Top 200 Vocabulary Word List for AP Calculus AB | Must Know Words for Common Examination Instructions

The 200-word examination instruction list

AP Calculus AB instructions tell you whether to find a value, interpret it or justify a conclusion. A derivative, an integral and an average rate can all describe change, but they answer different questions. Check the interval, units and requested output before choosing a method.

This study bank includes prompt words, response formats and terms that help you interpret the task. Check the official directions for the particular question and exam year.

Exam requirements · Worked examples · Fencing Method

Calculus instructions and representations

No.	Instruction or term	What it asks you to do
1	Average rate of change	Divide the change in output by the change in input over the stated interval.
2	Instantaneous rate of change	Evaluate the derivative at the specified input and report units when relevant.
3	Average value of a function	Divide the definite integral by the length of the interval.
4	Rate of accumulation	Identify the rate at which the accumulated quantity changes.
5	Net change	Integrate the signed rate over the stated interval.
6	Total distance	Integrate speed or add the magnitudes of displacement on intervals with constant direction.
7	Displacement	Find the signed change in position.
8	Speed increasing	Compare the signs of velocity and acceleration where both are nonzero.
9	Tangent line equation	Use the derivative as slope and the point of tangency in a line equation.
10	Linear approximation	Use the tangent line near the chosen input to estimate a function value.
11	Estimate a derivative from a table	Use a suitable nearby difference quotient and show the values used.
12	Estimate an integral from a table	Apply the requested sum with the actual subinterval widths.
13	Left Riemann sum	Use the left endpoint in each subinterval.
14	Right Riemann sum	Use the right endpoint in each subinterval.
15	Midpoint Riemann sum	Use the midpoint of each subinterval.
16	Trapezoidal sum	Multiply each interval width by the mean of its endpoint heights and add.
17	Fundamental Theorem of Calculus	Connect definite integrals, antiderivatives and derivatives of accumulation functions.
18	Evaluate a limit	Find the value approached by the function from the indicated direction or directions.
19	One-sided limit	Approach the given point from the side specified.
20	Justify continuity	Check the function value and the existence and equality of the limit there.
21	Justify differentiability	Use the derivative definition or an applicable theorem in the given context.
22	Intermediate Value Theorem	Check continuity and establish that the requested output lies between endpoint values.
23	Mean Value Theorem	Check continuity on the closed interval and differentiability on its interior before equating rates.
24	Candidates for an absolute extremum	Check eligible endpoints and interior critical points in the stated domain.
25	Critical point	Identify an interior domain point where the derivative is zero or undefined.
26	Relative extremum	Use local behaviour such as a change in sign of the first derivative.
27	Point of inflection	Establish an actual change in concavity.
28	Concave up	Identify where the derivative is increasing or use a positive second derivative when applicable.
29	Separate variables	Put expressions in the two variables on their respective sides before integrating.
30	Initial condition	Use the given input and output to select a particular solution.
31	Slope field	Match the local slopes to the differential equation and its solution behaviour.
32	Area between curves	Integrate the upper function minus the lower function with respect to the horizontal variable when appropriate.
33	Cross-sectional volume	Integrate the area of a cross section over the stated axis.
34	Horizontal slice	Use right minus left and integrate with respect to the vertical variable when appropriate.
35	Piecewise definition	Use the appropriate rule on each interval and split the calculation when needed.
36	Graphing calculator required	Check whether the exam part requires a graphing calculator and show relevant setup in free response.
37	Hybrid digital	Read the free-response prompts in Bluebook and write the answers in the paper booklet.
38	Interpret in context	State what the value means for the named quantity and include suitable units.
39	Justify using the derivative	Use derivative values or signs to explain the specific conclusion.
40	Signed area	Account for regions above and below the axis with the appropriate signs.
41	Chain rule	Differentiate the outer function at the inner input and multiply by the inner derivative.
42	Product rule	Differentiate each factor in turn and add the two products.
43	Quotient rule	Use the denominator times the derivative of the numerator minus the reverse product, divided by the denominator squared.
44	Implicit differentiation	Differentiate the relation with respect to the given variable while accounting for the dependent variable.
45	Derivative of an inverse	Use the reciprocal of the original derivative at the corresponding input when the conditions apply.
46	Related rates	Differentiate the relationship with respect to time and substitute values for the same moment.
47	Linearisation point	Use a nearby input where the function and derivative can be evaluated.
48	Derivative from first principles	Use the appropriate limit of a difference quotient.
49	Discontinuity	Identify how the function value or limit fails the continuity test.
50	Removable discontinuity	Check whether assigning the limiting value would make the function continuous.
51	Vertical asymptote	Use unbounded behaviour from the relevant side.
52	Horizontal asymptote	Check the limit as the input increases or decreases without bound.
53	Antiderivative	Find a function whose derivative gives the stated integrand.
54	Constant of integration	Include an arbitrary constant in an indefinite antiderivative.
55	Substitution in an integral	Change the variable and update the differential and bounds as needed.
56	Definite integral	Evaluate the signed accumulation over the specified interval.
57	Washers	Subtract the inner disk area from the outer disk area before integrating.
58	Disk method	Integrate π times the squared radius along the stated axis.
59	Optimization	Identify the quantity to optimise and check the candidates allowed by the constraints.
60	Absolute maximum value	Report the largest output on the domain, rather than only where it occurs.

