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

The 200-word examination instruction list

CLEP Precalculus asks you to connect formulas, graphs, tables and verbal descriptions. Decide which representation exposes the requested feature, then check the domain and how the answer must be entered.

Start with the list or jump to exam requirements, worked examples, the Fencing Method or practice. The entries help you recognise what a question asks and which details matter.

Essential instructions

No.	Instruction or term	Meaning or action
1	Calculate	Use numbers or other given information to work out a result.
2	Determine	Work from the given information to establish an answer.
3	Solve	Find the values that satisfy the equation or inequality.
4	Simplify	Rewrite the expression in an equivalent simpler form.
5	Evaluate	Weigh relevant evidence or criteria before reaching a judgment.
6	Identify	Name or pick out the item the question specifies.
7	Estimate	Find an approximate answer using the available clues.
8	Interpret	Say what a statement, result or display means in context.
9	Compare	Set the items side by side on the same relevant feature.
10	Find all solutions	Include every value that meets the stated equation and domain.
11	Give an exact value	Use a form that preserves the full mathematical value.
12	Check the solution	Substitute the result into the original equation to verify it.
13	Find the exact value	Retain radicals, fractions, logarithms or π in exact form where appropriate.
14	Set up an equation	Translate the given conditions into a mathematical relationship.
15	Use the formula	Substitute the appropriate values with consistent units.
16	Read the axes	Identify the quantities, units and intervals on a graph before using a value.

Function and graph tasks

No.	Instruction or term	Meaning or action
17	Numerical entry	Enter the requested number in the allowed format and precision.
18	Non-CAS graphing calculator	Use the integrated graphing calculator when available, with algebraic reasoning where needed.
19	Function representation	Connect equations, graphs, tables and verbal descriptions of the same relationship.
20	Evaluate a piecewise rule	Choose the rule that applies to the input before substituting.
21	Solve by graph intersection	Find the input where the two graphed expressions have the same output.
22	Verify a graph reading	Check the window, scale and whether the displayed point belongs to the domain.
23	One-to-one test	Check whether a horizontal line can meet the graph more than once.
24	Inverse function notation	Read f⁻¹ as an inverse function in context, distinct from a reciprocal.
25	Reflect across y = x	Swap coordinates to graph the inverse relation.
26	Even function	Check whether f(−x) = f(x) on a symmetric domain.
27	Odd function	Check whether f(−x) = −f(x) on a symmetric domain.
28	Average rate from a table	Divide the difference in outputs by the difference in their inputs.
29	Limit the model’s domain	Choose inputs meaningful in the situation.
30	Amplitude from extrema	Take half the difference between maximum and minimum.
31	Midline from extrema	Take the average of maximum and minimum.
32	Period from a graph	Find the smallest positive horizontal interval over which the pattern repeats.
33	Horizontal stretch	Multiply horizontal distances by the indicated scale.
34	Horizontal compression	Reduce horizontal distances by the indicated scale.
35	Vertical stretch	Multiply vertical distances from the baseline by a factor greater than one.
36	Exponential growth rate	Interpret the fractional increase per stated input unit.
37	Logarithmic scale	Read equal plotted intervals as equal multiplicative changes in the original quantity.
38	Unit-circle value	Use a point on the unit circle to read sine and cosine.
39	Coterminal angles	Angles differing by a whole number of full turns.
40	Principal inverse-trigonometric value	Select the answer within the inverse function’s designated output range.
41	Trigonometric equation	Solve for every permitted angle in the stated interval.
42	Model selection	Match the pattern and context to a suitable function family.
43	Check an asymptote	Use the behaviour near an excluded input or at large magnitude to identify the correct kind.
44	Interval of increase	Specify inputs over which output rises as input increases.
45	Real zero	A real input where the function output equals zero.
46	Sign of a function	Identify intervals where the graph lies above or below the horizontal axis.

