Tips to Earn Your Best Score

Drawings Used as Justification

You must explain what it is about your drawing which justifies your conclusion, and how you know the drawing is accurate.

Drawings Used as Justification You must explain what it is about your drawing which justifies your conclusion, and how you know the drawing is accurate. Example (Balloon problem of 2007, part (d)). Full credit was earned if the student said "the Riemann right sum is less than the definite integral because r ' is decreasing 0 < t < 12 since r is concave down there."

Drawings Used as Justification You must explain what it is about your drawing which justifies your conclusion, and how you know the drawing is accurate. Example (Balloon problem of 2007, part (d)). Full credit was earned if the student said "the Riemann right sum is less than the definite integral because r ' is decreasing 0 < t < 12 since r is concave down there." However, a student who drew a decreasing graph with accurate rectangles did not get credit unless he or she explained why the graph was correct (i.e. r ' was a decreasing function since r was given to be concave down).

The Three Decimal Place Rule

Decimal answers must be accurate to three decimal places (rounded or truncated).

The Three Decimal Place Rule Decimal answers must be accurate to three decimal places (rounded or truncated). The answer to the problem may be π, and π ≈ ,but if the answer is π, all these are acceptable:

The Three Decimal Place Rule Decimal answers must be accurate to three decimal places (rounded or truncated). The answer to the problem may be π, and π ≈ ,but if the answer is π, all these are acceptable: π,3.141,3.142, and even and , because the reader will stop after three decimal places.

The Three Decimal Place Rule Decimal answers must be accurate to three decimal places (rounded or truncated). The answer to the problem may be π, and π ≈ ,but if the answer is π, all these are acceptable: π,3.141,3.142, and even and , because the reader will stop after three decimal places. But you will not get credit for 3.1 or 3.14 !!!!

The Three Decimal Place Rule Decimal answers must be accurate to three decimal places (rounded or truncated). The answer to the problem may be π, and π ≈ ,but if the answer is π, all these are acceptable: π,3.141,3.142, and even and , because the reader will stop after three decimal places. But you will not get credit for 3.1 or 3.14 !!!! *This rule is for the AP Calculus exam only (not Physics, Chemistry, etc.)

Various Tips

Free Response Questions have multiple entry points. You can often be successful on part (b) even if you have left part (a) blank.

Various Tips Free Response Questions have multiple entry points. You can often be successful on part (b) even if you have left part (a) blank. If a calculator is permitted, use it.

Various Tips Free Response Questions have multiple entry points. You can often be successful on part (b) even if you have left part (a) blank. If a calculator is permitted, use it. Use standard mathematical notation

Various Tips Free Response Questions have multiple entry points. You can often be successful on part (b) even if you have left part (a) blank. If a calculator is permitted, use it. Use standard mathematical notation The first quadrant area under y=x 2 from x = 1 to x = 5 must be presented as, not as fnInt(x^2,x,1, 5).

Various Tips Free Response Questions have multiple entry points. You can often be successful on part (b) even if you have left part (a) blank. If a calculator is permitted, use it. Use standard mathematical notation The first quadrant area under y=x 2 from x = 1 to x = 5 must be presented as, not as fnInt(x^2,x,1, 5). Some abbreviations are understood For example, "DNE" for does not exist, "inc" and "dec" for increasing and decreasing, "pos", "neg" but it is probably best to avoid other abbreviations if you can.

Give Units if Requested

Time Savers Crossed out work will not be read

Time Savers Crossed out work will not be read To save time, don't erase, just cross out. However, don't cross out your work unless you know you can do better.

Time Savers Crossed out work will not be read To save time, don't erase, just cross out. However, don't cross out your work unless you know you can do better. Do not simplify answers

Time Savers Crossed out work will not be read To save time, don't erase, just cross out. However, don't cross out your work unless you know you can do better. Do not simplify answers If you make a mistake simplifying, you will not earn the "answer point". Graders will accept any mathematically equivalent form of the answer.

