AP Precalculus Exam Instructions | Top 200 Vocabulary Words

The 200-word examination instruction list

AP Precalculus asks you to move among equations, graphs, tables and verbal models. Look for equal input steps, then decide whether differences, ratios or repeating behaviour give the most useful evidence. Explain what a result means in the stated context.

Start with the list, or jump to exam requirements, worked examples, the Fencing Method or practice. The list includes command words and subject vocabulary that helps you read the task.

Essential instructions

No.	Instruction or term	Meaning or action
1	Identify	Name or pick out the item the question specifies.
2	State	Express the required point directly and clearly.
3	Describe	Report the relevant characteristics, events or pattern.
4	Explain	Connect the result to its cause, mechanism or reasoning.
5	Compare	Set the items side by side on the same relevant feature.
6	Interpret	Say what a statement, result or display means in context.
7	Justify	Give evidence for the claim and explain how that evidence supports, qualifies or defends it.
8	Evaluate	Weigh relevant evidence or criteria before reaching a judgment.
9	Determine	Work from the given information to establish an answer.
10	Calculate	Use numbers or other given information to work out a result.
11	Estimate	Find an approximate answer using the available clues.
12	Sketch	Show the required shape, relationships and labels.
13	Construct	Produce the specified representation using the information given.
14	Label	Attach the correct name to the indicated part.
15	Select	Choose only the number of options requested.
16	Check	Test the answer against the original instruction or condition.
17	Analyze	Break the information into relevant parts and explain how they relate.
18	Hybrid digital	Check which questions are displayed digitally and which answers go in a paper booklet.
19	Multiple-choice question	Select the answer that satisfies the full stem and any limiting words.
20	Free-response question	Produce your own answer and complete each labelled task.
21	Stimulus	Use the figure, extract or other material attached to the question.
22	Answer each subpart	Treat each lettered instruction as a separate job.

Subject terms and tasks

No.	Instruction or term	Meaning or action
23	Identify the function family	Use the pattern in the equation, table or graph to select an appropriate family.
24	Compare representations	Match equivalent features across equations, graphs, tables and verbal descriptions.
25	Polynomial function	A finite sum of terms with nonnegative integer powers of the input.
26	Leading term	Use the highest-degree term to determine polynomial end behaviour.
27	End behaviour	Describe how output behaves as input grows without bound in either direction.
28	Multiplicity of a zero	Count how many times the corresponding factor appears.
29	Rational function	A quotient of polynomials defined where its denominator is nonzero.
30	Removable discontinuity	A hole that may arise when a factor cancels but its original input remains excluded.
31	Vertical asymptote	A line the graph approaches near an input where outputs become unbounded.
32	Horizontal asymptote	A horizontal line approached at one or both infinite ends of the domain.
33	Average rate of change	Divide output change by input change over the interval named.
34	Equal input increments	Compare outputs at evenly spaced inputs to identify a model pattern.
35	Constant first differences	Evidence of a linear pattern at equal input increments.
36	Constant second differences	Evidence of a quadratic pattern at equal input increments when the second difference is nonzero.
37	Constant ratio	Evidence of an exponential pattern when successive outputs at equal input steps are nonzero.
38	Growth factor	Multiply by this number for each stated input increment in an exponential model.
39	Decay factor	A positive multiplier below one for each stated input increment.
40	Doubling time	The time needed for an exponentially growing amount to double.
41	Half-life	The time needed for an exponentially decreasing amount to halve.
42	Logarithm	The exponent to which a specified base must be raised to obtain the positive argument.
43	Logarithmic equation	Solve for the unknown while keeping every logarithm’s argument in its domain.
44	Semi-log plot	Use a logarithmic scale on one axis to recognise a possible exponential relationship.
45	Composition	Evaluate one function at the output of another in the stated order.
46	Inverse function	Reverse inputs and outputs on a domain where the original function is one-to-one.
47	Inverse relationship of exponential and logarithm	Use the same base and apply the domain conditions of both functions.
48	One-to-one	Different inputs give different outputs.
49	Domain restriction	Limit admissible inputs to match a context or make an inverse possible.
50	Piecewise model	Use the specified formula for the part of the domain containing the input.
51	Model residual	Subtract the predicted output from the observed output.
52	Interpolation	Estimate a value within the range of observed inputs.
53	Extrapolation	Extend a model beyond observed inputs and consider its limitations.
54	Radian measure	Divide arc length by radius to express an angle.
55	Unit circle	Use the coordinates of a point on the unit circle as cosine and sine.
56	Reference angle	Find the acute angle to the horizontal axis for a nonquadrantal angle.
57	Period	Find the smallest positive input shift that repeats a periodic pattern.
58	Frequency	Find cycles per unit of input.
59	Amplitude	Find half the difference between maximum and minimum for a sinusoid.
60	Midline	Find the horizontal line midway between maximum and minimum.
61	Phase shift	Identify the horizontal displacement relative to the chosen standard sinusoid.
62	Sinusoidal model	Use midline, amplitude, period and phase to represent repeated variation.
63	Trigonometric identity	An equality holding for every input where both expressions are defined.
64	Solve on a stated interval	List every valid solution in the interval and check its endpoint conditions.
65	Inverse trigonometric function	Return the angle in the specified principal-value range.
66	Polar function	Represent radial coordinate as a function of angle.
67	Negative polar radius	Place the point in the opposite direction from the angle’s ray.
68	Distance from the pole	Use the absolute value of the radial coordinate.
69	Polar zero	Identify angles for which the curve passes through the origin.
70	Function model parameters	Explain how a named parameter affects the model in context.
71	Function concepts	Use equations, tables, graphs or descriptions to reason about function features.
72	Model validation	Compare predictions with evidence and assess whether the model fits its intended range.
73	Logarithm domain check	Require each real logarithm’s argument to be positive.
74	Interpret a rate in context	State the input and output units and describe what the rate measures.
75	Exact trigonometric value	Use a known value or an identity to give a result without rounding.
76	Transformation order	Apply horizontal and vertical changes in a way consistent with the given formula.

