Everything You Need to Know for Calc Bc

Your guide to the 2022 AP Calculus BC exam

Nosotros know that studying for your AP exams tin exist stressful, but Fiveable has your back! We have created a study plan that will help you crush your calculus BC exam. Nosotros will go along to update this guide with more data almost the 2022 exams, as well as helpful resources to assistance y'all score that v.

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Format of the 2022 AP Calculus BC exam

This year, all AP exams will embrace all units and essay types. The 2022 Calculus BC exam format will be:

• Section 1: Multiple Pick - 50% of your full score

• 45 questions in 1 hr 45 mins

• Part A: 30 questions in sixty minutes (computer not permitted).

• Part B: 15 questions in 45 minutes (graphing calculator required).

• Section ii: Gratuitous Response - 50% of your total score

• 6 questions in i 60 minutes 30 mins

• Part A: ii questions in 30 minutes (graphing computer required).

• Part B: four questions in 60 minutes (reckoner non permitted).

Bank check out our study plan below to find resources and tools to prepare for your AP Calculus BC examination.

When is the 2022 AP Calculus BC exam and how do I take it?

The exam is on paper, in schoolhouse, on Monday, May 9, 2022, at 8 AM, your local time.

.

How should I fix for the examination?

• First, download the

  AP Calculus Cram Chart PDF

  - a single sheet that covers everything you need to know at a high level. Take annotation of your strengths and weaknesses!

• Review every unit and question type, and focus on the areas that need the virtually comeback and practice. We've put together this program to help you written report between now and May. This will embrace all of the units and essay types to prepare y'all for your exam

• Practise problems are your all-time friends! Both the FRQs and MCQs had several questions that were similar to

  previous FRQs

  and the open-sourced multiple-choice questions on College Board (essentially the same questions with unlike numbers).

• Join Hours 🤝to talk to existent students simply similar you studying for this exam! We have TAs in each subject aqueduct to back up yous this Spring.

• Finally, bank check out our cram replays

  so that y'all can review for the AP Calc examination with a rockstar teacher!

Resources:

Pre-work: set your study environment

Before we begin, take some time to get organized. Remote learning tin can be bully, but information technology also ways yous'll demand to hold yourself answerable more than usual.

🖥 Create a study space.

Make sure y'all have a designated place at home to written report. Somewhere you lot can proceed all of your materials, where you can focus on learning, and where you are comfortable. Spend some time prepping the infinite with everything you need and you can even let others in the family know that this is your written report space.

📚 Organize your study materials.

Get your notebook, textbook, prep books, or whatever other physical materials you take. Also create a space for you to go on track of review. Start a new department in your notebook to have notes or beginning a Google Doc to keep track of your notes. Get yourself gear up up!

📅 Programme designated times for studying.

The hardest part about studying from home is sticking to a routine. Decide on ane hour every solar day that you tin can dedicate to studying. This tin can be any fourth dimension of the day, whatever works best for you. Set a timer on your phone for that time and really try to stick to it. The routine will aid you stay on track.

🏆 Decide on an accountability programme.

How will you lot hold yourself answerable to this study plan? You may or may not have a teacher or rules set to help you stay on rail, then you demand to ready some for yourself. First set your goal. This could be studying for 10 number of hours or getting through a unit. Then, create a advantage for yourself. If y'all reach your goal, then x. This will help stay focused!

🤝 Get back up from your peers.

There are thousands of students all over the globe who are preparing for their AP exams just like y'all! Join Hours 🤝 to chat, ask questions, and see other students who are likewise studying for the jump exams. You can fifty-fifty build study groups and review material together!

AP Calculus BC 2022 Study Programme

👑 UNIT 1: Limits and Continuity

Big takeaways:

Unit one is the basic idea of all of Calculus. The limit is the concept that makes everything click. You inquire someone what they learned in calculus, and they will most likely answer "derivatives and integrals". These limits help u.s.a. to sympathize what is happening to a role as we arroyo a specific betoken. Limits can be one or two-sided, but the sides accept to match in social club for the limit from both directions to be! Well without the limit we wouldn't have either. A major concept used throughout the curriculum and within theorems is continuity. We prove continuity using limits and learn how to do that within this unit. We also learn about the Intermediate Value Theorem and the Squeeze Theorem, although this topic about likely won't be directly tested on this year's exam, it'southward the staff of life and butter of what'southward to come.