Time Savers Crossed out work will not be read To save time, don't erase, just cross out. However, don't cross out your work unless you know you can do better. Do not simplify answers If you make a mistake simplifying, you will not earn the "answer point". Graders will accept any mathematically equivalent form of the answer. 2(4.0) + 3(2.0) + 2(1.2) + 4(0.6) + 1(0.5) need not be simplified to 19.3 (Balloon Problem, 2007)

Label Graphs Properly

Is it the graph of f, f ' or f ", g, g ', g ", or what?

Label Graphs Properly Is it the graph of f, f ' or f ", g, g ', g ", or what? Related issue: Do not change the names of things - if the problem refers to Q(t), do not change it to f(x), etc.

Label Graphs Properly Is it the graph of f, f ' or f ", g, g ', g ", or what? Related issue: Do not change the names of things - if the problem refers to Q(t), do not change it to f(x), etc. If you do introduce a variable or change a name, define precisely what you have done.

Sign Charts are Not Enough

You may use sign charts to help you figure out max/min/what is happening, but the grader will ignore them.

Sign Charts are Not Enough You may use sign charts to help you figure out max/min/what is happening, but the grader will ignore them. The grader will look for the magic words:

Sign Charts are Not Enough You may use sign charts to help you figure out max/min/what is happening, but the grader will ignore them. The grader will look for the magic words: f has a relative maximum at x = c because f ' changes sign from positive to negative there.

Sign Charts are Not Enough You may use sign charts to help you figure out max/min/what is happening, but the grader will ignore them. The grader will look for the magic words: f has a relative maximum at x = c because f ' changes sign from positive to negative there. f has a relative minimum at x = c because f ' changes sign from negative to positive there.

Sign Charts are Not Enough You may use sign charts to help you figure out max/min/what is happening, but the grader will ignore them. The grader will look for the magic words: f has a relative maximum at x = c because f ' changes sign from positive to negative there. f has a relative minimum at x = c because f ' changes sign from negative to positive there. f has an inflection point at x = p because f " changes sign there

Sign Charts are Not Enough You may use sign charts to help you figure out max/min/what is happening, but the grader will ignore them. The grader will look for the magic words: f has a relative maximum at x = c because f ' changes sign from positive to negative there. f has a relative minimum at x = c because f ' changes sign from negative to positive there. f has an inflection point at x = p because f " changes sign there OR f has an inflection point at x = p because f ' goes from increasing to decreasing there.

Avoid the Lonesome "it".

Example: "It's increasing because it is positive" will not earn a point when what you mean to say is "f(x) is increasing on (a, b) because f ' (x) is positive there."

Global (Absolute) Max and Min on an Interval

Make a table with all the "candidates"

Global (Absolute) Max and Min on an Interval Make a table with all the "candidates" The candidates are the critical numbers (f ' = 0 or doesn't exist) and the endpoints.

Global (Absolute) Max and Min on an Interval Make a table with all the "candidates" The candidates are the critical numbers (f ' = 0 or doesn't exist) and the endpoints. Example (2010 #2) "Entries are being processed at a rate modeled by P(t) = hundred entries per hour for 8 ≤ t ≤ 12. At what time were entries being processed most quickly? (Calculators OK).

Global (Absolute) Max and Min on an Interval Make a table with all the "candidates" The candidates are the critical numbers (f ' = 0 or doesn't exist) and the endpoints. Example (2010 #2) "Entries are being processed at a rate modeled by P(t) = hundred entries per hour for 8 ≤ t ≤ 12. At what time were entries being processed most quickly? (Calculators OK). Here is a solution that would receive full credit:

Global (Absolute) Max and Min on an Interval

Note that a table is made showing all candidates (critical points and endpoints) and corresponding P(t) values. A student who simply graphed P(t) and picked out the "high point" received no credit.

The definite integral of the rate of change is the total change.

Remember this when you give the meaning of a definite integral.

The definite integral of the rate of change is the total change. Remember this when you give the meaning of a definite integral.

The definite integral of the rate of change is the total change. Remember this when you give the meaning of a definite integral.

