m2413c2 the limiting process. 4. Use the alternative form of the derivative to find the derivative of the function at. a. b. c. d. e.

Size: px
Start display at page:

Download "m2413c2 the limiting process. 4. Use the alternative form of the derivative to find the derivative of the function at. a. b. c. d. e."

Transcription

1 m2413c2 Multiple Choice Identify the choice that best completes the statement or answers the question 1 Find the derivative of the following function using the limiting process 2 Find the derivative of the following function using the limiting process 3 Find the derivative of the function by the limit process 4 Use the alternative form of the derivative to find the derivative of the function at 5 Find the derivative of the function 6 Find the slope of the graph of the function at the given valu when

2 7 Find the slope of the graph of the function at the given valu when 8 Find the slope of the graph of the function at 9 Find the slope of the graph of the function at 10 Determine all values of, (if any), at which the graph of the function has a horizontal tangent The graph has no horizontal tangents 11 Suppose the position function for a free-falling object on a certain planet is given by A silver coin is dropped from the top of a building that is 1370 feet tall Determine the velocity function for the coin 12 Use the Product Rule to differentiate 13 Find an equation of the tangent line to the graph of f at the given point 14 Find the second derivative of the function

3 18 Find the derivative of the function 15 Given the derivative below find the requested higher-order derivativ 16 Find the derivative of the function 19 Find the derivative of the function 20 Evaluate the derivative of the function 17 Find the derivative of the function at the point 21 Find by implicit differentiation

4 22 Find the slope of the tangent line at the given point decimal places Find in terms of x and y Round your answer to two 25 Find the rate of change of the distance between the origin and a moving point on the graph of if centimeters per secon 24 Differentiate with respect to t (x and y are functions of t) 26 The radius r of a sphere is increasing at a rate of inches per minut Find the rate of change of the volume when r = inches

5 27 A spherical balloon is inflated with gas at the rate of cubic centimeters per minut How fast is the radius of the balloon increasing at the instant the radius is centimeters? 28 All edges of a cube are expanding at a rate of centimeters per secon How fast is the volume changing when each edge is centimeters? 29 An airplane is flying in still air with an airspeed of miles per hour If it is climbing at an angle of, find the rate at which it is gaining altitud Round your answer to four decimal places 30 Find by implicit differentiation

6 m2413c2 Answer Section MULTIPLE CHOICE 1 ANS: C PTS: 1 DIF: Medium REF: 2121 OBJ: Calculate the derivative of a function by the limit process NOT: Section 21 2 ANS: E PTS: 1 DIF: Medium REF: 2122 OBJ: Calculate the derivative of a function by the limit process NOT: Section 21 3 ANS: D PTS: 1 DIF: Difficult REF: 2124 OBJ: Calculate the derivative of a function by the limit process NOT: Section 21 4 ANS: E PTS: 1 DIF: Easy REF: 2173 OBJ: Calculate the derivative of a function at a specified point using the alternative form NOT: Section 21 5 ANS: B PTS: 1 DIF: Medium REF: 2221 OBJ: Differentiate trigonometric functions NOT: Section 22 6 ANS: E PTS: 1 DIF: Easy REF: 2231 NOT: Section 22 7 ANS: D PTS: 1 DIF: Medium REF: 2232 NOT: Section 22 8 ANS: A PTS: 1 DIF: Medium REF: 2234 NOT: Section 22 9 ANS: E PTS: 1 DIF: Medium REF: 2235 NOT: Section ANS: C PTS: 1 DIF: Medium REF: 2260 OBJ: Calculate the values for which the slope of a function is zero NOT: Section ANS: B PTS: 1 DIF: Medium REF: 2297a OBJ: Write the velocity function for a specified position function MSC: Application NOT: Section ANS: D PTS: 1 DIF: Medium REF: 235 OBJ: Differentiate a function using the product rule NOT: Section ANS: C PTS: 1 DIF: Medium REF: 2364a OBJ: Write an equation of a line tangent to the graph of a function at a specified point NOT: Section ANS: A PTS: 1 DIF: Medium REF: 2398 OBJ: Calculate the second derivative of a function NOT: Section ANS: C PTS: 1 DIF: Medium REF: 23103

