f(x) = x +, then f '( ) = x + a. 9 b. 5 4 c. 5 d. 4 e lim cosx is x π x π. a. b. c. d. e. nonexistent The graph of the function f shown in the figure above has vertical tangents at (-,-) and (,) and a horizontal tangent at (0,0). For what values of x, -,x,, is f not differentiable? a. only b. 0 and only c. - and only d. -,, and only e. -, 0,, and

2 4. If f (x) = sec(x), then f '(x) = a. tan (x) b. tan (x) c. tan(x)sec(x) d. tan(x)sec(x) e. sin(x)sec (x) Ê ˆ 5. x x + 0 Á dx = a. 0 b. 5 6 c. 9 0 d. e. 6. What is the slope of the tangent line to the graph of xy + = at point (,)? y + a. - b c. 0.5 d. e. nonexistent 7. What is the x-coordinate of the point of inflection for the graph of y = x + x? a. - b. - c. 0 d. e. 8. sintcos t dt = 0 x a. cos x c. cos x e. cos x b. cos x d. cos x 9. A particle moves along the x-axis so that its position at time t > 0 is given by x(t) = lnt 6t + 7. At what time t > 0 is the velocity of the particle equal to zero? a. ln 0.5 b. 0.5 c. ln d. e. ln x 0. If F(x) = cost dt, then F ' (x) = a. cos x d. Ê ˆ b. cos Á x e. cos( lnx) x sin(lnx) cos( lnx) c. cos( lnx)

3 . The function f is differntiable on the closed interval [,4, and it has values as follows: f()=, f()=k, and f(4)=5k+. For which of the following values of k must there exist two points a and b on the open interval (,4) with f '(a) = f '(b)? a. -4 b. 5 c. d. e. 5. Which of the following is a solution to the differential equation dy dx = sec x? y a. y = secx b. y = tanx + c. y = tanx + d. y = tanx + e. y = tanx +. If g(x) = f(x ), what is g"(x)? a. xf "(x ) b. 4xf "(x ) c. (4x + x)f "(x ) d. 4x f "(x ) + f '(x ) e. 4x f "(x ) + xf '(x )

4 4. The graph of the derivative of the function f is shown above. If f(0)=0, then which of the following is true? a. f( ) < f '( ) < f "( ) b. f( ) < f "( ) < f '( ) c. f '( ) < f "( ) < f ( ) d. f "( ) < f ( ) < f '( ) e. f "( ) < f '( ) < f ( ) 5. What s the instanteneous rate of change of y=ln(cosx) at the point x = π 6? a. b. 6. For what values of x is the function f (x) = + x x 4 increasing? a. < x < c. d. e. b. x < and 0 < x < c. < x < 0 and x > d. x < and x > e. x > 0 7. Which of the following is an equation of the tangent line to the graph of y = x 4 x x + x + at the point (,)? a. y = b. y = x c. y = -x+ d. y = x- e. y = -x+ 4

5 8. The graph of the function f ' is shown in the figure above. Which of the following could be the graph of f? a. d. b. e. c. 5

6 9. x f (x) 4 The function f is continuous on the closed interval [0,0] and has values given in the table above. Using the subintervals È ÎÍ 0, È, ÎÍ, È, ÎÍ,7 and È ÎÍ 7,0, what is the left Riemann sum estimate for 0 0 f(x)dx? a. 5 b. 7.5 c. 0 d. e..5 Ï 0. The function f is given by f (x) = Ì Ô lnx, 0 < x <.The limit lim f (x) is ÓÔ lnx, x x a. 0 b. 0.5 c. d. ln e. nonexistent. The differentiable function f(x) achieves its maximum when x=0. Which of the following statements must be true? I. The function g(x)= x f(x) has a critical point when x=0. II. The function h(x)= (f(x)) achieves its maximum at x=0. III. The function k(x)= f(x ) achieves its maximum at x=0. a. None b. III only c. I and II only d. I and III only e. II and III only. 8 dx = x a. 6 8 b. 6 8 c. d. e. 9. If x + y =, what is the minimum value of x + y?` a. 0 b. c. d. 4 e. 8 6

7 4. A particle moves along the graph of y = x + sinx. As it passes the point (π,π), the particle s y-coordinate is increasing at a rate of units per second. How fast is the x-coordinate of the particle changing at this point Iin units per second)? a. 0 b. π c. d. e. 5. The graph of the piecewise linear function f on the closed interval [-,4] is shown above. What is f(x) dx? a. 4 b. c. d. 9 4 e A particle moves along the x-axis. Its position at time t is given by x(t) = t4 4 t + t. What is the maximum acceleration of the particle on the interval 0 t 4? a. 8 b. c. 0 d. e The function f is given by f (x) = (t )e t dt. For which value of x does f have a relative minimum? 0 x a. - b. c. 0 d. e. 7

8 8. Shown above is the slope field for which of the following differential equations? a. b. c. d. e. dy dx = x + y dy = x(x ) dx dy dx = xy dy dx = x y dy dx = y 8

9 . CALCULUS AB Answer Section MULTIPLE CHOICE. ANS: E. ANS: A. ANS: D 4. ANS: D 5. ANS: C 6. ANS: A 7. ANS: B 8. ANS: E 9. ANS: B 0. ANS: D. ANS: A. ANS: C. ANS: D 4. ANS: B 5. ANS: B 6. ANS: B 7. ANS: A 8. ANS: B 9. ANS: D 0. ANS: D. ANS: B. ANS: E. ANS: C 4. ANS: D 5. ANS: A 6. ANS: E 7. ANS: E 8. ANS: C

10 Class: _ Date: _. CALCULUS AB SECTION I, Part B Time- 50 Minutes Number of questions -7 A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAMINATION Directions: Solve each of the following problems, using available space for scratchwork. After examining the form of the choices, decide which is the best of the choices given and fill corresponding oval on the answer sheet. No credit will be given for anything written in the test book. Do not spend too much time on any one problem. In this test:. The exact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among the choices the number the best approximates the exact numerical value.. Unless otherwise specified, the domain of the function f is assumed to be the set of all real numbers x for which f(x) is a real number.. In the actual AP Calculus Exam, the questions in this Part B are numbered from 76 to 9 to eliminate confusion between Part A and Part B on the bubble sheet.. What is the average value of the function f (x) = sin x on the interval [,]? a b c d e..98. Right triangle ABC has its right angle at A. Leg AB is decreasing at a constant rate of cm per minute. Leg AC is increasing at a constant rate of 4 cm per minute. How is the hypotenuse BC changing at the moment when AB= and AC=5? a. It is decreasing at the rate of 6 cm per minute. b. it is decreasing at the rate of 6 cm per minute. c. It is not changing. d. It is increasing at the rate of cm per minute. e. it is increasing at a rate of 6 cm per minute.