✨Content to Focus On:

• Methods of Finding Limits

• From a table - Be able to judge values not given in a table past using values that were given in a table.

• From a graph - Be able to use a graph to interpret a limit at an x value.

• Algebraically

• Limit Properties

• Rationalization

• Some limits expect unsolvable, (0/0 or ∞/∞), but using algebraic manipulation, y'all can solve them! In unit 4 we learn about another helpful tool for this, L'Hospital's rule!

• Infinite Limits

• Squeeze Theorem

• The squeeze theorem helps us to find limits of functions that nosotros do not know, past using the limits of a function that is greater than or equal to and a office that is less than or equal to. If nosotros can observe the limits of those ii functions, and they are equal, so our part should accept that limit likewise!

• Continuity and Discontinuity

• Students should be able to prove if a function is continuous equally a point, and know the unlike types of discontinuity! Removable, jump, infinite.

• First existence theorem: Intermediate Value Theorem

  • This theorem helps usa to bear witness points that exist given sure data. Don't forget to always state or show the conditions! In this case, it would be that the function is continuous on [a, b].

Resources:

🎥Spotter these videos:

• Graphical Limits: FInding limits given a graph.

• Algebraic Limits: How do you find a limit?

• Continuity Function I & II: Defining a continuous function

• Limits at Infinity: Using limits at infinity to demonstrate function behavior

• Working with the Intermediate Value Theorem: At that place are two theorems that are related to Unit of measurement i: The Intermediate Value Theorem and The Farthermost Value Theorem. Learn about the Intermediate Value Theorem hither.

📚Read these study guides (Especially 1.three-1.16)

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🤓 UNIT 2: Differentiation: Definition and Basic Derivative Rules

Big takeaways:

Unit 2 introduces the first of the ii major halves of calculus: differentiation, or the instantaneous rate of change of a office. We beginning off with defining the derivative and applying it to our old friend, the limit. This unit of measurement also sets upward the rules so that yous can figure out the derivative of the simplest functions you lot will find on the FRQ section! Derivatives assist u.s.a. determine instantaneous rates of change. Nosotros will discuss the difference between boilerplate and instantaneous rates of change and how they announced differently. One thing is for sure, yous should still follow the order of operations!

✨Content to Focus On:

• Boilerplate Rate of Modify vs Instantaneous Charge per unit of Change

• If we utilize a limit to an average rate of change, nosotros are looking at an instantaneous charge per unit of change!

• Definition of the Derivative

• A long time ago, before nosotros learned the power rule, etc, for the derivative, we learned how to solve the instantaneous rate of modify using the limit definition of a derivative.

• Estimating The Derivative

• Connecting differentiability and continuity. Remember, differentiability implies continuity, just non the other way effectually! Brand sure you know how to tell if a function is differentiable. No cusps or corners, polynomials are always differentiable!

• Finding Simple Derivatives

• Power Dominion

• Derivative Backdrop

• Trigonometric Derivatives

• Exponential and Logarithmic Derivatives

• **While this year it may not be necessary to memorize certain derivatives like natural log or tangent, using fourth dimension out of your exam time to look them up tin be costly! Brand certain you are yet on your game when information technology comes to the derivatives you need to know.

• Production and Quotient Rules

Resources to utilise:

🎥Watch these videos:

• The Limit Definition of the Derivative: The derivative from first principles

• Introduction to Finding Derivatives: The power rule and trigonometric derivatives, a must-watch!

• The Production and Caliber Rules: The product and power rules, a powerful tool in your derivative-finding toolkit!

• Practicing Derivative Rules: Applying what y'all've learned in finding derivatives so far!

📚Read these study guides.