Techniques and representations

No.	Instruction or term	Meaning or action
47	Identify the function family	Use the pattern in the equation, table or graph to select an appropriate family.
48	Compare representations	Match equivalent features across equations, graphs, tables and verbal descriptions.
49	Polynomial function	A finite sum of terms with nonnegative integer powers of the input.
50	Leading term	Use the highest-degree term to determine polynomial end behaviour.
51	End behaviour	Describe how output behaves as input grows without bound in either direction.
52	Multiplicity of a zero	Count how many times the corresponding factor appears.
53	Rational function	A quotient of polynomials defined where its denominator is nonzero.
54	Removable discontinuity	A hole that may arise when a factor cancels but its original input remains excluded.
55	Vertical asymptote	A line the graph approaches near an input where outputs become unbounded.
56	Horizontal asymptote	A horizontal line approached at one or both infinite ends of the domain.
57	Average rate of change	Divide output change by input change over the interval named.
58	Equal input increments	Compare outputs at evenly spaced inputs to identify a model pattern.
59	Constant first differences	Evidence of a linear pattern at equal input increments.
60	Constant second differences	Evidence of a quadratic pattern at equal input increments when the second difference is nonzero.
61	Constant ratio	Evidence of an exponential pattern when successive outputs at equal input steps are nonzero.
62	Growth factor	Multiply by this number for each stated input increment in an exponential model.
63	Decay factor	A positive multiplier below one for each stated input increment.
64	Doubling time	The time needed for an exponentially growing amount to double.
65	Half-life	The time needed for an exponentially decreasing amount to halve.
66	Logarithm	The exponent to which a specified base must be raised to obtain the positive argument.
67	Logarithmic equation	Solve for the unknown while keeping every logarithm’s argument in its domain.
68	Semi-log plot	Use a logarithmic scale on one axis to recognise a possible exponential relationship.
69	Composition	Evaluate one function at the output of another in the stated order.
70	Inverse function	Reverse inputs and outputs on a domain where the original function is one-to-one.
71	Inverse relationship of exponential and logarithm	Use the same base and apply the domain conditions of both functions.
72	One-to-one	Different inputs give different outputs.
73	Domain restriction	Limit admissible inputs to match a context or make an inverse possible.
74	Piecewise model	Use the specified formula for the part of the domain containing the input.
75	Model residual	Subtract the predicted output from the observed output.
76	Interpolation	Estimate a value within the range of observed inputs.
77	Extrapolation	Extend a model beyond observed inputs and consider its limitations.
78	Radian measure	Divide arc length by radius to express an angle.
79	Unit circle	Use the coordinates of a point on the unit circle as cosine and sine.
80	Reference angle	Find the acute angle to the horizontal axis for a nonquadrantal angle.
81	Period	Find the smallest positive input shift that repeats a periodic pattern.
82	Frequency	Find cycles per unit of input.
83	Amplitude	Find half the difference between maximum and minimum for a sinusoid.
84	Midline	Find the horizontal line midway between maximum and minimum.
85	Phase shift	Identify the horizontal displacement relative to the chosen standard sinusoid.
86	Sinusoidal model	Use midline, amplitude, period and phase to represent repeated variation.
87	Trigonometric identity	An equality holding for every input where both expressions are defined.
88	Solve on a stated interval	List every valid solution in the interval and check its endpoint conditions.
89	Inverse trigonometric function	Return the angle in the specified principal-value range.
90	Distance from the pole	Use the absolute value of the radial coordinate.
91	Function model parameters	Explain how a named parameter affects the model in context.
92	Function concepts	Use equations, tables, graphs or descriptions to reason about function features.
93	Model validation	Compare predictions with evidence and assess whether the model fits its intended range.
94	Logarithm domain check	Require each real logarithm’s argument to be positive.
95	Interpret a rate in context	State the input and output units and describe what the rate measures.
96	Exact trigonometric value	Use a known value or an identity to give a result without rounding.
97	Transformation order	Apply horizontal and vertical changes in a way consistent with the given formula.
98	Piecewise function	Apply the rule for the part of the domain containing the input.
99	Increasing function	Compare outputs for ordered inputs and distinguish strict increase where required.
100	Decreasing function	Check whether outputs fall as inputs rise within the stated domain.
101	Absolute value	Use the distance from zero or separate cases based on the expression’s sign.
102	Solve the inequality	Find the set of values that make it true and keep the correct inequality direction.
103	Find the nth term	Write the expression that gives the term at position n.
104	Write in standard form	Express the number as a value from 1 up to but excluding 10 times a power of ten.
105	Round to the nearest integer	Choose the closest whole-number value under the rounding rule.
106	Identify a graph transformation	Determine how the expression changes the position or shape of the graph.
107	Upper bound	Identify the upper limit of values consistent with the stated precision.
108	Lower bound	Identify the lower limit of values consistent with the stated precision.
109	Exact expression	Keep the result in a form that preserves its exact value.
110	Reasonable approximation	Estimate at a precision that can distinguish the options.
111	Turning point	Read or find the maximum or minimum point of the graph when the task asks for it.
112	Change of sign	Use the sign changes and stated assumptions relevant to the inference.
113	Domain	Give the set of allowed input values in the context.
114	Parameter	Identify a quantity that sets a feature of the model.
115	One possible value	Supply a single value that satisfies the given conditions.
116	Discriminant	Use the sign of the quadratic discriminant to reason about real roots.
117	Repeated root	Identify a root with multiplicity greater than one.
118	Distinct roots	Count different values of the roots rather than multiplicities.
119	Intersection points	Find the coordinates at which the stated graphs share the same point.
120	Sufficient condition	Identify what guarantees the stated outcome.
121	Necessary condition	Identify what must hold whenever the stated outcome holds.
122	Counterexample	Give one valid case that disproves a general claim.
123	At least one	Find one permitted example to establish existence.
124	At most one	Show there cannot be two or more valid cases.
125	Exactly one	Allow one qualifying case and exclude zero and all cases with two or more.
126	Excluded endpoint	Use a strict boundary where the endpoint itself is not allowed.
127	Included endpoint	Use a non-strict boundary where the endpoint is allowed.
128	Equivalent transformation	Use an operation that preserves the solution set under the stated conditions.
129	Squaring both sides	Check signs and verify candidate answers in the original statement afterwards.
130	Divide by a variable	Check whether the divisor can be zero before taking the step.
131	Check all cases	Test each permitted case against the original question.
132	Factorise	Write the expression as a product of factors.
133	Coordinate	Give the position using the specified ordered values.
134	Determine the graph shift	Identify the direction and size of the translation from the new expression.
135	Integer solutions	Include only the whole-number values, including negative values or zero where allowed.
136	Constant term	Identify the part of the expression with no variable factor.
137	Repeated percentage change	Apply each period’s multiplier to the result from the previous period.
138	Gradient from a graph	Calculate change in the vertical quantity per change in the horizontal quantity.
139	Calculate a rate	Divide the relevant change or quantity by the appropriate time or other denominator.
140	Calculate the percentage change	Divide the change by the starting value and multiply by 100.
141	Unit rate	Calculate the amount corresponding to one unit of the other quantity.
142	Initial value	The value at the stated starting point.
143	Final value	The value at the stated end point.
144	Ratio	Compare two quantities by division in the order specified.
145	Relative change	Divide the difference by the initial value when that baseline is meaningful.
146	Direction of change	State whether the quantity increases, decreases or stays unchanged.