11 . If g'(x) = x(lnx) and g() =, what is g()? a..6 b..660 c..780 d. 5.6 e lim x x + x x x + x + x a. - b. c. d. e. 5. The derivative of a function f is given by f '(x) = sin(cosx) 0.x. How many critical points does f have on the open interval (0,8)? a. None b. One c. Two d. Three e. Four x 6. The function f is given by f (x) = Ì Ô x, x 0. Which of the following statements are true? ÓÔ 0, x = 0 I. f is continuous at the point x=0. II. f is differentiable at the point x=0. III. x=0 is a point of inflection for a graph of f. a. I only b. III only c. I and II only d. I and III only e. I,II, and III Ï 7. What is the area of the region bounded by the graphs of y = e x and y=tanx and the vertical lines x= and x=? a..5 b..58 c..49 d e

12 8. Let f be a function whose domain is the open interval (-,). The graph of the derivative of f is shown in the figure above. Which of the following describes the relative extrema of f and the points of inflection on the graph of f? a. relative minimum, relative maximum, and point of inflection. b. relative minimum and point of inflection. c. relative maximum and point of inflection. d. relative minimum and point of inflection. e. No relative extrema and point of inflection. 9. What is the x-value of the point at which the tangent line to the graph of y = e x + x perpendicular to the line y = x + a b c d. 0.6 e. 0.6

13 0. Water is leaking from the tank at the rate of R(t) gallons per hour. The graph R(t) from t=0 to t=0, where t is measured in hours, is shown above. Which of the following best approximates the total loss of water, in gallons, over the ten-hour period? a. 00 b. 000 c. 700 d. 400 e The base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the graph of y = x, as shown in the figure above. If cross-sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid? a. 0.5 b c..00 d..00 e..56 4

14 . The graph of f is shown above. Which of the following statements about f is false? a. lim f (x) exists. x b b. lim f (x) exists. x a + c. f has a relative minimum at x=a. d. f has a relative maximum at x=b. e. f ' is continuous at x=b.. The region enclosed by the graphs of y = e x and y = x and the vertical lines x=0 and x= is rotated about the line y=-. Which of the following gives the volume of the generated solid? a. Ê Ê π e x ˆ ˆ Á ( x ) Á 0 b. Ê Ê π e x ˆ ˆ + Á ( x + ) Á 0 c. Ê Ê π e x ˆ ˆ Á ( x) Á 0 d. e Ê π Ê Álny ˆ Ê Á y ˆ ˆ Á e. e Ê π Ê Álny + 4ˆ Ê Á y + ˆ ˆ Á 5

15 4. Which of the following is an equation of the tangent line to the graph of the function f (x) = e x + x at the point where f '(x) =? a. y=x-0.60 b. y=x+0.57 c. y=x+0.89 d. y=x+0.96 e. y=x x 0 f (x) The function f is twice differentiable on the closed interval [0,] and has values that are given in the table above. Which of the following statements is false? 6. a. The equation f(x)= has at least two solutions on the open interval (0,). b. The equation f (x)= 0 has a solutions on the open interval (0,). c. There exists a point c on the open interval (0,) such that f (c)=. d. f (x)> 0 for all x on the open interval (0,). e. f has a relative maximum on the open interval (0,). x 0 f (x) 5 4 The function f is continuous on the closed interval [0,] and has values that are given in the table above. Using the subintervals [0,],[,], and [,], what is the trapezoidal approximation to 0 f (x)dx? a. b..5 c. d..5 e. 7. A population of bacteria given by y(t) grows according to the equation dy = ky, where k is a constant dt and t is measured in minutes. If y(0)=0 and y(0)=5, what is the value of k? a b c d. 0.5 e

16 . CALCULUS AB Answer Section MULTIPLE CHOICE. ANS: C. ANS: B. ANS: D 4. ANS: D 5. ANS: D 6. ANS: E 7. ANS: A 8. ANS: C 9. ANS: A 0. ANS: C. ANS: A. ANS: E. ANS: B 4. ANS: C 5. ANS: D 6. ANS: B 7. ANS: B

17 Class: _ Date: _. AP CALCULUS - SECTION II - GENERAL INSTRUCTIONS You may wish to look over all problems before starting to work on them, since it is not expected that everyone will be able to complete all parts of all problems. All problems are given equal weight, but the parts of a particular problem are not necessarily given equal weight. A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS ON THIS SECTION OF THE EXAMINATION * You should write all work for each part of each problem in the space provided for that part in the booklet. Be sure to write crearly and legibly. If you make an error, you may save time by crossing it out rather than trying to erase it. Erased or crossed-out work will not be graded. * Show all your work. You will be graded on the correctness and completeness of your methods as well as your answers. Correct answers without supporting work may not receive credit. *Justifications require that you give mathematical (noncalculator) reasons and that you clearly identify functions, graphs, tables, or other objects you use. * You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your problem, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. * Your work must be expressed in standard mathematical notation rather than calculator syntax. For example, 5 x Ê dx may not be written as fnint X ˆ,X,,5 Á. * Unless otherwise specified (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. * Unless otherwise specified, the domai of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. SECTION II, Part A Time- 45 minutes Number of problems- A graphing calculator is required for some problems or parts of problems. During the timed portion for Part A, you may work only on the problems in Part A. On Part A, you are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your problem, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results.