Calculations and representations

No.	Instruction or term	Meaning or action
77	Piecewise function	Apply the rule for the part of the domain containing the input.
78	Increasing function	Compare outputs for ordered inputs and distinguish strict increase where required.
79	Decreasing function	Check whether outputs fall as inputs rise within the stated domain.
80	Absolute value	Use the distance from zero or separate cases based on the expression’s sign.
81	Solve the inequality	Find the set of values that make it true and keep the correct inequality direction.
82	Find all solutions	Include every value that meets the stated equation and domain.
83	Find the nth term	Write the expression that gives the term at position n.
84	Write in standard form	Express the number as a value from 1 up to but excluding 10 times a power of ten.
85	Round to the nearest integer	Choose the closest whole-number value under the rounding rule.
86	Draw to scale	Use the scale given to make a drawing with the required proportions.
87	Identify a graph transformation	Determine how the expression changes the position or shape of the graph.
88	Upper bound	Identify the upper limit of values consistent with the stated precision.
89	Lower bound	Identify the lower limit of values consistent with the stated precision.
90	Exact expression	Keep the result in a form that preserves its exact value.
91	Reasonable approximation	Estimate at a precision that can distinguish the options.
92	Turning point	Read or find the maximum or minimum point of the graph when the task asks for it.
93	Change of sign	Use the sign changes and stated assumptions relevant to the inference.
94	Domain	Give the set of allowed input values in the context.
95	Parameter	Identify a quantity that sets a feature of the model.
96	One possible value	Supply a single value that satisfies the given conditions.
97	Discriminant	Use the sign of the quadratic discriminant to reason about real roots.
98	Repeated root	Identify a root with multiplicity greater than one.
99	Distinct roots	Count different values of the roots rather than multiplicities.
100	Intersection points	Find the coordinates at which the stated graphs share the same point.
101	Sufficient condition	Identify what guarantees the stated outcome.
102	Necessary condition	Identify what must hold whenever the stated outcome holds.
103	Counterexample	Give one valid case that disproves a general claim.
104	At least one	Find one permitted example to establish existence.
105	At most one	Show there cannot be two or more valid cases.
106	Exactly one	Allow one qualifying case and exclude zero and all cases with two or more.
107	Excluded endpoint	Use a strict boundary where the endpoint itself is not allowed.
108	Included endpoint	Use a non-strict boundary where the endpoint is allowed.
109	Equivalent transformation	Use an operation that preserves the solution set under the stated conditions.
110	Squaring both sides	Check signs and verify candidate answers in the original statement afterwards.
111	Divide by a variable	Check whether the divisor can be zero before taking the step.
112	Check all cases	Test each permitted case against the original question.
113	Simplify	Rewrite the expression in an equivalent simpler form.
114	Factorise	Write the expression as a product of factors.
115	Coordinate	Give the position using the specified ordered values.
116	Determine the graph shift	Identify the direction and size of the translation from the new expression.
117	Set up an equation	Translate the given conditions into a mathematical relationship.
118	Use the formula	Substitute the appropriate values with consistent units.
119	Integer solutions	Include only the whole-number values, including negative values or zero where allowed.
120	Constant term	Identify the part of the expression with no variable factor.
121	Repeated percentage change	Apply each period’s multiplier to the result from the previous period.
122	Enlargement scale factor	Use the multiplier of corresponding lengths from the centre of enlargement.
123	Read the axes	Identify the quantities, units and intervals on a graph before using a value.
124	Gradient from a graph	Calculate change in the vertical quantity per change in the horizontal quantity.
125	Calculate a rate	Divide the relevant change or quantity by the appropriate time or other denominator.
126	Calculate the percentage change	Divide the change by the starting value and multiply by 100.
127	Unit rate	Calculate the amount corresponding to one unit of the other quantity.
128	Initial value	The value at the stated starting point.