Other examination vocabulary

No.	Instruction or term	Meaning or action
147	Magnitude	The size of a quantity, considered separately from direction.
148	Unit conversion	Use a conversion factor to change the units while keeping the quantity the same.
149	Positive output condition	Require positive outputs when the context or a logarithmic transformation calls for them.
150	Equivalent function formulas	Check that the formulas produce the same outputs on the same intended domain.
151	Polynomial zero	Find an input where the polynomial evaluates to zero.
152	Factor theorem	Connect a zero at a to the factor x − a.
153	Rational intercept	Find valid zeros of the numerator for horizontal-axis intercepts and evaluate at zero for the vertical-axis intercept if defined.
154	Estimate from the graph	Use the plotted trend to obtain a sensible approximate value.
155	Interpret the slope	Give the predicted change in response per one unit increase in the explanatory variable.
156	Interpret the intercept	Explain the predicted response at zero if zero makes sense in context.
157	Line of best fit	Draw a line representing the overall pattern of plotted data.
158	Use the scale of the display	Check axis intervals and group labels before comparing.
159	Horizontal translation	Read a shift from the input expression relative to the original function.
160	Vertical translation	Add or subtract a constant from each output.
161	Choose an appropriate display	Match the display to the variable type and comparison.
162	Exact value	Leave the answer in a form that preserves its full value.
163	Give units	Attach the required measurement unit to the final result.
164	In terms of	Use the specified quantity or symbol in the final expression.
165	Substitute	Replace a variable with the given value or expression.
166	Decimal places	Give the requested number of digits to the right of the decimal point.
167	Significant figures	Give the requested number of meaningful digits.
168	Round	Adjust a number to the requested precision using the next digit.
169	Plot	Place the supplied points on the correct axes and scale.
170	Closed interval	Include both endpoints when the interval is closed.
171	Open interval	Exclude both endpoints when the interval is open at both ends.
172	Range of values	Find all possible outputs under the stated restrictions.
173	Boundary condition	Identify a requirement at an endpoint or boundary.
174	Rate of change	Find the change in one quantity per unit change in another.
175	Interpolate	Estimate within the range covered by the data.
176	Extrapolate	Estimate outside the observed range using an assumed pattern.
177	Residual	Find the observed value minus the model’s predicted value.
178	Horizontal scaling	Use the factor applied to the input and track its reciprocal effect on horizontal distances.
179	Baseline scenario	Use the stated reference case against which an intervention is compared.
180	Per capita	Divide the total by the number of people represented.
181	Percentage point	Find the simple difference between two percentage values.
182	Vertical scaling	Multiply output distances from the horizontal axis by the specified factor.
183	Solve for a model parameter	Use a known feature or point to form an equation for the unknown constant.
184	Periodic context	Identify which quantity repeats and the input change that returns it to the same phase.
185	Quadrant sign	Determine the signs of sine, cosine and tangent from the angle’s position.
186	Increasing on an interval	Compare outputs as inputs increase throughout the stated interval.
187	Decreasing on an interval	Check whether outputs fall as inputs rise throughout the interval.
188	Contrast	Show how the items differ on a shared point of comparison.
189	Infer	Use clues to reach a conclusion the material implies.
190	Predict	Use available evidence to say what is likely to happen.
191	Suggest	Offer a plausible answer suited to the information given.
192	Assess	Judge the extent, value or strength of something using evidence.
193	Discuss	Develop a structured response that considers the relevant issues.
194	Distinguish	Give the feature that lets the reader tell two things apart.
195	Support	Supply evidence that helps establish the claim.
196	Illustrate	Make an idea clear with a relevant example or diagram.
197	Demonstrate	Show how a fact, process or result can be established.
198	Arrange	Put items into the order or grouping requested.
199	Sequence	Put stages into a meaningful order.
200	Classify	Assign each item to a category using the stated rule.