18 . Let R and S be regions in the first quadrant shown in the figure above. The region R is bounded by the y-axis and the graphs of y= x and y=cos x. The region S is bounded by the x-axis and the graphs of y=x and y=cos x. a. Find the area of R. b. Find the area of S. c. Find the volume of the solid generated when R is revolved about the line y=.

19 . Because of rainfall from 9 a.m. to 9 p.m. on given day, water enters an open reservoir at the rate of 7000 R(t) =, where R(t) is measured in gallons per hour and t is measured in hours after 9 a.m. t 8t + 5 (so 0 t ). To prevent overflow, water is pumped out the reservoir at the constant rate of k gallons per hour. The reservoir holds 500,000 gallons of water both at 9 a.m. and at 9 p.m. a. What is k? Round your answer to the nearest whole number. b. To the nearest gallon, how much water is in the reservoir at 7 p.m. (t=0)? c. At what time t, 0 t, does the reservoir hold the greatest amount of water?

20 . t (hours) v(t) (miles per hour) _ The table above gives the velocity v(t) at selected times t of a car traveling along a straight road. a. Use the values of the table to approximate the acceleration of the car at time t=6. Show your work that leads to your answer and indicate units of measure. b. Use a right Riemann sum with the subintervals given in the table to approximate 0 v(t)dt. Indicate units of measure. What physical quantity does this integral 0 represent? c. The function v(t) is twice differentiable on the interval [0,0]. Show that there must be a moment of time when the acceleration of the car is equal to zero. 4

21 SECTION II, Part B Time- 45 minutes Number of problems- No calculator is allowed for these problems. During the timed portion for Part B, you may continue to work on the problems in Part A without the use of any calculator. Ê 4. Let f be a differentiable function whose graph is passing through the point, ˆ For all points Á. (x,y), the slope on the graph of y=f(x) is given by dy dx = y ( x). (a) Find d y Ê dx.is the graph of f concave up, concave down, or neither at the point, ˆ Á? Ê (b) Write an equation of the tangent line to the graph of f at point, ˆ Á. (c) Find y=f(x) by solving the separable differentiable equation dy condition f() =. dx = y ( x) with the initial 5

22 5. Let f be the function defined by f (x) = e x (ax + bx + 6), where a and b are constants. The function f has arelative extremum at the point x= - and f ( ) = 7e. (a) Find a and b. (b) Ê Is the point,7e ˆ Á a relative minimum or relative maximim of f? (c) Find all the points of inflection of the graph of f... 6

23 6. A spherical baloon is shrinking at a variable rate so that when its radius is r inches, its volume is decreasing at π r cubic inches per second. (The volume of a sphere of radius r is given by V = 4 πr.) (a) How fast is the radius of the baloon decreasing when r=5 inches? Include units of measure. (b) Show that the surface area of the baloon is decreasing at a constant rate. (The surface area of a sphere with radius r is given by S=S = 4πr.) (c) If the balloon s initial radius is 0 inches, how long will it take until its surface area is zero? Indicate units of measure. 7

24 . AP CALCULUS - SECTION II - GENERAL INSTRUCTIONS Answer Section MULTIPLE CHOICE. ANS: C see TOP: Trigonometry. ANS: C. ANS: C SHORT ANSWER 4. ANS: c 5. ANS: see 6. ANS: see

AB Calculus Diagnostic Test

AB Calculus Diagnostic Test AB Calculus Diagnostic Test The Exam AP Calculus AB Exam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time hour and 5 minutes Number of Questions

More information

The Princeton Review AP Calculus BC Practice Test 2

The Princeton Review AP Calculus BC Practice Test 2 0 The Princeton Review AP Calculus BC Practice Test CALCULUS BC SECTION I, Part A Time 55 Minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each

More information

The Princeton Review AP Calculus BC Practice Test 1

The Princeton Review AP Calculus BC Practice Test 1 8 The Princeton Review AP Calculus BC Practice Test CALCULUS BC SECTION I, Part A Time 55 Minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each

More information

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA CALCULUS AB SECTION I, Part A Time 55 minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM. Directions: Solve each of the following problems,

More information

Sample Questions PREPARING FOR THE AP (AB) CALCULUS EXAMINATION. tangent line, a+h. a+h

Sample Questions PREPARING FOR THE AP (AB) CALCULUS EXAMINATION. tangent line, a+h. a+h Sample Questions PREPARING FOR THE AP (AB) CALCULUS EXAMINATION B B A B tangent line,, a f '(a) = lim h 0 f(a + h) f(a) h a+h a b b f(x) dx = lim [f(x ) x + f(x ) x + f(x ) x +...+ f(x ) x ] n a n B B

More information

DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.

DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. AP Calculus AB Exam SECTION I: Multiple Choice 016 DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time 1 hour, 45 minutes Number of Questions 45 Percent of Total Score 50% Writing

More information

BC Calculus Diagnostic Test

BC Calculus Diagnostic Test BC Calculus Diagnostic Test The Eam AP Calculus BC Eam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time hour and 5 minutes Number of Questions

More information

Chapter 27 AB Calculus Practice Test

Chapter 27 AB Calculus Practice Test Chapter 7 AB Calculus Practice Test The Eam AP Calculus AB Eam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time 1 hour and 45 minutes Number

More information

AP Calculus AB Unit 3 Assessment

AP Calculus AB Unit 3 Assessment Class: Date: 2013-2014 AP Calculus AB Unit 3 Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. A calculator may NOT be used on this part of the exam.