7 OBJ: Calculate a higher derivative of a function NOT: Section ANS: B PTS: 1 DIF: Medium REF: 248 OBJ: Differentiate a function using the chain rule NOT: Section ANS: B PTS: 1 DIF: Medium REF: 2423 OBJ: Differentiate a function using the chain rule and product rule NOT: Section ANS: E PTS: 1 DIF: Medium REF: 2426 OBJ: Differentiate a function using the chain rule and product rule NOT: Section ANS: C PTS: 1 DIF: Easy REF: 2445 OBJ: Differentiate a function using the chain rule NOT: Section ANS: E PTS: 1 DIF: Medium REF: 2472 OBJ: Evaluate the derivative of a function at a point NOT: Section ANS: B PTS: 1 DIF: Medium REF: 2511 OBJ: Differentiate an equation using implicit differentiation NOT: Section ANS: B PTS: 1 DIF: Difficult REF: 2530 OBJ: Evaluate the derivative of an implicit function at a given point NOT: Section ANS: E PTS: 1 DIF: Easy REF: 2545 OBJ: Calculate the second derivative implicitly NOT: Section ANS: B PTS: 1 DIF: Medium REF: 2568b OBJ: Differentiate an equation in x and y using implicit differentiation with respect to t NOT: Section ANS: A PTS: 1 DIF: Medium REF: 2611 OBJ: Solve a related rate problem involving the distance between points NOT: Section ANS: C PTS: 1 DIF: Easy REF: 2616a OBJ: Solve a related rate problem involving the volume of a sphere and its MSC: Application NOT: Section ANS: C PTS: 1 DIF: Easy REF: 2617 OBJ: Solve a related rate problem involving the volume of a sphere and its radius MSC: Application NOT: Section ANS: D PTS: 1 DIF: Easy REF: 2618 OBJ: Solve a related rate problem involving the volume of a cube and the length of a side MSC: Application NOT: Section ANS: E PTS: 1 DIF: Medium REF: 2647 OBJ: Solve a related rate problem involving the altitude of an airplane MSC: Application NOT: Section ANS: B PTS: 1 DIF: Easy REF: 251 OBJ: Differentiate an equation using implicit differentiation NOT: Section 25

MATH1910Chapter2TestReview

MATH1910Chapter2TestReview Class: Date: MATH1910Chapter2TestReview Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the slope m of the line tangent to the graph of the function

More information

Math 2413 t2rsu14. Name: 06/06/ Find the derivative of the following function using the limiting process.

Math 2413 t2rsu14. Name: 06/06/ Find the derivative of the following function using the limiting process. Name: 06/06/014 Math 413 trsu14 1. Find the derivative of the following function using the limiting process. f( x) = 4x + 5x. Find the derivative of the following function using the limiting process. f(

More information

Implicit Differentiation

Implicit Differentiation Implicit Differentiation Much of our algebraic study of mathematics has dealt with functions. In pre-calculus, we talked about two different types of equations that relate x and y explicit and implicit.

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

College Calculus Final Review

College Calculus Final Review College Calculus Final Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the following limit. (Hint: Use the graph to calculate the limit.)

More information

Period: Unit 2 Differentiation Date: mole rat QUIZ 4 Implicit differentiation (calculator OK but unnecessary)

Period: Unit 2 Differentiation Date: mole rat QUIZ 4 Implicit differentiation (calculator OK but unnecessary) Unit Differentiation mole rat QUIZ 4 Implicit differentiation (calculator OK but unnecessary) Standard.5: I can find the slope of an equation implicitly (when explicit differentiation is impossible*).