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🤙🏽 UNIT 3: Differentiation: Composite, Implicit & Inverse Functions

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Big takeaways:

In Unit of measurement 3, we expand on the methods of finding derivatives from Unit 2 in order to evaluate whatever derivative that the Collegeboard tin can throw at y'all! This department includes the very important chain rule. Implicit differentiation is a big takeaway from this unit. It allows u.s.a. to find derivatives of whatever variable when we may exist finding the derivative with respect to something else.

✨Content to Focus On:

• Concatenation Rule

• The concatenation rule allows us to differentiate composite functions. But make certain y'all encounter every function! Sometimes the chain dominion tin can be more one chain! For example: (sin(x2))2. We accept 3 functions to consider hither!

• Implicit Differentiation

• Implicit differentiation gives us the tools to derive any variable with respect to any variable. The main concept is that if the variable you are deriving is not the same equally the variable you are taking the derivative of, the concatenation rule applies and you must also multiply by the derivative of that variable. For instance, the derivative of y2with respect to x is 2ydydx.

• Derivatives of Inverse Functions (Including Trigonometric Functions)

• Remember how to find an changed? Switch x and y and solve for y? Well and so take the derivative of that!, or follow the formula we have! The important part to think on problems like this is the ten and y values. If you are supposed to be using the x value of an inverse part, that means information technology was the y-value of your original function!

Resources to use:

🎥Scout these videos:

• The Chain Rule: The chain rule, used to evaluate the derivative of composite functions, very important!

• Implicit Derivatives: Derivatives of implicitly defined functions/curves

• Practicing Derivative Rules Ii: Applying what yous take learned through the previous ii units!

• Using Tables to Discover Derivatives: Finding derivatives when the equation may non be nowadays

📚Read these report guides

Resources:

👀 Unit 4: Contextual Applications of Differentiation

Big takeaways:

Unit 4 allows y'all to apply the derivative in different contexts, nigh of which accept to exercise with dissimilar rates of modify. You will too larn how to solve problems containing multiple rates, how to estimate values of functions, and how to notice some limits you may not have known how to solve before! Related rates are a very popular topic in the FRQ section of the exam. Information technology is very of import you label every variable yous use! Limits yous may non accept been able to know how to solve before yous can at present solve using L'Hospital's rule, but make sure you know the requirements!

✨Content to Focus On:

• Rates of Change

• Position, Velocity, Acceleration

• Velocity is the derivative of position, and acceleration is the derivative of velocity. Velocity has a direction. If the velocity and acceleration match signs, the particle is speeding upwardly. If their signs are contrary, the particle is slowing down. Speed is the absolute value of velocity and has no management. On the AP test, you tin exist asked to map out the path of a particle, which direction it is going, and if it is speeding upward or slowing down.

• Related Rates

• Related Rates take to do with nothing other than relating rates! There are a set up of steps to follow when solving a related rate:

• 1. Assign letters to quantities and characterization their derivatives with respect to time. If A=surface area, and so dA/dt would be the rate of modify of the expanse.
• 2. Place the rates that are known and the rate that needs to be institute.
• three. Find an equation that relates the variables whose rates of modify y'all need in step 2. Describe a motion-picture show to help you detect this equation!
• 4. Differentiate the equation with respect to fourth dimension. Remember it is necessary to recollect about this every bit implicit differentiation.
• 5.  Substitute in all known values and variables, and solve for the unknown rate of change.
• One special blazon of related charge per unit is that of a cone. You lot should practise a related rate problem with a cone, because information technology is necessary to write r, the radius, in terms of h before differentiating.

• Linearization and Tangent Line Approximations

• In these types of problems, we use a tangent line approximation for 1 value that we know and use it to approximate another very close value. Let twenty-four hours, x0 is the one we know about, and x1 is the one we need. Then we would apply: f(x1)-f(x0)=f'(x0)(x1–x0) to find f(x1).

• 50'Hopital'due south Rule

• When using Fifty'Hospital's rule, we have a few things we demand to remember! To use L'Infirmary'due south dominion, your limit needs to exist in 1 of two forms: 0/0 or ∞/∞. To show this in a free-response question, you demand to show the limits in the numerator and the denominator goes to either 0 or infinity carve up from each other, so you can use Fifty'Infirmary's rule, which says: xaf(x)g(10)=xaf'(x)g'(x).