More information

Chapter 29 BC Calculus Practice Test

Chapter 29 BC Calculus Practice Test Chapter 9 BC Calculus Practice Test The Eam AP Calculus BC Eam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time hour and 5 minutes Number

More information

Sample Questions PREPARING FOR THE AP (BC) CALCULUS EXAMINATION. tangent line, a+h. a+h

Sample Questions PREPARING FOR THE AP (BC) CALCULUS EXAMINATION. tangent line, a+h. a+h Sample Questions PREPARING FOR THE AP (BC) CALCULUS EXAMINATION B B A B tangent line,, a f '(a) = lim h 0 f(a + h) f(a) h a+h a b b f(x) dx = lim [f(x ) x + f(x ) x + f(x ) x +...+ f(x ) x ] n a n B B

More information

+ 1 for x > 2 (B) (E) (B) 2. (C) 1 (D) 2 (E) Nonexistent

+ 1 for x > 2 (B) (E) (B) 2. (C) 1 (D) 2 (E) Nonexistent dx = (A) 3 sin(3x ) + C 1. cos ( 3x) 1 (B) sin(3x ) + C 3 1 (C) sin(3x ) + C 3 (D) sin( 3x ) + C (E) 3 sin(3x ) + C 6 3 2x + 6x 2. lim 5 3 x 0 4x + 3x (A) 0 1 (B) 2 (C) 1 (D) 2 (E) Nonexistent is 2 x 3x

More information

Spring 2015 Sample Final Exam

Spring 2015 Sample Final Exam Math 1151 Spring 2015 Sample Final Exam Final Exam on 4/30/14 Name (Print): Time Limit on Final: 105 Minutes Go on carmen.osu.edu to see where your final exam will be. NOTE: This exam is much longer than

More information

2007 AP Calculus AB Free-Response Questions Section II, Part A (45 minutes) # of questions: 3 A graphing calculator may be used for this part

2007 AP Calculus AB Free-Response Questions Section II, Part A (45 minutes) # of questions: 3 A graphing calculator may be used for this part 2007 AP Calculus AB Free-Response Questions Section II, Part A (45 minutes) # of questions: 3 A graphing calculator may be used for this part 1. Let R be the region in the first and second quadrants bounded

More information

Limits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4

Limits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4 Limits and Continuity t+ 1. lim t - t + 4. lim x x x x + - 9-18 x-. lim x 0 4-x- x 4. sinq lim - q q 5. Find the horizontal asymptote (s) of 7x-18 f ( x) = x+ 8 Summer Packet AP Calculus BC Page 4 6. x

More information

AB CALCULUS SEMESTER A REVIEW Show all work on separate paper. (b) lim. lim. (f) x a. for each of the following functions: (b) y = 3x 4 x + 2

AB CALCULUS SEMESTER A REVIEW Show all work on separate paper. (b) lim. lim. (f) x a. for each of the following functions: (b) y = 3x 4 x + 2 AB CALCULUS Page 1 of 6 NAME DATE 1. Evaluate each it: AB CALCULUS Show all work on separate paper. x 3 x 9 x 5x + 6 x 0 5x 3sin x x 7 x 3 x 3 5x (d) 5x 3 x +1 x x 4 (e) x x 9 3x 4 6x (f) h 0 sin( π 6

More information

Sample Examination VI 203

Sample Examination VI 203 Sample Examination VI 203 Section II Part A: Graphing Calculator MAY BE USED. 1. Two particles move in the xy-plane: Particle A moves along the graph of y = 1 + e- X and particle B moves along the graph

More information

A.P. Calculus BC First Semester Exam Calculators Allowed Two Hours Number of Questions 10

A.P. Calculus BC First Semester Exam Calculators Allowed Two Hours Number of Questions 10 A.P. Calculus BC First Semester Exam Calculators Allowed Two Hours Number of Questions 10 Each of the ten questions is worth 10 points. The problem whose solution you write counted again, so that the maximum

More information

CALCULUS AB. SECTION I, Part A. Time minutes. Number of questions - 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION.

CALCULUS AB. SECTION I, Part A. Time minutes. Number of questions - 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION. E E S f CALCULUS AB SECTION I, Part A Time -- 55 minutes Number of questions - 28 Calculus AS ~.l Part A -J A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION. Directions: Solve each of the following

More information

Free Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom

Free Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions

More information

Calculus with the Graphing Calculator

Calculus with the Graphing Calculator Calculus with the Graphing Calculator Using a graphing calculator on the AP Calculus exam Students are expected to know how to use their graphing calculators on the AP Calculus exams proficiently to accomplish

More information

AP Calculus Exam Format and Calculator Tips:

AP Calculus Exam Format and Calculator Tips: AP Calculus Exam Format and Calculator Tips: Exam Format: The exam is 3 hours and 15 minutes long and has two sections multiple choice and free response. A graphing calculator is required for parts of

More information

Sudoku Puzzle A.P. Exam (Part B) Questions are from the 1997 and 1998 A.P. Exams A Puzzle by David Pleacher

Sudoku Puzzle A.P. Exam (Part B) Questions are from the 1997 and 1998 A.P. Exams A Puzzle by David Pleacher Sudoku Puzzle A.P. Exam (Part B) Questions are from the 1997 and 1998 A.P. Exams A Puzzle by David Pleacher Solve the 4 multiple-choice problems below. A graphing calculator is required for some questions

More information

Final Exam. Math 3 December 7, 2010

Final Exam. Math 3 December 7, 2010 Final Exam Math 3 December 7, 200 Name: On this final examination for Math 3 in Fall 200, I will work individually, neither giving nor receiving help, guided by the Dartmouth Academic Honor Principle.

More information

LSU AP Calculus Practice Test Day

LSU AP Calculus Practice Test Day LSU AP Calculus Practice Test Day AP Calculus AB 2018 Practice Exam Section I Part A AP CALCULUS AB: PRACTICE EXAM SECTION I: PART A NO CALCULATORS ALLOWED. YOU HAVE 60 MINUTES. 1. If y = ( 1 + x 5) 3

More information

AP Calculus Free-Response Questions 1969-present AB

AP Calculus Free-Response Questions 1969-present AB AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions

More information

AP Æ Calculus AB Sample Multiple-Choice Questions

AP Æ Calculus AB Sample Multiple-Choice Questions AP Æ Calculus AB Sample Multiple-Choice Questions The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must

More information

Puxi High School Examinations Semester 1, AP Calculus (BC) Part 1. Wednesday, December 16 th, :45 pm 3:15 pm.