More information

m2413f 4. Suppose that and . Find the following limit b. 10 c. 3 d Determine the limit (if it exists). 2. Find the lmit. a. 1 b. 0 c. d.

m2413f 4. Suppose that and . Find the following limit b. 10 c. 3 d Determine the limit (if it exists). 2. Find the lmit. a. 1 b. 0 c. d. m2413f Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find an equation of the line that passes through the point and has the slope. 4. Suppose that and

More information

Chapter 2 THE DERIVATIVE

Chapter 2 THE DERIVATIVE Chapter 2 THE DERIVATIVE 2.1 Two Problems with One Theme Tangent Line (Euclid) A tangent is a line touching a curve at just one point. - Euclid (323 285 BC) Tangent Line (Archimedes) A tangent to a curve

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

Days 3 & 4 Notes: Related Rates

Days 3 & 4 Notes: Related Rates AP Calculus Unit 4 Applications of the Derivative Part 1 Days 3 & 4 Notes: Related Rates Implicitly differentiate the following formulas with respect to time. State what each rate in the differential equation

More information

Chapter 2: Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point.

Chapter 2: Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point. Chapter : Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point. f( ) 10, (, ) 10 1 E) none of the above. Find the slope of the tangent line to the

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

The radius of a circle is increasing at a constant rate of the rate of increase in the area of the circle at the instant when the circumference is?

The radius of a circle is increasing at a constant rate of the rate of increase in the area of the circle at the instant when the circumference is? Unit #11: Related Rates Topic: More Related Rates Problems Objective: SWBAT apply derivatives to real life applications. Warm Up #5: The radius of a circle is increasing at a constant rate of. What is

More information

Chapters 1 and 2 Test

Chapters 1 and 2 Test Class: Date: Chapters 1 and 2 Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2r 9 6 Solve the inequality. Graph the solution set. a. r 1 1 2 c. r

More information

Trigonometric Identity Practice

Trigonometric Identity Practice Trigonometric Identity Practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the expression that completes the equation so that it is an identity.

More information

Algebra II: Chapter 6 Test Review

Algebra II: Chapter 6 Test Review Class: Date: Algebra II: Chapter 6 Test Review 1. Simplify 8 4 /. 1 2 a. c. 2 b. 8 d. 16 2. Which is equivalent to 81 1/4? a. 9 b. c. 1 9 d. 1. The volume of a sphere can be given by the formula V = 4.18879r.

More information

p144 Section 2.6: Related Rates Find a related rate Use related rates to solve real life problems

p144 Section 2.6: Related Rates Find a related rate Use related rates to solve real life problems 1 2 p144 Section 2.6: Related Rates Find a related rate Use related rates to solve real life problems Finding Related Rates We have used the chain rule to find dy/dx implicitly, but you can also use the

More information

p144 Section 2.6: Related Rates Find a related rate Use related rates to solve real life problems

p144 Section 2.6: Related Rates Find a related rate Use related rates to solve real life problems p144 Section 2.6: Related Rates Find a related rate Use related rates to solve real life problems Finding Related Rates We have used the chain rule to find dy/dx implicitly, but you can also use the chain

More information

SHOW WORK! Chapter4Questions. NAME ID: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

SHOW WORK! Chapter4Questions. NAME ID: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. NAME ID: Date: Chapter4Questions Multiple Choice Identify the choice that best completes the statement or answers the question. SHOW WORK! 1. Find the indefinite integral 1u 4u du. a. 4u u C b. 1u 4u C

More information

Math 131. Related Rates Larson Section 2.6

Math 131. Related Rates Larson Section 2.6 Math 131. Related Rates Larson Section 2.6 There are many natural situations when there are related variables that are changing with respect to time. For example, a spherical balloon is being inflated

More information

CHAPTER 3: DERIVATIVES

CHAPTER 3: DERIVATIVES (Exercises for Section 3.1: Derivatives, Tangent Lines, and Rates of Change) E.3.1 CHAPTER 3: DERIVATIVES SECTION 3.1: DERIVATIVES, TANGENT LINES, and RATES OF CHANGE In these Exercises, use a version

More information

Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section

Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example

More information

Algebra 1, Absolute Value Functions Review

Algebra 1, Absolute Value Functions Review Name: Class: Date: ID: A Algebra 1, Absolute Value Functions Review 3.7.1: I can solve absolute value equations. 1. (1 point) x + 10 = 1 2. (1 point) Starting from 1.5 miles away, a car drives towards