Resources to use:

🎥Watch this video:

• Related Rates: How to solve related rates issues

📚Read these study guides (Emphasize iv.2, 4.5-four.7)

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✨ UNIT 5: Analytical Applications of Differentiation

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Big takeaways:

Unit 5 continues our discussion on the applications of derivatives, this time looking at graphs and how the value of the first and 2nd derivatives of a graph influences its behavior. We volition review two of the three existence theorems, the mean and extreme value theorems. Nosotros'll besides learn how to solve another type of trouble commonly seen in the real earth (and as well on FRQ issues): optimization bug.

✨Content to Focus On:

• Ii of the three Existence Theorems

• It is important when using theorems to brand sure their weather are met before you lot use them!

• Mean Value Theorem

• In order to employ the Mean Value Theorem, the functions must be continuous on a closed interval and differentiable on that same interval, but open. Once you tin say for sure that these things are truthful, the mean value theorem tells usa that there must exist a betoken in that interval where the average rate of alter equals the instantaneous rate of change, or the derivative, at a point within the interval. f'(c)=f(b)-f(a)b-a.

• Extreme Value Theorem

• For this being theorem, the status is that the function continuous on a finite closed interval. If it is, that means there must be an absolute maximum and an accented minimum.

• Increasing/Decreasing Functions and The Start Derivative

• If the derivative of a function is positive, then the part is increasing! If the derivative is negative, then the function is decreasing!

• Local and Global Extrema

• Beginning and Second Derivative Tests for Local Extrema

• Candidates Test for Global Extrema

• Concavity, Inflection Points, and The Second Derivatives

• If the second derivative is positive, the office will be concave up. If the second derivative is negative, the function will be concave down. Whenever the second derivative changes sign, there will be an inflection betoken, a modify in concavity, on the original function.

• Curve/Derivative Sketching

• All of the information you learned from how the beginning and 2d derivatives relate to the original function can assist you to sketch graphs based on the information y'all have about their derivatives!

• Optimization Problems

• These are as well known as applied maximum and minimum problems. These are problems well-nigh finding an absolute maximum and an absolute minimum in an applied situation. When trying to detect an absolute max or min, y'all must discover all critical points (f'(x)=0 or undefined). So plug those and the endpoints into the original role to notice out which has the highest or lowest value, depending on what yous are looking for.

Resources to use:

🎥Watch these videos:

• Interpreting Derivatives Through Graphs: Graphical estimation of derivatives

• Existence Theorems: Mean Value Theorem, Extreme Value Theorem, Intermediate Value Theorem

• Increasing and Decreasing Functions: Using the first derivative to testify where function increases and decreases

• Concavity: Using the 2nd derivative to find concavity

• f, f', and f": Relating a function and its

• Optimization Problems: How to solve optimization problems

📚Read these study guides

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🔥 UNIT 6: Integration and Accumulation of Change

Big takeaways:

Unit of measurement 6 introduces united states to the integral! We volition learn about the integral first every bit terms of an area and Reimann sums, and then working into the fundamental theorem of calculus and the integral'due south relationship with the derivative. Nosotros will learn nearly the definite integral and the indefinite integral. We learned about methods of integration from bones rules to substitution. In BC, there are also the methods of integration past parts, fractional fractions, and improper integrals. In some cases, the integral is called the antiderivative, and if f is the function, then F would be the antiderivative of that function.

✨Content to Focus On:

• Approximating an integral equally an area

• When given a graph, nosotros can find the area under the curve and between the x-axis to find the integral. Nevertheless, if an area is underneath the 10-axis, that would be considered negative.

• Riemann Sums

• A mode of evaluating an area under a bend by making rectangles to find the area and calculation them up. This is useful with a table of values or with a curve that we do not know the verbal surface area of its shape. At that place are iv kinds: Left, Right, Midpoint, and Trapezoidal sum. Depending on the office, these may exist over or underestimates of the actual area.

• Students should also be able to write a Reimann sum in summation notation and integral notation.