Puxi High School Examinations Semester 1, AP Calculus (BC) Part 1. Wednesday, December 16 th, :45 pm 3:15 pm. Puxi High School Examinations Semester 1, 2009 2010 AP Calculus (BC) Part 1 Wednesday, December 16 th, 2009 12:45 pm 3:15 pm Time: 45 minutes Teacher: Mr. Surowski Testing Site: HS Gymnasium Student Name:

More information

Puxi High School Examinations Semester 1, AP Calculus (BC) Part 1. Wednesday, December 16 th, :45 pm 3:15 pm.

Puxi High School Examinations Semester 1, AP Calculus (BC) Part 1. Wednesday, December 16 th, :45 pm 3:15 pm. Puxi High School Examinations Semester 1, 2009 2010 AP Calculus (BC) Part 1 Wednesday, December 16 th, 2009 12:45 pm 3:15 pm Time: 45 minutes Teacher: Mr. Surowski Testing Site: HS Gymnasium Student Name:

More information

Final Exam Solutions

Final Exam Solutions Final Exam Solutions Laurence Field Math, Section March, Name: Solutions Instructions: This exam has 8 questions for a total of points. The value of each part of each question is stated. The time allowed

More information

AP Calculus AB 2nd Semester Homework List

AP Calculus AB 2nd Semester Homework List AP Calculus AB 2nd Semester Homework List Date Assigned: 1/4 DUE Date: 1/6 Title: Typsetting Basic L A TEX and Sigma Notation Write the homework out on paper. Then type the homework on L A TEX. Use this

More information

MATH 1241 Common Final Exam Fall 2010

MATH 1241 Common Final Exam Fall 2010 MATH 1241 Common Final Exam Fall 2010 Please print the following information: Name: Instructor: Student ID: Section/Time: The MATH 1241 Final Exam consists of three parts. You have three hours for the

More information

AP CALCULUS AB SECTION I, Part A Time 55 Minutes Number of questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM

AP CALCULUS AB SECTION I, Part A Time 55 Minutes Number of questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM AP CALCULUS AB SECTION I, Part A Time 55 Minutes Number of questions 28 Time Began: Time Ended: A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM Directions: Solve each of the following problems, using

More information

A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the

A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the attached packet of problems, and turn it in on Monday, August

More information

AP Calculus AB 2015 Free-Response Questions

AP Calculus AB 2015 Free-Response Questions AP Calculus AB 015 Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online

More information

2. Which of the following is an equation of the line tangent to the graph of f(x) = x 4 + 2x 2 at the point where

2. Which of the following is an equation of the line tangent to the graph of f(x) = x 4 + 2x 2 at the point where AP Review Chapter Name: Date: Per: 1. The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of the circumference C, what is the rate of change of the area of the

More information

(2) Let f(x) = a 2 x if x<2, 4 2x 2 ifx 2. (b) Find the lim f(x). (c) Find all values of a that make f continuous at 2. Justify your answer.

(2) Let f(x) = a 2 x if x<2, 4 2x 2 ifx 2. (b) Find the lim f(x). (c) Find all values of a that make f continuous at 2. Justify your answer. (1) Let f(x) = x x 2 9. (a) Find the domain of f. (b) Write an equation for each vertical asymptote of the graph of f. (c) Write an equation for each horizontal asymptote of the graph of f. (d) Is f odd,

More information

MA 113 Calculus I Fall 2012 Exam 3 13 November Multiple Choice Answers. Question

MA 113 Calculus I Fall 2012 Exam 3 13 November Multiple Choice Answers. Question MA 113 Calculus I Fall 2012 Exam 3 13 November 2012 Name: Section: Last 4 digits of student ID #: This exam has ten multiple choice questions (five points each) and five free response questions (ten points

More information

L. Function Analysis. ). If f ( x) switches from decreasing to increasing at c, there is a relative minimum at ( c, f ( c)

L. Function Analysis. ). If f ( x) switches from decreasing to increasing at c, there is a relative minimum at ( c, f ( c) L. Function Analysis What you are finding: You have a function f ( x). You want to find intervals where f ( x) is increasing and decreasing, concave up and concave down. You also want to find values of

More information

AP Calculus BC Fall Final Part IA. Calculator NOT Allowed. Name:

AP Calculus BC Fall Final Part IA. Calculator NOT Allowed. Name: AP Calculus BC 18-19 Fall Final Part IA Calculator NOT Allowed Name: 3π cos + h 1. lim cos 3π h 0 = h 1 (a) 1 (b) (c) 0 (d) -1 (e) DNE dy. At which of the five points on the graph in the figure below are

More information

BC Exam 2 - Part I 28 questions No Calculator Allowed. C. 1 x n D. e x n E. 0

BC Exam 2 - Part I 28 questions No Calculator Allowed. C. 1 x n D. e x n E. 0 1. If f x ( ) = ln e A. n x x n BC Exam - Part I 8 questions No Calculator Allowed, and n is a constant, then f ( x) = B. x n e C. 1 x n D. e x n E.. Let f be the function defined below. Which of the following

More information

AP Calculus. Prep Session I. February 2, 2008 Houston ISD

AP Calculus. Prep Session I. February 2, 2008 Houston ISD AP Calculus Prep Session I February, 008 Houston ISD Presented by: Advanced Placement Strategies, Inc. Advanced Placement, AP, and Advanced Placement Strategies are trademarks of the College Entrance Examination

More information

Calculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016

Calculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016 Name: Class: Date: Calculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016 Short Answer 1. Decide whether the following problem can be solved using precalculus, or whether calculus is required.

More information

MA 113 Calculus I Fall 2016 Exam Final Wednesday, December 14, True/False 1 T F 2 T F 3 T F 4 T F 5 T F. Name: Section:

MA 113 Calculus I Fall 2016 Exam Final Wednesday, December 14, True/False 1 T F 2 T F 3 T F 4 T F 5 T F. Name: Section: MA 113 Calculus I Fall 2016 Exam Final Wednesday, December 14, 2016 Name: Section: Last 4 digits of student ID #: This exam has five true/false questions (two points each), ten multiple choice questions

More information

AP Calculus AB Winter Break Packet Happy Holidays!