More information

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. 3A Worksheet 3A Short Answer Find an equation for the line: 1. through (2, 6) and perpendicular to y = 5 4 x + 1. 2. through ( 7, 4) and vertical. Determine whether y varies directly with x. If so, find

More information

Test one Review Cal 2

Test one Review Cal 2 Name: Class: Date: ID: A Test one Review Cal 2 Short Answer. Write the following expression as a logarithm of a single quantity. lnx 2ln x 2 ˆ 6 2. Write the following expression as a logarithm of a single

More information

AP Calculus AB Chapter 4 Packet Implicit Differentiation. 4.5: Implicit Functions

AP Calculus AB Chapter 4 Packet Implicit Differentiation. 4.5: Implicit Functions 4.5: Implicit Functions We can employ implicit differentiation when an equation that defines a function is so complicated that we cannot use an explicit rule to find the derivative. EXAMPLE 1: Find dy

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

4.1 Implicit Differentiation

4.1 Implicit Differentiation 4.1 Implicit Differentiation Learning Objectives A student will be able to: Find the derivative of variety of functions by using the technique of implicit differentiation. Consider the equation We want

More information

Review Algebra Test

Review Algebra Test Name: Class: Date: Review Algebra Test.4-2.3 Multiple Choice Identify the choice that best completes the statement or answers the question. Solve the equation.. 5y 9 (y ) a. 2 b. 2 2 c. 2 d. 2 5 Use an

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

Chapter 8: Radical Functions

Chapter 8: Radical Functions Chapter 8: Radical Functions Chapter 8 Overview: Types and Traits of Radical Functions Vocabulary:. Radical (Irrational) Function an epression whose general equation contains a root of a variable and possibly

More information

Prof. Israel Nwaguru PLANE TRIGONOMETRY - MATH 1316, CHAPTER REVIEW

Prof. Israel Nwaguru PLANE TRIGONOMETRY - MATH 1316, CHAPTER REVIEW Prof. Israel Nwaguru PLANE TRIGONOMETRY - MATH 1316, CHAPTER 1.1-1.4 REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the quadrant in which

More information

AP Calculus Related Rates Worksheet

AP Calculus Related Rates Worksheet AP Calculus Related Rates Worksheet 1. A small balloon is released at a point 150 feet from an observer, who is on level ground. If the balloon goes straight up at a rate of 8 feet per second, how fast

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

Trigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED

Trigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED Name: Class: Date: ID: A Trigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED 1. A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower a = 190 feet above the ground.

More information

Name Date Class. Logarithmic/Exponential Differentiation and Related Rates Review AP Calculus. Find dy. dx. 1. y 4 x. y 6. 3e x.

Name Date Class. Logarithmic/Exponential Differentiation and Related Rates Review AP Calculus. Find dy. dx. 1. y 4 x. y 6. 3e x. Name Date Class Find dy d. Logarithmic/Eponential Differentiation and Related Rates Review AP Calculus 1. y 4. 1 y ln. y ln 1 4. y log9 1 5. e y 6. y log 7. y e 8. e y e 4 1 1 9. y e e 10. 1 y ln 1 e 11.

More information

Calculus 1st Semester Final Review

Calculus 1st Semester Final Review Calculus st Semester Final Review Use the graph to find lim f ( ) (if it eists) 0 9 Determine the value of c so that f() is continuous on the entire real line if f ( ), c /, > 0 Find the limit: lim 6+

More information

MAC 2311 Review

MAC 2311 Review Name: Class: Date: MAC 2311 Review 2.6-2.9 Numeric Response 1. Calculate y. xy 4 +x 2 y =2x +3y 2. Calculate y. cos xy =x 6 y 3. The position function of a particle is given by s =t 3 10.5t 2 2t,t 0 When

More information

MATH 2413 TEST ON CHAPTER 4 ANSWER ALL QUESTIONS. TIME 1.5 HRS.