129	Final value	The value at the stated end point.
130	Ratio	Compare two quantities by division in the order specified.
131	Relative change	Divide the difference by the initial value when that baseline is meaningful.
132	Direction of change	State whether the quantity increases, decreases or stays unchanged.
133	Magnitude	The size of a quantity, considered separately from direction.
134	Unit conversion	Use a conversion factor to change the units while keeping the quantity the same.
135	Positive output condition	Require positive outputs when the context or a logarithmic transformation calls for them.
136	Equivalent function formulas	Check that the formulas produce the same outputs on the same intended domain.
137	Polynomial zero	Find an input where the polynomial evaluates to zero.
138	Factor theorem	Connect a zero at a to the factor x − a.
139	Rational intercept	Find valid zeros of the numerator for horizontal-axis intercepts and evaluate at zero for the vertical-axis intercept if defined.
140	Estimate from the graph	Use the plotted trend to obtain a sensible approximate value.
141	Interpret the slope	Give the predicted change in response per one unit increase in the explanatory variable.
142	Interpret the intercept	Explain the predicted response at zero if zero makes sense in context.
143	Line of best fit	Draw a line representing the overall pattern of plotted data.
144	Scatterplot	Describe form, direction, strength and unusual points when relevant.
145	Regression prediction	Use the fitted relationship to estimate the response for a stated input.
146	Difference versus association	Distinguish a numerical group contrast from an inference about the relationship.
147	Use the scale of the display	Check axis intervals and group labels before comparing.
148	Horizontal translation	Read a shift from the input expression relative to the original function.
149	Vertical translation	Add or subtract a constant from each output.
150	Choose an appropriate display	Match the display to the variable type and comparison.
151	Exact value	Leave the answer in a form that preserves its full value.
152	Give units	Attach the required measurement unit to the final result.
153	Find the exact value	Retain radicals, fractions, logarithms or π in exact form where appropriate.
154	Check the solution	Substitute the result into the original equation to verify it.
155	In terms of	Use the specified quantity or symbol in the final expression.
156	Solve	Find the values that satisfy the equation or inequality.
157	Substitute	Replace a variable with the given value or expression.
158	Decimal places	Give the requested number of digits to the right of the decimal point.
159	Significant figures	Give the requested number of meaningful digits.
160	Round	Adjust a number to the requested precision using the next digit.
161	Plot	Place the supplied points on the correct axes and scale.
162	Closed interval	Include both endpoints when the interval is closed.
163	Open interval	Exclude both endpoints when the interval is open at both ends.
164	Range of values	Find all possible outputs under the stated restrictions.
165	Boundary condition	Identify a requirement at an endpoint or boundary.
166	Rate of change	Find the change in one quantity per unit change in another.
167	Interpolate	Estimate within the range covered by the data.
168	Extrapolate	Estimate outside the observed range using an assumed pattern.
169	Residual	Find the observed value minus the model’s predicted value.
170	Horizontal scaling	Use the factor applied to the input and track its reciprocal effect on horizontal distances.
171	Baseline scenario	Use the stated reference case against which an intervention is compared.
172	Per capita	Divide the total by the number of people represented.
173	Percentage point	Find the simple difference between two percentage values.
174	Vertical scaling	Multiply output distances from the horizontal axis by the specified factor.
175	Solve for a model parameter	Use a known feature or point to form an equation for the unknown constant.
176	Periodic context	Identify which quantity repeats and the input change that returns it to the same phase.
177	Quadrant sign	Determine the signs of sine, cosine and tangent from the angle’s position.
178	Polar graph feature	Identify an angle and radius that explain the named point or part of a polar graph.
179	Increasing on an interval	Compare outputs as inputs increase throughout the stated interval.
180	Decreasing on an interval	Check whether outputs fall as inputs rise throughout the interval.