Algebra, functions and graph reasoning

No.	Instruction or term	What it asks you to do
61	Use a function model	Translate the stated scenario into a function and use only its allowed inputs.
62	Mathematical Reasoning	Use the supplied conditions and mathematical relationships to establish the requested conclusion.
63	Exactly one	Establish that there is a solution and that a second one cannot occur.
64	Direct proof	Use valid steps from the assumptions to establish the conclusion.
65	Proof by contradiction	Assume the claim fails, then show that this contradicts an established fact.
66	Proof by cases	Cover all possible cases and establish the conclusion for each.
67	Extraneous solution	Identify a value introduced by a manipulation that fails the original condition.
68	Lost solution	Check whether dividing or simplifying excluded a value that could work.
69	Domain restriction	Keep only the inputs for which the original expression or situation is defined.
70	Range of values	Find all possible outputs under the stated restrictions.
71	Parameter	Use the fixed or adjustable quantity that defines a family of cases.
72	Change of sign	Use the sign changes and stated assumptions relevant to the inference.
73	Open interval	Exclude both endpoints when the interval is open at both ends.
74	Closed interval	Include both endpoints when the interval is closed.
75	Piecewise function	Apply the rule for the part of the domain containing the input.
76	Increasing function	Compare outputs for ordered inputs and distinguish strict increase where required.
77	Decreasing function	Check whether outputs fall as inputs rise within the stated domain.
78	Absolute value	Use the distance from zero or separate cases based on the expression’s sign.
79	Solve the inequality	Find the set of values that make it true and keep the correct inequality direction.
80	Find all solutions	Include every value that meets the stated equation and domain.
81	Give an exact value	Use a form that preserves the full mathematical value.
82	Not drawn accurately	Use the supplied mathematical facts rather than the apparent appearance of the diagram.
83	Draw to scale	Use the scale given to make a drawing with the required proportions.
84	Identify a graph transformation	Determine how the expression changes the position or shape of the graph.
85	Error interval	Give the range of possible original values using the correct endpoint signs.
86	Estimate from a graph	Use the scale and plotted information to obtain a sensible approximate value.
87	Explain a limitation	Identify the assumption or data issue that restricts the conclusion.
88	Give units	Attach the required measurement unit to the final result.
89	Change to	Express the value in the requested form or unit.
90	Do not use a graphical method	Use an algebraic method or interpretation as the task directs.
91	Integer solutions	Include only the whole-number values, including negative values or zero where allowed.
92	Enlargement scale factor	Use the multiplier of corresponding lengths from the centre of enlargement.
93	Repeated percentage change	Apply each period’s multiplier to the result from the previous period.
94	Optimise over the domain	Check the allowed values before deciding which output is largest or smallest.
95	Diagrams are not accurately drawn	Base calculations on the provided labels and established geometry.
96	Determine the graph shift	Identify the direction and size of the translation from the new expression.
97	Calculate a rate	Divide the relevant change or quantity by the appropriate time or other denominator.
98	Calculate the percentage change	Divide the change by the starting value and multiply by 100.
99	To scale	Use the stated relationship between drawing distances and actual distances.
100	Not to scale	Use the stated measurements and relationships when calculating.
101	Exact value	Leave the answer in a form that preserves its full value.
102	Solve	Find the values that satisfy the equation or inequality.
103	Estimate from the graph	Use the plotted trend to obtain a sensible approximate value.
104	Illustrate	Make an idea clear with a relevant example or diagram.
105	Demonstrate	Show how a fact, process or result can be established.
106	Check the solution	Substitute the result into the original equation to verify it.
107	Find the exact value	Retain radicals, fractions, logarithms or π in exact form where appropriate.
108	Identify the feature of the graph	Use the graph or equation to decide what the named point represents.
109	Find the area	Find a non-negative area and account for changes in sign or intersecting curves.
110	Set up an equation	Translate the given conditions into a mathematical relationship.
111	Resolve a ratio	Divide the total into parts using the stated ratio.
112	Initial amount plus net change	Add the accumulated signed change to the amount present at the start.
113	Rounding interval	Use the stated precision to find the range of values that could produce the rounded result.
114	Rate of change	Find the change in one quantity per unit change in another.
115	One possible value	Supply a single value that satisfies the given conditions.
116	Equation	Use or form a statement that two expressions have equal value.
117	Unit rate	Calculate the amount corresponding to one unit of the other quantity.
118	Calculator-free part	Use analytic or numerical reasoning without a calculator where the directions prohibit it.
119	Best value	Compare costs on a common unit basis or by the criterion named in the task.
120	Within the interval	Keep solutions inside the stated endpoints, respecting whether the endpoints are included.
121	Limits of a local estimate	Use a tangent estimate near its base point and check any error direction from concavity.
122	Initial value	Find the starting quantity, often the output at input zero.
123	Calculate	Use numbers or other given information to work out a result.
124	Read the calculator designation	Check the official section and part before using calculator tools.
125	Unit conversion	Convert quantities to consistent units before comparing or calculating.
126	Scale factor	Use the multiplier between corresponding quantities and apply the correct power when needed.
127	Exact expression	Keep the result in a form that preserves its exact value.
128	Reasonable approximation	Estimate at a precision that can distinguish the options.
129	Gradient from a graph	Calculate change in the vertical quantity per change in the horizontal quantity.
130	Area under a graph	Use the area only where the graph’s quantities make it the requested accumulated value.
131	Balance the rate equation	Use the rates entering and leaving the system to express net change.
132	Limiting value	Find the value approached under the direction or unbounded behaviour named.
133	Rate in context	Interpret the derivative for the quantity and time units supplied.
134	Keep rate units consistent	Express the output and input units correctly before reporting a rate.
135	Velocity change	Subtract the initial velocity from the final velocity with the stated direction convention.
136	Accumulated change	Use the integral of the signed rate over the stated interval.
137	Coefficient of the derivative term	Identify the constant multiplier when simplifying the derivative.
138	Fold change	Divide the later or treatment value by the comparison value as the item defines it.
139	Direction of change	State or select whether the result increases, decreases or remains similar.
140	Approximate calculation	Use values and rounding that distinguish the available answers.
141	Resolution	Identify the smallest change that the device or scale can display.
142	Domain	Give the set of allowed input values in the context.
143	Difference from predicted value	Compare the observation with the model’s expected value in the same units.
144	Approximation	Give a suitably rounded or estimated value.
145	Best illustrates	Choose the example or quotation that most directly shows the idea.
146	Function value at an endpoint	Evaluate the original function at the endpoint rather than its derivative.