MATH 2413 TEST ON CHAPTER 4 ANSWER ALL QUESTIONS. TIME 1.5 HRS. MATH 1 TEST ON CHAPTER ANSWER ALL QUESTIONS. TIME 1. HRS. M1c Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the summation formulas to rewrite the

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

Implicit Differentiation and Related Rates

Implicit Differentiation and Related Rates Math 3A Discussion Notes Week 5 October 7 and October 9, 05 Because of the mierm, we re a little behind lecture, but this week s topics will help prepare you for the quiz. Implicit Differentiation and

More information

6.2 Related Rates Name: Notes

6.2 Related Rates Name: Notes Calculus Write your questions and thoughts here! 6.2 Related Rates Name: Notes Guidelines to solving related rate problems 1. Draw a picture. 2. Make a list of all known and unknown rates and quantities.

More information

9. (1 pt) Chap2/2 3.pg DO NOT USE THE DEFINITION OF DERIVATIVES!! If. find f (x).

9. (1 pt) Chap2/2 3.pg DO NOT USE THE DEFINITION OF DERIVATIVES!! If. find f (x). math0spring0-6 WeBWorK assignment number 3 is due : 03/04/0 at 0:00pm MST some kind of mistake Usually you can attempt a problem as many times as you want before the due date However, if you are help Don

More information

Algebra 2 Matrices. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find.

Algebra 2 Matrices. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find. Algebra 2 Matrices Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find. Evaluate the determinant of the matrix. 2. 3. A matrix contains 48 elements.

More information

Section MWF 12 1pm SR 117

Section MWF 12 1pm SR 117 Math 1431 Section 12485 MWF 12 1pm SR 117 Dr. Melahat Almus almus@math.uh.edu http://www.math.uh.edu/~almus COURSE WEBSITE: http://www.math.uh.edu/~almus/1431_sp16.html Visit my website regularly for announcements

More information

PDF Created with deskpdf PDF Writer - Trial ::

PDF Created with deskpdf PDF Writer - Trial :: y 3 5 Graph of f ' x 76. The graph of f ', the derivative f, is shown above for x 5. n what intervals is f increasing? (A) [, ] only (B) [, 3] (C) [3, 5] only (D) [0,.5] and [3, 5] (E) [, ], [, ], and

More information

MATH 135 Calculus 1 Solutions/Answers for Exam 3 Practice Problems November 18, 2016

MATH 135 Calculus 1 Solutions/Answers for Exam 3 Practice Problems November 18, 2016 MATH 35 Calculus Solutions/Answers for Exam 3 Practice Problems November 8, 206 I. Find the indicated derivative(s) and simplify. (A) ( y = ln(x) x 7 4 ) x Solution: By the product rule and the derivative

More information

MCR3U - Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

MCR3U - Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question. MCR3U - Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following relations is not a function? 2. Which graph is not a function?

More information

Name: Date: Period: Calculus Honors: 4-2 The Product Rule

Name: Date: Period: Calculus Honors: 4-2 The Product Rule Name: Date: Period: Calculus Honors: 4- The Product Rule Warm Up: 1. Factor and simplify. 9 10 0 5 5 10 5 5. Find ' f if f How did you go about finding the derivative? Let s Eplore how to differentiate

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 142 (Summer 2018) Business Calculus 5.8 Notes

Math 142 (Summer 2018) Business Calculus 5.8 Notes Math 142 (Summer 2018) Business Calculus 5.8 Notes Implicit Differentiation and Related Rates Why? We have learned how to take derivatives of functions, and we have seen many applications of this. However

More information

Implicit Differentiation

Implicit Differentiation Week 6. Implicit Differentiation Let s say we want to differentiate the equation of a circle: y 2 + x 2 =9 Using the techniques we know so far, we need to write the equation as a function of one variable

More information

BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: Unlimited and Continuous! (21 points)

BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: Unlimited and Continuous! (21 points) BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: United and Continuous! ( points) For #- below, find the its, if they eist.(#- are pt each) ) 7 ) 9 9 ) 5 ) 8 For #5-7, eplain why

More information

Name: Date: Block: Quarter 2 Summative Assessment Revision #1

Name: Date: Block: Quarter 2 Summative Assessment Revision #1 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

More information

PERT Practice Test #2

PERT Practice Test #2 Class: Date: PERT Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. Ê 1. What is the quotient of 6y 6 9y 4 + 12y 2 ˆ Ê 3y 2 ˆ? a. 2y 4 + 3y

More information

n th Roots and Rational Exponents (Part I) Read 5.1 Examples 1-3

n th Roots and Rational Exponents (Part I) Read 5.1 Examples 1-3 HW # n th Roots and Rational Exponents (Part I) Read. Examples - Section. s a. Vocabulary Rewrite the expression t in radical form. Then state the index of the radical.. Complete the Sentence For an integer

More information

*Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P.

*Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P. The Derivative & Tangent Line Problem *Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P. 1 The Derivative & Tangent Line Problem We can approximate using

More information

Final Exam Review Packet

Final Exam Review Packet Final Exam Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to scale. 6 8 a.

More information

AP Calculus AB Chapter 2 Test Review #1

AP Calculus AB Chapter 2 Test Review #1 AP Calculus AB Chapter Test Review # Open-Ended Practice Problems:. Nicole just loves drinking chocolate milk out of her special cone cup which has a radius of inches and a height of 8 inches. Nicole pours

More information

Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question.

Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question. Review Unit 3 1201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers is not both a perfect square and a perfect cube? a. 531

More information

Stewart - Calculus 8e Chapter 2 Form A. 1. Differentiate. 2. Find the limit. 3. Differentiate.

Stewart - Calculus 8e Chapter 2 Form A. 1. Differentiate. 2. Find the limit. 3. Differentiate. Stewart - Calculus 8e Chapter 2 Form A Multivariable Calculus 8th Edition Stewart TEST BANK Full clear download at: https://testbankreal.com/download/multivariable-calculus-8th-editionstewart-test-bank/

More information

MATH 2413 TEST ON CHAPTER 4 ANSWER ALL QUESTIONS. TIME 1.5 HRS

MATH 2413 TEST ON CHAPTER 4 ANSWER ALL QUESTIONS. TIME 1.5 HRS MATH 1 TEST ON CHAPTER ANSWER ALL QUESTIONS. TIME 1. HRS M1c Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the general solution of the differential

More information

Section 2.1 Intercepts and symmetry. #1 4: Find the x and y-intercepts

Section 2.1 Intercepts and symmetry. #1 4: Find the x and y-intercepts Section 2.1 Intercepts and symmetry #1 4: Find the x and y-intercepts 1) 2) 3) Section 2.1 Intercepts and symmetry 4) #5-18: Find the x and y-intercepts. 5) 3x - 6y = 24 6) 2x + 4y = 12 7) y 2 = x + 9

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

Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree.

Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree. Ch. 9 Test - Geo H. Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree. 1. 2. 3. a. about 58.0 c. about 1.0 b. about 49.4 d. about 32.0 a. about 52.2

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 (BC) Summer Assignment (169 points)

AP Calculus (BC) Summer Assignment (169 points) AP Calculus (BC) Summer Assignment (69 points) This packet is a review of some Precalculus topics and some Calculus topics. It is to be done NEATLY and on a SEPARATE sheet of paper. Use your discretion

More information

Module 5 Study Guide--Linear Functions

Module 5 Study Guide--Linear Functions Module Stud Guide--Linear Functions The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation.. The table shows the cost of a ski rental

More information

Algebra II Final Exam Semester II Practice Test

Algebra II Final Exam Semester II Practice Test Name: Class: Date: Algebra II Final Exam Semester II Practice Test 1. (10 points) A bacteria population starts at,03 and decreases at about 15% per day. Write a function representing the number of bacteria

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

Algebra 1 First Semester Exam Answer Section

Algebra 1 First Semester Exam Answer Section Algebra 1 First Semester Exam Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Level B REF: MALG0086 TOP: Lesson 1.2 Apply Order of Operations KEY: whole variable evaluate substitute rational expression

More information

lim 2 x lim lim sin 3 (9) l)

lim 2 x lim lim sin 3 (9) l) MAC FINAL EXAM REVIEW. Find each of the following its if it eists, a) ( 5). (7) b). c). ( 5 ) d). () (/) e) (/) f) (-) sin g) () h) 5 5 5. DNE i) (/) j) (-/) 7 8 k) m) ( ) (9) l) n) sin sin( ) 7 o) DNE

More information

CHANCE Program. Admissions Mathematics Practice Test. Part One will test your background in basic arithmetic, while Part Two will cover basic algebra.