• The Central Theorem of Calculus

• This theorem tells us two very important things:

• abf(x)dx=F(b)-F(a)

• ddx(axf(t)dt)=f(x), where a is a abiding.

• Nosotros employ this theorem very often when working with integrals.

• Definite vs. Indefinite Integrals

• Integrals must ever include a dx (if not x, whichever variable you are using) at the end.

• If an integral is indefinite, it has no premises. This means information technology cannot be evaluated using the fundamental theorem of calculus. Instead, nosotros add on a +C, to go far know that there could accept been a constant at the terminate of the function and that there are lots of possibilities for what that constant would exist.

• Definite integrals take bounds, and we use the fundamental theorem of calculus often with them. The bounds let us know the endpoints of the integral, or in terms of a graph, what 2 points we are finding the area under the bend betwixt.

• Integral Rules

• Brand certain you lot call up how to integrate and its connection to deriving!

• You lot can check an integral past taking its derivative to see if you get back to where yous started.

• U-Substitution

• When you have a composition of functions in an integral, it is necessary to use u-exchange to make sure you are integrating each part. It is ordinarily the inside office that is called. Sometimes it can be hard to tell. You will know once y'all try! If you discover yourself going in circles and needing to substitute more than, I would attempt using a different piece of the office as u.

• Integrating using integration past parts

• Integration by parts y'all tin can utilize when you are multiplying two functions, information technology looks like this:

• udv=uv-vdu.

• When trying to figure out which function to prioritize every bit u, make sure to go to this helpful order:

• LIPET (Logs, Inverse Trig, Polynomials, Exponentials, Trig). Whichever one appears outset, use that for u, and then use the other for dv. Find du and 5, and plug-in from there!

• Integrating using partial fraction decomposition

• This is helpful when dealing with a rational role in your integral. The denominator should be a higher power than the numerator to use this. It helps turn terms into sums of ratios of linear nonrepeating decimals that are integrable.

• Evaluating Improper Integrals

• An improper integral has one or both limits at infinity. In society to integrate these, we denote that infinite bound equally a variable, a, and take the limit as a approaches infinity of the integral of our office. The fundamental theorem of calculus really helps us here!

Resources to utilise:

🎥Watch these videos:

• The Cardinal Theorem of Calculus: Explains the Primal Theorem of Calculus and its uses as the nigh important theorem in calculus

• Some Integration Techniques: How to exercise integration techniques found in Calculus AB

📚Read these report guides

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💎 UNIT seven: Differential Equations

Large takeaways:

Unit seven takes us to a great connection between integrals and derivatives in differential equations. We will learn how to model and solve differential equations using initial conditions. This ever requires the separation of variables when it comes to free-response questions! We will likewise larn how to identify differential equations from their slope fields and how to draw those fields too. BC Calculus adds in Euler'southward method and logistic models in this unit.

✨Content to Focus On:

• Differential Equations

• Modeling

• If you are given information, can you write a differential equation from information technology?

• Verifying Solutions

• Beingness able to plug in given information and deduce if the solution is true.

• Separation of variables

• This often appears in the FRQ section. Students are given a differential equation and demand to put all of the terms for one variable on one side and for the other variable on the other, then they integrate both sides and solve for y, usually y, but really whichever the dependent variable it.

• NOTE: If you skip the step of separating variables on AP exams in the past, they have offered you no credit for the rest of that section of the problem.

• Using initial conditions

• In one case you have done your separation of variables, don't forget to accept a +C! This is where the initial status comes in. You lot plug in the terms given from ten and y in your initial status, then you solve for C, rewriting the part at the terminate with C plugged in!

• Slope fields

• Gradient fields are coordinate planes of ane by 1 sections of slopes at each 10 and y value. If given a differential equation and asked to find a slope field, you plug in an ten and y pair into the differential equation, the value it outputs is the slope at the point, and is the steepness you used to draw a line at that detail pair.

BC Only

• Euler'south Method

• This is some other method for approximating a solution to a differential equation or a point on a solution curve.

• Logistic Models with Differential Equations

• This is a joint proportional differential equation. dy/dt=ky(a-y). Y'all can interpret the initial status and the differential equation without solving the differential equation.