Problem conditions and answer checks

No.	Instruction or term	What it asks you to do
147	Recognise	Find a familiar feature in a new example.
148	Identify	Name or pick out the item the question specifies.
149	Select	Choose only the number of options requested.
150	Match	Pair each item with the option that corresponds to it.
151	Complete	Fill in what is missing while keeping the supplied structure.
152	Label	Attach the correct name to the indicated part.
153	Locate	Find the specified detail, point or region.
154	Indicate	Make the chosen feature or answer clear.
155	Record	Write the result in the space and form provided.
156	Answer	Respond directly to the question being asked.
157	Give	Supply the requested fact, example or result.
158	State	Express the required point directly and clearly.
159	Name	Supply the correct term, person or item.
160	List	Set out the requested items separately.
161	Define	Give the precise meaning used in the subject or question.
162	Describe	Report the relevant characteristics, events or pattern.
163	Outline	Give the main steps or points in brief.
164	Summarise	Select the central points and leave out minor details.
165	Explain	Connect the result to its cause, mechanism or reasoning.
166	Compare	Set the items side by side on the same relevant feature.
167	Contrast	Show how the items differ on a shared point of comparison.
168	Analyse	Break down the evidence and explain how its parts relate.
169	Interpret	Say what a statement, result or display means in context.
170	Infer	Use clues to reach a conclusion the material implies.
171	Predict	Use available evidence to say what is likely to happen.
172	Suggest	Offer a plausible answer suited to the information given.
173	Justify	Give evidence for the claim and explain how that evidence supports, qualifies or defends it.
174	Evaluate	Weigh relevant evidence or criteria before reaching a judgment.
175	Assess	Judge the extent, value or strength of something using evidence.
176	Discuss	Develop a structured response that considers the relevant issues.
177	Distinguish	Give the feature that lets the reader tell two things apart.
178	Support	Supply evidence that helps establish the claim.
179	Determine	Work from the given information to establish an answer.
180	Estimate	Find an approximate answer using the available clues.
181	Check	Test the answer against the original instruction or condition.
182	Arrange	Put items into the order or grouping requested.
183	Sequence	Put stages into a meaningful order.
184	Classify	Assign each item to a category using the stated rule.
185	Group	Put items with a shared feature together.
186	Order	Sort items by the criterion given in the prompt.
187	Omit	Leave out the indicated item or detail.
188	Include	Make sure the requested part appears in the response.
189	Exclude	Keep the named item or category outside your answer.
190	Refer to	Use the specified passage, figure or notes when responding.
191	Based on	Ground the answer in the material named in the question.
192	According to	Use what the specified source says.
193	In context	Use the meaning that fits this passage or situation.
194	Most likely	Choose the conclusion with the strongest support among the options.
195	Best supported	Prefer the conclusion backed most directly by the evidence.
196	Explicit	Stated directly in the source.
197	Implicit	Suggested by the source and recoverable from clues.
198	Evidence	A fact, detail or observation that supports a claim.
199	Claim	An assertion that can be tested against evidence or reasoning.
200	Example	A particular case used to make a general idea clear.