CHANCE Program. Admissions Mathematics Practice Test. Part One will test your background in basic arithmetic, while Part Two will cover basic algebra. CHANCE Program Admissions Mathematics Practice Test Part One will test your background in basic arithmetic, while Part Two will cover basic algebra. Each part of the test has 30 questions and has been

More information

APPLICATIONS OF DERIVATIVES UNIT PROBLEM SETS

APPLICATIONS OF DERIVATIVES UNIT PROBLEM SETS APPLICATIONS OF DERIVATIVES UNIT PROBLEM SETS PROBLEM SET #1 Related Rates ***Calculators Allowed*** 1. An oil tanker spills oil that spreads in a circular pattern whose radius increases at the rate of

More information

4.1 Related Rates Goal: 1. Understand how variables change with respect to time. 2. Understand "with respect to".

4.1 Related Rates Goal: 1. Understand how variables change with respect to time. 2. Understand with respect to. Goal: 1. Understand how variables change with respect to time. 2. Understand "with respect to". Study 4.1, # 1 7, 11, 17, 19, 23, 25, 29, 35 water drop ripples pour cement high rise @ 1:30 water drop ripples

More information

MAT 210 TEST 2 REVIEW (Ch 12 and 13)

MAT 210 TEST 2 REVIEW (Ch 12 and 13) Class: Date: MAT 0 TEST REVIEW (Ch and ) Multiple Choice Identify the choice that best completes the statement or answers the question.. The population P is currently 0,000 and growing at a rate of 7,000

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

Distributive Property, Expressions, and Equations Study Guide

Distributive Property, Expressions, and Equations Study Guide Distributive Property, Expressions, and Equations Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which word phrase could represent the variable

More information

1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and

1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and Practice Test 2 Numeric Response 1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and with in QIII 2. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and

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

Chapter 1 Test Review

Chapter 1 Test Review Name Per ID: A Chapter 1 Test Review Short Answer Insert , or = to make the sentence true. 1. 7 12 2. 5 9 1 8 3. 16 + 6 8 + 7 Name the property of real numbers illustrated by the equation. 4. 2(x +

More information

Mesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc. Page 1 of 44

Mesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc.   Page 1 of 44 Mesa Public Schools Assessment Summary: Q3 practice test Powered by SchoolCity Inc. www.schoolcity.com Page 1 of 44 Assessment Summary: Q3 practice test Year: 2016-2017 Subject: Math Total Items: 43 Total

More information

the distance from the top to the bottom of an object height a measurement of how heavy something is weight

the distance from the top to the bottom of an object height a measurement of how heavy something is weight height the distance from the top to the bottom of an object weight a measurement of how heavy something is length the distance from one side of an object to another measure to find the number that shows

More information

North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry

North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry Name: Class: _ Date: _ North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the

More information

Created by T. Madas. Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications.

Created by T. Madas. Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications. IYGB Special Paper Q Time: 3 hours 30 minutes Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications. Information for Candidates This practice paper follows

More information

Math 1131Q Section 10

Math 1131Q Section 10 Math 1131Q Section 10 Section 3.9 and 3.10 Oct 19, 2010 Find the derivative of ln 3 5 e 2 ln 3 5 e 2 = ln 3 + ln 5/2 + ln e 2 = 3 ln + ( 5 ) ln + 2 2 (ln 3 5 e 2 ) = 3 + 5 2 + 2 Find the derivative of

More information

Algebra 2 Summer Math Answer Section

Algebra 2 Summer Math Answer Section Algebra 2 Summer Math Answer Section 1. ANS: A PTS: 1 DIF: Level B REF: MALG0064 STA: SC.HSCS.MTH.00.AL1.A1.I.C.4 TOP: Lesson 1.1 Evaluate Expressions KEY: word volume cube area solid 2. ANS: C PTS: 1