• The limiting value, likewise known as the carrying capacity, tin exist determined using a logistic growth model.

• The logistic growth model can also exist used to determine the value of the dependent variable in the logistic differential equation at the point when information technology is irresolute the fastest.

Resources to apply:

🎥Watch this video:

• Separable Differential Equations: How to solve separable differential equations

📚Read these study guides

Resources:

🐶 UNIT viii: Applications of Integration

Large takeaways:

Unit 8 teaches u.s. more useful applications of the integral as nosotros enter the 3D graph world! We learn how to find the boilerplate value of a function and the particle move co-ordinate to an integral. BC Calculus too adds in the arc length here! Nosotros also use cross-sections and disks and washers to find the volume of shapes as functions are revolved around either a vertical or horizontal line. We put our spatial reasoning and geometry skills to utilize in this section.

✨Content to Focus On:

• Average Value of a function

• The average value of a office is denoted by 1b-aabf(x)dx. Nosotros can only find the boilerplate value of a function that nosotros have a definite integral for.

• Position, Velocity, Acceleration

• Position is the integral of velocity, and velocity is the integral of acceleration! If yous take the accented value of velocity, you are able to find speed.

• Distance, the integral of the absolute value of velocity

• Displacement, the integral of velocity

• To remember this, I think nearly a track! Later ane lap around, your altitude is 400 m, but your displacement is 0. Brand sure if you are asked for distance, you lot think to utilise absolute value!

• Finding the surface area between curves

• If given 2 curves on a coordinate plane and endpoints, students should exist able to integrate those functions, either with respect to the x or y-centrality, in guild to determine the area betwixt them. When talking about the 10-axis, all functions should be in terms of x, the premises should be in terms of x, and it will be the integral of the upper functions minus the lower. When talking about with respect to the y-axis, all functions should be in terms of y, the premises should exist in terms of y, and information technology will be an integral of an outer function minus the inner.

• Finding the area betwixt curves that intersect at more than two points.

• Sometimes, your function will have different parts where you may need to split the area and add your answers together, because the upper functions changes or some other function changes.

• When in dubiety, break it upward into pieces, you lot know how to work with, and add those together.

• The expanse nether the x-axis is already accounted for as negative when evaluating using an integral, then don't worry virtually that!

• Volumes of cross-sections

• When using cross-sections, yous integrate the area of whatsoever shape is given to you (this could be a square, rectangle, triangle, or semicircle).

• You will integrate the surface area on a given interval, but it is important that you interpret the function for the variable in the shape that it represents.

• If it says perpendicular to the x-axis, all should be in terms of x.

• Perpendicular to the y-axis, all should exist in terms of y.

• Volumes by disks and washers

• In this example, nosotros are integrating an area again, but this time the shape will always exist a circle, so we will ever be using the expanse formula for a circle. The variable that changes hither is r, the radius, which you tin interpret using the role.

• If the rotation is around merely the x-axis, all should be in terms of 10 (premises and functions) and the radius volition be your office.

• If the rotation is around just the y-axis, all should be in terms of y (bounds and functions) and the radius volition exist your part.

• If it is rotated around any other vertical or horizontal line, you may need to add together or subtract value from your function to find the radius.

• A washer is when two functions are used, and you must decrease out the volume the inner function would have added into your full volume to account for the missing piece.

• Arc Length

• BC Students are also required to know how to find the arc length of a polish, planar curve and distance traveled.

• A definite integral can be used to calculate this. due south(x)=ax1+[f'(t)]2dt.

Resource to use:

🎥Watch these videos:

• Interpreting the Meaning of the Derivative and the Integral: Showing derivatives and integrals applied in different contexts

• Position, Velocity, and Acceleration: Exploring the relationship between position, velocity, and acceleration

📚Read these study guides

Resources:

🦖 UNIT 9: Parametric Equations, Polar Coordinates & Vector-Valued Functions

Big takeaways:

Unit 9 is only BC, and we'll acquire most parametric functions and polar functions. Nosotros'll be expected to solve parametrically defined functions, vector-valued functions, and polar curves using practical cognition of differentiation and integration.