What the examination requires

May 2027 multiple-choice section

College Board lists 42 questions in 100 minutes. Part A has 29 questions in 62 minutes without a calculator. Part B has 13 questions in 38 minutes and requires a graphing calculator. This section contributes half of the exam score.

Free response and the hybrid format

There are six free-response questions in 90 minutes, worth the other half. Part A has two calculator-required questions in 30 minutes. Part B has four questions in 60 minutes without a calculator. Multiple choice is completed in Bluebook. Free-response prompts appear in Bluebook, and students handwrite answers in the exam booklet.

Match the output to the instruction

A calculation needs a value or expression. An interpretation explains what it means for the named quantity. A justification gives the facts and reasoning that establish the conclusion. A graphing calculator may help find a number on a permitted part, but check whether the question also asks for a setup, interpretation or reason.

The College Board Advanced Placement programme is based in the United States and its exams are also offered internationally. Check arrangements with your exam centre and confirm credit or placement policies with the institution that will receive your score.

Worked examples of common examination instructions

Use these original examples to see how the wording changes the answer you need to give.

Average rate versus instantaneous rate

Suppose position in metres is s(t) = t² over 1 ≤ t ≤ 3 seconds. The average velocity on that interval is (9 − 1) ÷ (3 − 1) = 4 m/s. The instantaneous velocity at t = 3 is s′(3) = 6 m/s. Read whether the stem gives an interval or asks for a rate at one moment.

Justify an extremum from the sign of a derivative

If f′ is positive just before x = 2 and negative just after, f changes from increasing to decreasing, so f has a relative maximum there. This argument needs a sign change. A statement that f′(2) = 0 alone leaves several outcomes possible.

Keep the starting amount in an accumulation problem

If a tank initially contains 20 litres and its net inflow over the next two minutes is 6 litres, the change is 6 litres and the amount after two minutes is 26 litres. When the task asks for the amount, add the initial quantity to the integral of the rate.

Use the Fencing Method to practise instructions

Start with a short, accurate answer. Add a precise detail, then explain the relationship or evidence the prompt calls for. Apply the same instruction to a fresh example.

1. The function has a relative maximum.
2. The function has a relative maximum at x = 2.
3. The function has a relative maximum at x = 2 because its derivative changes from positive to negative there.
4. Repeat with a derivative that touches zero without changing sign. Explain which part of the justification fails.

Read the eduKate Fencing Method for Vocabulary.

Practise and check your answers

Take one function represented by a table, graph or equation. Ask for an average rate, then an instantaneous rate, then a net change over an interval. Mark where the output and units change. When reviewing a free-response solution, underline the step that provides the justification rather than only checking its final number.

Read a released scoring guide alongside one practice response. Check the relevant conditions and make sure the conclusion follows. Then try a timed set using the correct calculator rules for that exam part.

Frequently asked questions

What do you check for total distance?

Use the integral of speed or add the magnitudes of the displacement on intervals with a constant direction.

What belongs in a theorem justification?

Name the applicable conditions, show that they hold in the problem and explain the conclusion.

How should I use older AP questions?

Use them for mathematical practice and the released scoring guidance. Use the current AP Central format for timing and answer entry.

Official sources and next reading

• College Board AP Calculus AB exam format
• AP Calculus AB released exam questions and scoring guidance

Related guide · TMUA mathematical reasoning instructions

Read eduKateSG’s 200-word vocabulary guide for more ways to group and practise vocabulary.

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