Evidence and other exam wording

No.	Instruction or term	Meaning or action
181	Contrast	Show how the items differ on a shared point of comparison.
182	Infer	Use clues to reach a conclusion the material implies.
183	Predict	Use available evidence to say what is likely to happen.
184	Suggest	Offer a plausible answer suited to the information given.
185	Assess	Judge the extent, value or strength of something using evidence.
186	Discuss	Develop a structured response that considers the relevant issues.
187	Distinguish	Give the feature that lets the reader tell two things apart.
188	Support	Supply evidence that helps establish the claim.
189	Illustrate	Make an idea clear with a relevant example or diagram.
190	Demonstrate	Show how a fact, process or result can be established.
191	Arrange	Put items into the order or grouping requested.
192	Sequence	Put stages into a meaningful order.
193	Classify	Assign each item to a category using the stated rule.
194	Order	Sort items by the criterion given in the prompt.
195	Omit	Leave out the indicated item or detail.
196	Include	Make sure the requested part appears in the response.
197	Exclude	Keep the named item or category outside your answer.
198	Refer to	Use the specified passage, figure or notes when responding.
199	Based on	Ground the answer in the material named in the question.
200	According to	Use what the specified source says.

What the AP Precalculus exam requires

College Board lists the regular 2027 exam for May 11. The exam is hybrid digital. Answer multiple-choice questions and read free-response prompts in Bluebook, then handwrite the free responses in the supplied booklet.

Exam component	Format and weighting
I · Multiple choice	42 questions in 105 minutes, worth 62.5%. Part A has 29 questions in 65 minutes without a calculator. Part B has 13 questions in 40 minutes with a graphing calculator required.
II · Free response	4 questions in 70 minutes, worth 37.5%. Part A has 2 questions in 35 minutes with a graphing calculator required. Part B has 2 questions in 35 minutes without a calculator.
Calculator policy	Use a permitted graphing calculator or the built-in Desmos graphing calculator on the designated parts. Practise the calculator-free parts separately.

AP is a U.S.-based exam programme taken domestically and internationally. Confirm registration and local reporting time with your school or test centre. Use the official materials for your exact subject and exam year.

Read the task before choosing a method

The 2027 free-response tasks cover function concepts, a nonperiodic model, a periodic model and symbolic manipulation. The exam assesses Units 1–3. College Board identifies Unit 4 as optional course material outside the exam’s assessed scope.

Worked examples for common exam instructions

Identify a model from a table

Prompt. At consecutive integer inputs starting at zero, the outputs are 3, 6, 12 and 24. Which family fits these data and why?

Answer. An exponential model fits because the inputs increase by one while each output is twice its predecessor. One model is f(x) = 3·2ˣ.

Interpret a rate in context

Prompt. A reservoir contains 80 litres at minute 2 and 110 litres at minute 8. Find and interpret the average rate of change.

Answer. The average rate is (110−80)/(8−2) = 5 litres per minute. Over those six minutes, the stored volume increased by 5 litres per minute on average.

Build a sinusoidal model

Prompt. A tide model has a maximum of 5 m at hour zero, a minimum of 1 m and a period of 12 hours. Write one suitable model.

Answer. The midline is 3 and amplitude is 2. The maximum at zero suggests a cosine model, h(t) = 3 + 2 cos(πt/6), with t measured in hours.

Distinguish a hole from an asymptote

Prompt. Describe the discontinuity of (x²−1)/(x−1) at x = 1.

Answer. For x ≠ 1 the expression simplifies to x + 1. The original input x = 1 remains excluded, so the graph has a hole at (1, 2).

Use the Fencing Method to build an answer

Begin with one accurate answer. Add a detail that fixes it to the question, then add the rule or mechanism that justifies it. Transfer the same structure to a fresh case.

Start. The data fit an exponential model.

Add context. At equal one-hour steps, the outputs are multiplied by 1.2.

Add reasoning. Because the multiplier is 1.2 each hour, the measured quantity increases by 20% per hour under the model.

Transfer. Try a different table with a constant additive difference and explain why that evidence points to a different family.

Practise with the 200 terms

Choose one calculation, one interpretation and one justification. Underline the part of the answer that fulfils each verb. Repeat with a different representation, such as a table instead of an equation.

Check all solutions

Try it. Solve sin θ = 1/2 on 0 ≤ θ < 2π.

Check. θ = π/6 and 5π/6. The reference angle is π/6 and sine is positive in quadrants I and II.

Frequently asked questions

When should I write the setup?

Show the expression, equation or model that produces the result when the prompt calls for work or reasoning. Use the requested precision and state units when the quantities have them.

Official sources and next reading

College Board AP Precalculus exam information and released questions · AP calculator policy · 2027 AP exam schedule

College Board AP Precalculus course scope

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