✨Content to Focus On:

• nine.1: Defining and Differentiating Parametric Equations

• Parametric functions are a set of related functions where x and y are independent of each other but continued using the variable t.

• ten(t)=t^2-ane, y(t)=3t

• To find the slope of the tangent line, nosotros need to find dy/dx

• nine.4 Defining and Differentiating Vector-Valued Functions

• Parametric functions are associated with time and are more often than not used to calculate motion and velocity.

• Each point on a vector-valued function is determined past a position vector, a vector that starts at the origin.

• Vector-valued functions tell us how much the particle is moving in the management of ten and how much it is moving in the direction of y.

• 9.7: Defining Polar Coordinates and Differentiating in Polar Course

• Polar functions are functions that are graphed around a pole in a circular arrangement and with the points (r, theta) instead of (x, y).

• The slope of the tangent lines for polar functions can be found using the formula dy/dx = (rcos(theta)+(dx/d(theta))sin(theta))/(-rsin(theta)+cos(theta)(dx/d(theta))

• 9.nine: Finding the Area of the Region Bounded by Ii Polar Curves

• To find the expanse between ii curves, you lot subtract "outer minus inner".

• Arc length for polar functions can be found using the formula

Resources to Use:

📚Read these written report guides .

Resources:

♾ UNIT 10: Infinite Sequences and Series

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Big takeaways:

Unit of measurement 10 is only BC and covers many topics under the umbrella of sequences and serial. We learn how series tin can diverge or diverge and how to know. We larn many dissimilar types of convergence tests along with many dissimilar types of series! This twelvemonth some sections have been taken out to account for what you may have learned so far in class. We outline those specific sections to focus on beneath.

✨Content to Focus On:

• 10.2: Working with geometric series

• A geometric series has a abiding ratio betwixt successive terms.

• n=0arn=a1-r, and r>0

• If r<1, and so the series converges but diverges otherwise.

• 10.5 Harmonic Series and p-series

• This department includes the harmonic series, the alternating harmonic series, and the p-serial.

• The harmonic series is a divergent infinite series. k=11k. This class should exist familiar to you lot.

• The alternating harmonic series converges conditionally. yard=1(-i)k-1k because this series converges, merely the absolute value of its series, the harmonic series, does not.

• P series is whatsoever serial in the form n=101np. If p is greater than 1, it converges. Otherwise, information technology diverges!

• ten.seven: Alternating series exam for convergence

• An alternating series is one that changes sign, and so information technology is in the course an=(-one)n+1bn where bn>0 for all n and bn is decreasing, and nbn =0, then n=1an converges.

• This ways you need to observe nbn. If it is zip and all of the other weather condition are met, you accept a convergent series.

• 10.8: Ratio Examination for Convergence

• The ratio test compares a term from the series to a different value in the serial by taking its limit.

• If our serial is and then to apply the ratio test, nosotros want to find L, where L=nan+1an. If 50 < i, the serial is absolutely convergent. If L > i, the series is divergent, if L=1, we accept more than work to do, because the series could still exist divergent, conditionally convergent, or absolutely convergent.

NOTE: These are the only tests for convergence that are on the AP exam. If asked explicitly to use them, you lot should! If you are told to effigy out whether a series is convergent or non and not given a specific method, feel gratuitous to use another method y'all learned even if information technology is not on the test.

• 10.11: Finding Taylor Polynomial Approximation of Functions

• A Taylor polynomial centered at x=a can be found using this form:

f(x)=f(a)+f'(a)(x-a)+f"(a)(x-a)22!+f"'(a)(x-a)33!+…..+f(n)(a)(x-a)nn!.

• These Taylor polynomials can exist used to estimate function values near x=a.

• The more terms yous find in an nth caste Taylor polynomial, the closer you are to approximating the bodily function.

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Resources:

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Source: https://library.fiveable.me/ap-calc/finals-and-exam-prep/2022-ap-calculus-bc-exam-guide/study-guide/pMRZ62p1vlmkff5mTcDe

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