What CLEP Precalculus requires

Exam component	Format and scope
Section 1	25 questions in about 50 minutes. The integrated TI-84 Plus CE graphing calculator is available.
Section 2	23 questions in about 40 minutes. This section is calculator-free.
Response format	Most items are multiple choice. Some ask you to enter a number.

CLEP is a U.S.-based college-credit examination programme. The receiving institution decides which exams and scores it accepts and how credit applies. Candidates outside the United States should confirm testing options with their test centre and acceptance with their institution.

Read the task before choosing a method

In the calculator section, the graph can help locate an intersection, but the window may hide another one. In the calculator-free section, use algebraic structure, common angle values and known function behaviour.

Worked examples for common instructions

Infer a model from a table

Prompt. At x = 0, 1 and 2 the outputs are 5, 15 and 45. Find a suitable simple model.

Answer. Each one-unit step multiplies the output by 3. An exponential model matching the values is f(x) = 5·3ˣ.

Interpret a transformation

Prompt. Describe how the graph of f(x − 4) relates to the graph of f(x).

Answer. It moves four units to the right. An old feature at input a appears at a + 4 because (a + 4) − 4 = a.

Determine an inverse value

Prompt. If f(x) = 2x + 5, find f⁻¹(11).

Answer. Solve f(x) = 11. Since 2x + 5 = 11, the inverse value is 3.

Select a principal angle

Prompt. Evaluate arcsin(−1/2).

Answer. The principal arcsine range is from −π/2 to π/2. The angle in that range with sine −1/2 is −π/6.

Use the Fencing Method to build an answer

Start with one accurate result. Add the condition, unit or interval that fixes its meaning. Then give the reason that connects the result to the problem. Apply that reasoning again in a different example.

Start. The pattern is exponential.

Add context. The output triples for every one-unit input step.

Add reasoning. The constant multiplier 3 and initial output 5 support f(x) = 5·3ˣ for the observed values.

Transfer. Try a table with a constant additive change and choose a model that fits it.

Practise with the 200 terms

Choose one term about a calculation, one about interpretation and one about checking. Solve a short task that uses all three. Check your answer against the original conditions before selecting or entering it.

Find amplitude and midline

Try it. A sinusoid reaches a maximum of 7 and a minimum of −1. Find both features.

Check. Amplitude is (7 − (−1))/2 = 4. The midline is y = (7 + (−1))/2 = 3.

Frequently asked questions

How should I decide whether to use the calculator?

Read the section’s calculator rule first. Where the calculator is available, decide whether a graph or numerical estimate answers the question. If the prompt asks for an exact result, use the algebraic relationship and check the requested format.

Official sources and next reading

College Board CLEP Precalculus exam description and sample resources

Related examination vocabulary guide · eduKateSG vocabulary learning guide · Learn the Fencing Method