AP Calculus AB Winter Break Packet Happy Holidays! AP Calculus AB Winter Break Packet 04 Happy Holidays! Section I NO CALCULATORS MAY BE USED IN THIS PART OF THE EXAMINATION. Directions: Solve each of the following problems. After examining the form of

More information

2008 CALCULUS AB SECTION I, Part A Time 55 minutes Number of Questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION

2008 CALCULUS AB SECTION I, Part A Time 55 minutes Number of Questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION 8 CALCULUS AB SECTION I, Part A Time 55 minutes Number of Questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each of the following problems. After eamining the form

More information

1998 AP Calculus AB: Section I, Part A

1998 AP Calculus AB: Section I, Part A 55 Minutes No Calculator Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f () is a real number.. What is the -coordinate of the point

More information

NO CALCULATOR 1. Find the interval or intervals on which the function whose graph is shown is increasing:

NO CALCULATOR 1. Find the interval or intervals on which the function whose graph is shown is increasing: 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

More information

Formulas that must be memorized:

Formulas that must be memorized: Formulas that must be memorized: Position, Velocity, Acceleration Speed is increasing when v(t) and a(t) have the same signs. Speed is decreasing when v(t) and a(t) have different signs. Section I: Limits

More information

A.P. Calculus BC Test Four Section Two Free-Response Calculators Allowed Time 45 minutes Number of Questions 3

A.P. Calculus BC Test Four Section Two Free-Response Calculators Allowed Time 45 minutes Number of Questions 3 A.P. Calculus BC Test Four Section Two Free-Response Calculators Allowed Time 45 minutes Number of Questions Each of the three questions is worth 9 points. The maximum possible points earned on this section

More information

Without fully opening the exam, check that you have pages 1 through 11.

Without fully opening the exam, check that you have pages 1 through 11. Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

More information

Resources: http://www.calcchat.com/book/calculus-9e/ http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/27.html http://www.calculus.org/ http://cow.math.temple.edu/ http://www.mathsisfun.com/calculus/

More information

Answer Key for AP Calculus AB Practice Exam, Section I

Answer Key for AP Calculus AB Practice Exam, Section I Answer Key for AP Calculus AB Practice Exam, Section I Multiple-Choice Questions Question # Key B B 3 A 4 E C 6 D 7 E 8 C 9 E A A C 3 D 4 A A 6 B 7 A 8 B 9 C D E B 3 A 4 A E 6 A 7 A 8 A 76 E 77 A 78 D

More information

Exam 2 - Part I 28 questions No Calculator Allowed. x n D. e x n E. 0

Exam 2 - Part I 28 questions No Calculator Allowed. x n D. e x n E. 0 1. If f x! ( ) = ln e A.!n x " x n # $ Exam - Part I 8 questions No Calculator Allowed, and n is a constant, then f % ( x) = B. x n e C.!1 x n D. e x n E. 0. Let f be the function defined below. Which

More information

Calculus I Practice Exam 2

Calculus I Practice Exam 2 Calculus I Practice Exam 2 Instructions: The exam is closed book, closed notes, although you may use a note sheet as in the previous exam. A calculator is allowed, but you must show all of your work. Your

More information

Problem Worth Score Total 14

Problem Worth Score Total 14 MATH 241, Fall 14 Extra Credit Preparation for Final Name: INSTRUCTIONS: Write legibly. Indicate your answer clearly. Revise and clean up solutions. Do not cross anything out. Rewrite the page, I will

More information

MLC Practice Final Exam

MLC Practice Final Exam Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

More information

Solutions to Math 41 Final Exam December 10, 2012

Solutions to Math 41 Final Exam December 10, 2012 Solutions to Math 4 Final Exam December,. ( points) Find each of the following limits, with justification. If there is an infinite limit, then explain whether it is or. x ln(t + ) dt (a) lim x x (5 points)

More information

Calculus Test Chapter 5 You can use a calculator on all of the test. Each multiple choice & each part of the free response is worth 5 points.

Calculus Test Chapter 5 You can use a calculator on all of the test. Each multiple choice & each part of the free response is worth 5 points. Calculus Test 2013- Chapter 5 Name You can use a calculator on all of the test. Each multiple choice & each part of the free response is worth 5 points. 1. A bug begins to crawl up a vertical wire at time

More information

sin x (B) sin x 1 (C) sin x + 1

sin x (B) sin x 1 (C) sin x + 1 ANSWER KEY Packet # AP Calculus AB Eam Multiple Choice Questions Answers are on the last page. NO CALCULATOR MAY BE USED IN THIS PART OF THE EXAMINATION. On the AP Eam, you will have minutes to answer

More information

Calculus I (Math 241) (In Progress)

Calculus I (Math 241) (In Progress) Calculus I (Math 241) (In Progress) The following is a collection of Calculus I (Math 241) problems. Students may expect that their final exam is comprised, more or less, of one problem from each section,

More information

1998 AP Calculus AB: Section I, Part A

1998 AP Calculus AB: Section I, Part A 998 AP Calculus AB: 55 Minutes No Calculator Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f () is a real number.. What is the -coordinate

More information

Test 3 Review. fx ( ) ( x 2) 4/5 at the indicated extremum. y x 2 3x 2. Name: Class: Date: Short Answer

Test 3 Review. fx ( ) ( x 2) 4/5 at the indicated extremum. y x 2 3x 2. Name: Class: Date: Short Answer Name: Class: Date: ID: A Test 3 Review Short Answer 1. Find the value of the derivative (if it exists) of fx ( ) ( x 2) 4/5 at the indicated extremum. 7. A rectangle is bounded by the x- and y-axes and

More information

AP Calculus AB. Free-Response Questions

AP Calculus AB. Free-Response Questions 2018 AP Calculus AB Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online

More information

Semester 1 Review. Name. Period

Semester 1 Review. Name. Period P A (Calculus )dx Semester Review Name Period Directions: Solve the following problems. Show work when necessary. Put the best answer in the blank provided, if appropriate.. Let y = g(x) be a function

