General functions
Evaluating functions worksheets
Evaluate twelve polynomial and exponential functions. Choose numbers, variable expressions or a mixture, with exact answers and substitution steps.
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12th grade math worksheets
Strengthen functions, unit-circle values, sequences and graph analysis as a general Precalculus pathway. A separate optional group introduces calculus only for learners with secure algebra and function prerequisites.
30 printable resources, grouped by skill. Start where the learner is ready; grade expectations vary by school and curriculum.
A useful starting point
For the Precalculus groups, begin when Algebra 2 function notation, equation solving and graph transformations are secure. The optional calculus extension assumes confident polynomial, rational, exponential and logarithmic work; return to those prerequisites whenever algebra obscures the new idea.
Discuss together
If f(x) = x² − 1, what is the average rate of change from x = 1 to x = 3?
4Compute the endpoint outputs: f(3) = 8 and f(1) = 0. Divide the output change by the input change: (8 − 0) ÷ (3 − 1) = 8 ÷ 2 = 4.
Five-resource starter
Open an editable Grade 12 packet
Load five existing worksheets in the packet builder. Reorder them, add or remove resources, choose a student or teacher packet, then download the version you need.
- Evaluating functions
- Average rate of change
- Inverse functions
- Exact Unit Circle Trigonometry
- Arithmetic sequences
Step 1
Functions and graph transformations
Track inputs, outputs and domains while connecting symbolic rules to graph behavior. Verify inverses by composition and by reflection across y = x.
General functions
Function operations and composition worksheets
Add, subtract, multiply, divide and compose polynomial functions. Choose numbers, variables or mixed inputs, with ten questions and a separate worked answer key.
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General functions
Difference quotient worksheets
Simplify eight difference quotients with polynomial, factored and rational functions. Choose two inputs or an increment, add a formula reminder and print worked answers.
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General functions
Inverse functions worksheets
Identify inverse pairs or find inverse functions in twelve original questions. Practice linear functions and powers with explicit domains, exact radicals and worked answers.
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General functions
Graphing inverse functions worksheets
Find and graph four inverse functions. Choose fractional or integer linear rules, lines through the origin, quadratic branches and cubic functions, with completed graph keys.
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General functions
Graphing exponential functions worksheets
Graph eight exponential functions or write equations from curves with exact marked points. Compare growth, decay and translations on fixed unit grids with separate answer keys.
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General functions
Graphing logarithmic functions worksheets
Find exact domains and all-real ranges, then graph eight logarithmic functions with vertical asymptotes on fixed square grids. Includes affine arguments, fractional boundaries and separate answer keys.
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General functions
Graphing radical functions worksheets
Find the domain and range, then graph eight transformed square-root and cube-root functions on unit grids. Choose square roots, cube roots or balanced mixed practice with separate completed graph keys.
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Trigonometry: values, graphs, identities and equations
Use reference angles and quadrant signs to recover exact values. Then connect transformations to sine and cosine graphs, retain domain restrictions in identities, and find every solution in the stated interval.
Advanced math
Exact Unit Circle Trigonometry worksheets
Practice radians, coterminal reduction, quadrants, reference angles, and exact sine, cosine, and tangent values.
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Trigonometry
Sine and Cosine Graphs worksheets
Graph transformed sine and cosine functions or write one valid equation from a graph, using exact radians or degrees.
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Trigonometry
Basic Trigonometric Identities worksheets
Simplify and verify finite reciprocal, quotient, and Pythagorean identity recipes with the original-domain restrictions made explicit.
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Trigonometry
Trigonometric Equations on Bounded Intervals worksheets
Find all exact sine, cosine, and tangent solutions in explicit half-open radian or degree intervals, including simple frequency and phase transformations.
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Sequences and finite series
Identify whether change is additive or multiplicative before selecting a rule, and connect each finite-series formula to the terms it summarizes.
Sequences and series
Arithmetic sequences worksheets
Identify arithmetic sequences, find common differences, evaluate specified terms and write explicit formulas with integer or tenths practice.
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Sequences and series
Geometric sequences worksheets
Identify geometric sequences, find common ratios, evaluate specified terms and write explicit formulas with integer or tenths first terms.
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Sequences and series
Finite geometric series worksheets
Sum geometric lists, evaluate finite sigma notation and find the number of terms from a first term, last term and total. Choose integers, tenths or mixed practice.
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Rational functions and conic graphs
Use zeros, restrictions and asymptotes to organize rational graphs. For conics, identify the center or vertex and the defining distance or radius relationships.
Rational expressions
Graphing simple rational functions worksheets
Graph reciprocal functions and their horizontal or vertical shifts on labeled grids, with exact asymptotes, intercepts and reference points in a separate answer key.
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Rational expressions
Graphing general rational functions worksheets
Analyze and graph rational functions whose numerator and denominator each have degree at most 2, including poles, removable holes and horizontal, slant or polynomial end behavior.
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Conic sections
Properties of parabolas worksheets
Find exact vertices, axes, openings, extrema, latus rectum lengths and coordinate intercepts from vertical and horizontal parabola equations.
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Conic sections
Graphing circles worksheets
Read a circle in standard form, find its center and radius, and graph the complete circle on an equal-scale coordinate grid.
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Optional introductory calculus extension
Use only after the Precalculus prerequisites are secure. Connect limits to local behavior, derivatives to instantaneous change and antiderivatives to reversing a power-rule derivative.
Calculus
Simple Limit Evaluation worksheets
Evaluate exact finite-point limits for polynomial, rational, exponential and trigonometric functions.
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Calculus
Jump Discontinuity Limits from Graphs worksheets
Read finite one-sided limits and endpoint values from piecewise graphs.
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Calculus
Determining Continuity from Graphs
Read completed graphs or sketch exact piecewise, absolute-value, kinked-polynomial, and rational functions before finding continuity intervals.
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Calculus
Derivative by definition worksheets
Differentiate polynomial, rational, signed-power composite and trigonometric functions from the limit definition.
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Calculus
Power, Constant, and Sum Rules worksheets
Differentiate constants, polynomial sums, reciprocal monomials, and exact rational powers with the original real-domain conditions preserved.
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Calculus
Evaluate Derivatives at Points worksheets
Differentiate polynomial, rational, exponential and trigonometric functions, then evaluate exactly at a given point.
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Calculus
Power Rule Integration worksheets
Find exact indefinite integrals of polynomial, reciprocal integer-power, and reciprocal rational-power functions while preserving the original real domain.
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Triangle laws and probability reasoning
Use after triangle ratios, inverse trigonometric functions and fraction arithmetic are secure. Solve non-right triangles, choose ordered or unordered counting methods, and update a sample space when a condition is known.
Trigonometry
Law of Sines worksheets
Solve AAS, ASA, and ambiguous SSA triangles, including cases with zero, one, or two valid solutions.
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Trigonometry
Law of Cosines worksheets
Find a missing side from SAS data or a missing angle from SSS data, with acute and obtuse examples.
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Probability
Counting Applications worksheets
Choose among the multiplication principle, ordered selections without replacement, and unordered combinations in varied finite contexts.
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Probability
Conditional Probability worksheets
Compare conditional and joint probabilities using complete two-way count tables and two sequential draws without replacement.
Preview and downloadChoose what to practice next
Begin with one short resource, review the learner's written reasoning and adjust the difficulty on the activity page. Revisit an earlier group when arithmetic errors obscure the new idea.