The definite integral of the rate of change is the total change. Remember this when you give the meaning of a definite integral. Answer: ≈ 19.3 means the change in radius of the balloon from time t = 0 to t= 12 minutes is approximately 19.3 ft.

The definite integral of the rate of change is the total change. Remember this when you give the meaning of a definite integral. Important: When giving the meaning of a definite integral, be sure to include the meaning of the limits of integration. Answer: ≈ 19.3 means the change in radius of the balloon from time t = 0 to t= 12 minutes is approximately 19.3 ft.

Riemann Sums from Tabular Information Often, "∆x" will vary in the table.

Riemann Sums from Tabular Information Often, "∆x" will vary in the table. Be able to do left, right, trapezoid and midpoint sums, given enough information.

Riemann Sums from Tabular Information Often, "∆x" will vary in the table. Be able to do left, right, trapezoid and midpoint sums, given enough information. A trapezoid formula is ∆x(left + right)/2. The sum will approximate the integral. This is often easier than the long formula, and the long formula doesn't work when "∆x" varies.

Differential Equations

The routine for solving these on AP is always the same:

Differential Equations The routine for solving these on AP is always the same: Separate the variables (x's and dx to the RHS, y's and dy to the LHS).

Differential Equations The routine for solving these on AP is always the same: Separate the variables (x's and dx to the RHS, y's and dy to the LHS). Antidifferentiate each side and add C to the RHS. (C must be added in this step only!)

Differential Equations The routine for solving these on AP is always the same: Separate the variables (x's and dx to the RHS, y's and dy to the LHS). Antidifferentiate each side and add C to the RHS. (C must be added in this step only!) Plug in the x and y of the initial condition and find C.

Differential Equations The routine for solving these on AP is always the same: Separate the variables (x's and dx to the RHS, y's and dy to the LHS). Antidifferentiate each side and add C to the RHS. (C must be added in this step only!) Plug in the x and y of the initial condition and find C. Replace C by its value and solve for y in terms of x.

Differential Equations The routine for solving these on AP is always the same: Separate the variables (x's and dx to the RHS, y's and dy to the LHS). Antidifferentiate each side and add C to the RHS. (C must be added in this step only!) Plug in the x and y of the initial condition and find C. Replace C by its value and solve for y in terms of x. (In steps 3&4, it is OK to solve for y before plugging in the initial condition to find C. The results will be equivalent.)

Slope Fields and Solution Curves

Draw the slope field by calculating dy/dx at the given points and then draw line segments with the corresponding slope.

Slope Fields and Solution Curves Draw the slope field by calculating dy/dx at the given points and then draw line segments with the corresponding slope. If asked to draw a solution curve through the initial condition point, the curve must be tangent to the slope field segment, then "go with the flow", but avoid the other points.

Slope Fields and Solution Curves Draw the slope field by calculating dy/dx at the given points and then draw line segments with the corresponding slope. If asked to draw a solution curve through the initial condition point, the curve must be tangent to the slope field segment, then "go with the flow", but avoid the other points. Reason: If you hit another point, you are obligated to make the segment and your curve be tangent to each other.

Slope Fields and Solution Curves Draw the slope field by calculating dy/dx at the given points and then draw line segments with the corresponding slope. If asked to draw a solution curve through the initial condition point, the curve must be tangent to the slope field segment, then "go with the flow", but avoid the other points. Reason: If you hit another point, you are obligated to make the segment and your curve be tangent to each other.

Slope Fields and Solution Curves Here is a good slope field and solution curve question from (2005 BC 4) Sketch the slope field for the differential equation, then sketch the curve with the initial condition f(0) = 1.

Slope Fields and Solution Curves Below is the solution.

And don't forget

Radian mode

And don't forget Radian mode Leave nothing blank on the multiple choice part

And don't forget Radian mode Leave nothing blank on the multiple choice part Get a good night's sleep!

And don't forget Radian mode Leave nothing blank on the multiple choice part Get a good night's sleep! Eat a great breakfast high in protein!