More information

CALCULUS AB SECTION II, Part A

CALCULUS AB SECTION II, Part A CALCULUS AB SECTION II, Part A Time 45 minutes Number of problems 3 A graphing calculator is required for some problems or parts of problems. pt 1. The rate at which raw sewage enters a treatment tank

More information

y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions

y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)

More information

Practice problems from old exams for math 132 William H. Meeks III

Practice problems from old exams for math 132 William H. Meeks III Practice problems from old exams for math 32 William H. Meeks III Disclaimer: Your instructor covers far more materials that we can possibly fit into a four/five questions exams. These practice tests are

More information

AP Calculus BC. Practice Exam. Advanced Placement Program

AP Calculus BC. Practice Exam. Advanced Placement Program Advanced Placement Program AP Calculus BC Practice Eam The questions contained in this AP Calculus BC Practice Eam are written to the content specifications of AP Eams for this subject. Taking this practice

More information

Without fully opening the exam, check that you have pages 1 through 11.

Without fully opening the exam, check that you have pages 1 through 11. Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

More information

Teacher: Olsen Verner Williams

Teacher: Olsen Verner Williams Name 4/29-5//9 Teacher: Olsen Verner Williams For both days of this exam multiple choice problems will be worth 2.5 points each and free response problems will be worth 9 points each. Answer the following

More information

Calculus BC: Section I

Calculus BC: Section I Calculus BC: Section I Section I consists of 45 multiple-choice questions. Part A contains 28 questions and does not allow the use of a calculator. Part B contains 17 questions and requires a graphing

More information

Purdue University Study Guide for MA Credit Exam

Purdue University Study Guide for MA Credit Exam Purdue University Study Guide for MA 16010 Credit Exam Students who pass the credit exam will gain credit in MA16010. The credit exam is a two-hour long exam with multiple choice questions. No books or

More information

Motion with Integrals Worksheet 4: What you need to know about Motion along the x-axis (Part 2)

Motion with Integrals Worksheet 4: What you need to know about Motion along the x-axis (Part 2) Motion with Integrals Worksheet 4: What you need to know about Motion along the x-axis (Part 2) 1. Speed is the absolute value of. 2. If the velocity and acceleration have the sign (either both positive

More information

AP Calculus BC Summer Assignment (June)

AP Calculus BC Summer Assignment (June) AP Calculus BC Summer Assignment (June) Solve each problem on a separate sheet of paper as if they are open ended AP problems. This means you must include all justifications necessary as on the AP AB exam.

More information

Summer Review for Students Entering AP Calculus AB

Summer Review for Students Entering AP Calculus AB Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation

More information

a b c d e GOOD LUCK! 3. a b c d e 12. a b c d e 4. a b c d e 13. a b c d e 5. a b c d e 14. a b c d e 6. a b c d e 15. a b c d e

a b c d e GOOD LUCK! 3. a b c d e 12. a b c d e 4. a b c d e 13. a b c d e 5. a b c d e 14. a b c d e 6. a b c d e 15. a b c d e MA23 Elem. Calculus Spring 206 Final Exam 206-05-05 Name: Sec.: Do not remove this answer page you will turn in the entire exam. No books or notes may be used. You may use an ACT-approved calculator during

More information

AP Calculus AB/BC ilearnmath.net

AP Calculus AB/BC ilearnmath.net CALCULUS AB AP CHAPTER 1 TEST Don t write on the test materials. Put all answers on a separate sheet of paper. Numbers 1-8: Calculator, 5 minutes. Choose the letter that best completes the statement or

More information

(a) Find the area of RR. (b) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is

(a) Find the area of RR. (b) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is Calculus AB Final Review Name: Revised 07 EXAM Date: Tuesday, May 9 Reminders:. Put new batteries in your calculator. Make sure your calculator is in RADIAN mode.. Get a good night s sleep. Eat breakfast

More information

NO CALCULATORS: 1. Find A) 1 B) 0 C) D) 2. Find the points of discontinuity of the function y of discontinuity.

NO CALCULATORS: 1. Find A) 1 B) 0 C) D) 2. Find the points of discontinuity of the function y of discontinuity. AP CALCULUS BC NO CALCULATORS: MIDTERM REVIEW 1. Find lim 7x 6x x 7 x 9. 1 B) 0 C) D). Find the points of discontinuity of the function y of discontinuity. x 9x 0. For each discontinuity identify the type

More information

AP Calculus BC Chapter 4 AP Exam Problems A) 4 B) 2 C) 1 D) 0 E) 2 A) 9 B) 12 C) 14 D) 21 E) 40

AP Calculus BC Chapter 4 AP Exam Problems A) 4 B) 2 C) 1 D) 0 E) 2 A) 9 B) 12 C) 14 D) 21 E) 40 Extreme Values in an Interval AP Calculus BC 1. The absolute maximum value of x = f ( x) x x 1 on the closed interval, 4 occurs at A) 4 B) C) 1 D) 0 E). The maximum acceleration attained on the interval

More information

a x a y = a x+y a x a = y ax y (a x ) r = a rx and log a (xy) = log a (x) + log a (y) log a ( x y ) = log a(x) log a (y) log a (x r ) = r log a (x).

a x a y = a x+y a x a = y ax y (a x ) r = a rx and log a (xy) = log a (x) + log a (y) log a ( x y ) = log a(x) log a (y) log a (x r ) = r log a (x). You should prepare the following topics for our final exam. () Pre-calculus. (2) Inverses. (3) Algebra of Limits. (4) Derivative Formulas and Rules. (5) Graphing Techniques. (6) Optimization (Maxima and

More information

c) xy 3 = cos(7x +5y), y 0 = y3 + 7 sin(7x +5y) 3xy sin(7x +5y) d) xe y = sin(xy), y 0 = ey + y cos(xy) x(e y cos(xy)) e) y = x ln(3x + 5), y 0

c) xy 3 = cos(7x +5y), y 0 = y3 + 7 sin(7x +5y) 3xy sin(7x +5y) d) xe y = sin(xy), y 0 = ey + y cos(xy) x(e y cos(xy)) e) y = x ln(3x + 5), y 0 Some Math 35 review problems With answers 2/6/2005 The following problems are based heavily on problems written by Professor Stephen Greenfield for his Math 35 class in spring 2005. His willingness to