More information

Honors Algebra 2 Quarterly #3 Review

Honors Algebra 2 Quarterly #3 Review Name: Class: Date: ID: A Honors Algebra Quarterly #3 Review Mr. Barr Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the expression. 1. (3 + i) +

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine algebraically whether the function is even, odd, or neither even nor odd. ) f(x)

More information

Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive:

Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: a) (x 3 y 6 ) 3 x 4 y 5 = b) 4x 2 (3y) 2 (6x 3 y 4 ) 2 = 2. (2pts) Convert to

More information

Ï ( ) Ì ÓÔ. Math 2413 FRsu11. Short Answer. 1. Complete the table and use the result to estimate the limit. lim x 3. x 2 16x+ 39

Ï ( ) Ì ÓÔ. Math 2413 FRsu11. Short Answer. 1. Complete the table and use the result to estimate the limit. lim x 3. x 2 16x+ 39 Math 43 FRsu Short Answer. Complete the table and use the result to estimate the it. x 3 x 3 x 6x+ 39. Let f x x.9.99.999 3.00 3.0 3. f(x) Ï ( ) Ô = x + 5, x Ì ÓÔ., x = Determine the following it. (Hint:

More information

Chapter 3 Algebra (pearson)

Chapter 3 Algebra (pearson) Class: Date: Chapter 3 Algebra (pearson) What inequality represents the verbal expression? 1. 8 less than a number n is less than 13 a. 8 n < 13 c. n 8 < 13 b. 13 8 < n d. 13 < 8 n Which number is a solution

More information

1. sin 2. Honors Pre-Calculus Final Exam Review 2 nd semester June TRIGONOMETRY Solve for 0 2. without using a calculator: 2. csc 2 3.

1. sin 2. Honors Pre-Calculus Final Exam Review 2 nd semester June TRIGONOMETRY Solve for 0 2. without using a calculator: 2. csc 2 3. Honors Pre-Calculus Name: Final Eam Review nd semester June 05 TRIGONOMETRY Solve for 0 without using a calculator:. sin. csc. tan. cos ) ) ) ) Solve for in degrees giving all solutions. 5. sin 6. cos

More information

Exam 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find dy/dx by implicit differentiation. x3 + y3 = 5 A)

More information

5.1 Practice A. Name Date ( ) 23 15, , x = 20. ( ) 2

5.1 Practice A. Name Date ( ) 23 15, , x = 20. ( ) 2 Name Date. Practice A In Exercises, find the indicated real nth root(s) of a.. n =, a =. n =, a = 9. n =, a = 8 In Exercises 9, evaluate the expression without using a calculator.. 7. 6 8. ( ) 7. 6 6.

More information

Algebra 1a Final Exam Review

Algebra 1a Final Exam Review Algebra 1a Final Exam 2016-2017 Review Short Answer Graph the inequality. 1. x < 1 2. Solve the inequality. Then graph your solution. 3. 4. 5. 5 8 v < 7 5 6. 7. 8. 10 < 3x 7 < 17 9. Solve the inequality.

More information

Algebra Chapter 4 (pearson) review

Algebra Chapter 4 (pearson) review Class: Date: Algebra Chapter 4 (pearson) review What are the variables in each graph? Describe how the variables are related at various points on the graph. 1. The graph shows the height of a hiker above

More information

1. Use. What are the vertices of A.,, B.,, C.,, D.,,

1. Use. What are the vertices of A.,, B.,, C.,, D.,, 1. Use. What are the vertices of A.,, B.,, C.,, D.,, 2. Given, how are the distances to the origin from each image point related to the distance to the origin from each corresponding preimage point? A.

More information

Problem 1. What is the force between two small charged spheres that have charges of C and C and are placed 30 cm apart in air?

Problem 1. What is the force between two small charged spheres that have charges of C and C and are placed 30 cm apart in air? 5. NAME: Problem 1. What is the force between two small charged spheres that have charges of 2 10 7 C and 3 10 7 C and are placed 30 cm apart in air? 2. What is the value of charge of a body that carries

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