More information

AP Calculus AB. Review for Test: Applications of Integration

AP Calculus AB. Review for Test: Applications of Integration Name Review for Test: Applications of Integration AP Calculus AB Test Topics: Mean Value Theorem for Integrals (section 4.4) Average Value of a Function (manipulation of MVT for Integrals) (section 4.4)

More information

AP Calculus AB Semester 1 Practice Final

AP Calculus AB Semester 1 Practice Final Class: Date: AP Calculus AB Semester 1 Practice Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the limit (if it exists). lim x x + 4 x a. 6

More information

1 + x 2 d dx (sec 1 x) =

1 + x 2 d dx (sec 1 x) = Page This exam has: 8 multiple choice questions worth 4 points each. hand graded questions worth 4 points each. Important: No graphing calculators! Any non-graphing, non-differentiating, non-integrating

More information

Final Exam Review / AP Calculus AB

Final Exam Review / AP Calculus AB Chapter : Final Eam Review / AP Calculus AB Use the graph to find each limit. 1) lim f(), lim f(), and lim π - π + π f 5 4 1 y - - -1 - - -4-5 ) lim f(), - lim f(), and + lim f 8 6 4 y -4 - - -1-1 4 5-4

More information

Test Your Strength AB Calculus: Section A 35 questions No calculator allowed. A. 0 B. 1 C. 2 D. nonexistent. . Which of the following

Test Your Strength AB Calculus: Section A 35 questions No calculator allowed. A. 0 B. 1 C. 2 D. nonexistent. . Which of the following Test Your Strength AB Calculus: Section A 35 questions No calculator allowed Directions: Use the answer sheet to input your answers. Caps or lower case are OK. If you need to guess, put an X in the guess

More information

MTH 132 Solutions to Exam 2 November 21st, Without fully opening the exam, check that you have pages 1 through 11.

MTH 132 Solutions to Exam 2 November 21st, Without fully opening the exam, check that you have pages 1 through 11. Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

More information

Math 1431 Final Exam Review

Math 1431 Final Exam Review Math 1431 Final Exam Review Comprehensive exam. I recommend you study all past reviews and practice exams as well. Know all rules/formulas. Make a reservation for the final exam. If you miss it, go back

More information

SCORE. Exam 3. MA 114 Exam 3 Fall 2016

SCORE. Exam 3. MA 114 Exam 3 Fall 2016 Exam 3 Name: Section and/or TA: Do not remove this answer page you will return the whole exam. You will be allowed two hours to complete this test. No books or notes may be used. You may use a graphing

More information

Exam Review Sheets Combined

Exam Review Sheets Combined Exam Review Sheets Combined Fall 2008 1 Fall 2007 Exam 1 1. For each part, if the statement is always true, circle the printed capital T. If the statement is sometimes false, circle the printed capital

More information

Level 1 Calculus Final Exam Day 1 50 minutes

Level 1 Calculus Final Exam Day 1 50 minutes Level 1 Calculus Final Exam 2013 Day 1 50 minutes Name: Block: Circle Teacher Name LeBlanc Normile Instructions Write answers in the space provided and show all work. Calculators okay but observe instructions

More information

AP Calculus AB Semester 2 Practice Final

AP Calculus AB Semester 2 Practice Final lass: ate: I: P alculus Semester Practice Final Multiple hoice Identify the choice that best completes the statement or answers the question. Find the constants a and b such that the function f( x) = Ï

More information

Math 121: Final Exam Review Sheet

Math 121: Final Exam Review Sheet Exam Information Math 11: Final Exam Review Sheet The Final Exam will be given on Thursday, March 1 from 10:30 am 1:30 pm. The exam is cumulative and will cover chapters 1.1-1.3, 1.5, 1.6,.1-.6, 3.1-3.6,

More information

Part Two. Diagnostic Test

Part Two. Diagnostic Test Part Two Diagnostic Test AP Calculus AB and BC Diagnostic Tests Take a moment to gauge your readiness for the AP Calculus eam by taking either the AB diagnostic test or the BC diagnostic test, depending

More information

I. Horizontal and Vertical Tangent Lines

I. Horizontal and Vertical Tangent Lines How to find them: You need to work with f " x Horizontal tangent lines: set f " x Vertical tangent lines: find values of x where f " x I. Horizontal and Vertical Tangent Lines ( ), the derivative of function

More information

1. Determine the limit (if it exists). + lim A) B) C) D) E) Determine the limit (if it exists).

1. Determine the limit (if it exists). + lim A) B) C) D) E) Determine the limit (if it exists). Please do not write on. Calc AB Semester 1 Exam Review 1. Determine the limit (if it exists). 1 1 + lim x 3 6 x 3 x + 3 A).1 B).8 C).157778 D).7778 E).137778. Determine the limit (if it exists). 1 1cos

More information

(b) x = (d) x = (b) x = e (d) x = e4 2 ln(3) 2 x x. is. (b) 2 x, x 0. (d) x 2, x 0

(b) x = (d) x = (b) x = e (d) x = e4 2 ln(3) 2 x x. is. (b) 2 x, x 0. (d) x 2, x 0 1. Solve the equation 3 4x+5 = 6 for x. ln(6)/ ln(3) 5 (a) x = 4 ln(3) ln(6)/ ln(3) 5 (c) x = 4 ln(3)/ ln(6) 5 (e) x = 4. Solve the equation e x 1 = 1 for x. (b) x = (d) x = ln(5)/ ln(3) 6 4 ln(6) 5/ ln(3)

More information

Math Exam 02 Review

Math Exam 02 Review Math 10350 Exam 02 Review 1. A differentiable function g(t) is such that g(2) = 2, g (2) = 1, g (2) = 1/2. (a) If p(t) = g(t)e t2 find p (2) and p (2). (Ans: p (2) = 7e 4 ; p (2) = 28.5e 4 ) (b) If f(t)

More information