General functions
Evaluating functions worksheets
Evaluate twelve polynomial and exponential functions. Choose numbers, variable expressions or a mixture, with exact answers and substitution steps.
Preview and downloadA path toward advanced mathematics
Precalculus worksheets
Connect the algebra and function ideas that make advanced mathematics easier to understand. Follow the groups in order or choose the skill your learner needs today.
51 printable resources, with student worksheets and worked answer editions.
Choose a useful starting point
Begin with secure equation solving, function notation and algebraic manipulation. Use exact unit-circle values before assigning trigonometric identities and equations. Course sequences vary; these focused resources are a learning path rather than a complete local curriculum.
Connect a rule to its graph
For y = 2 sin(x − π/2) + 1, what changes from y = sin x?
Amplitude 2; period 2π; shift right π/2 and up 1.
The coefficient 2 changes the distance from the midline, not the period. The midline is y = 1 and the range is [−1, 3]. These values use radians.
Five-resource starter
Prepare a functions and trigonometry packet
Start with function evaluation and unit-circle values, then add graphs, identities and equations. Open the editable selection, remove anything the learner is not ready for, and choose student or teacher PDFs.
Load the Precalculus starter →Step 1
Functions, rates and inverses
Identify inputs, outputs and domains, then compare rates and undo functions. Check an inverse by composition before graphing it.
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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Precalculus
Function Transformations
Map key points across shifts, reflections, stretches, and compressions for seven common parent-function families.
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Polynomial structure and zeros
Use division and theorem-based candidates to find and check zeros. A possible root is a candidate until substitution confirms it.
Polynomials
Dividing polynomials worksheets
Divide polynomials by monic linear divisors in ten expression problems or six long-division problems. Choose binomial, trinomial, four-term or mixed dividends and check exact quotient-and-remainder keys.
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Polynomials
Remainder theorem worksheets
Use the Remainder Theorem in twelve structured problems: evaluate four polynomials at a point, make four factor decisions from zero remainders, and divide four polynomials by signed monic linear divisors with exact quotient-and-remainder answers.
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Polynomials
Rational Root Theorem worksheets
List every possible rational zero from the printed leading and constant coefficients, then find exact rational zeros and their multiplicities in twelve degree-two through degree-four problems.
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Polynomials
Descartes Rule of Signs worksheets
Use sign changes in P(x) and P(−x) to list every possible number of positive and negative real zeros for twelve degree-two through degree-six polynomials.
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Polynomials
Binomial Theorem worksheets
Find exact coefficients, identify requested ordinal terms, and write complete ordered expansions for twelve one-variable, two-variable, linear, higher-power, and hybrid binomials.
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Exponential and logarithmic relationships
Connect inverse graphs to logarithm laws and equations. Keep logarithm arguments positive and check proposed solutions in the original equation.
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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Exponents and radicals
Properties of logarithms worksheets
Expand and condense logarithms with 16 selectable product, quotient and power forms. Practice natural logs, base-ten logs and fractional powers with exact symbolic answers.
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Exponents and radicals
Logarithmic equations worksheets
Solve six types of logarithmic equations with exact answers. Choose 12, 14 or 16 questions and check every solution in the original logarithms.
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Calculus
Exponential Growth and Decay worksheets
Build and solve contextual continuous, periodic, doubling, half-life, and observation-based exponential models.
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Trigonometry: values, graphs, identities and equations
Start with exact unit-circle values. Use periodic graphs to explain transformations, identities to rewrite expressions, and explicit intervals to list all equation solutions.
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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Precalculus
Tangent, Cotangent, Secant, and Cosecant Graphs
Analyze, draw, and write transformed reciprocal-trigonometric graphs with numerical scales, exact anchors, periods, and vertical asymptotes.
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Precalculus
Advanced Trigonometric Identities
Apply sum, difference, double-angle, half-angle, power-reduction, and product-sum identities with explicit domain and sign conditions.
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Precalculus
Advanced Trigonometric Equations
Solve factored, quadratic-in-form, identity-rewrite, double-angle, and multiple-angle equations over bounded or general scopes.
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Precalculus
Sinusoidal Modeling
Build exact sine or cosine models from noiseless extrema, tables, or graphs in circular, tide, seasonal, and harmonic contexts.
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Solve non-right triangles
Match each side with its opposite angle. Use the law of sines for AAS/ASA and check all SSA possibilities; use the law of cosines for SAS and SSS. Keep full calculator precision until the final answer.
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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Sequences and finite series
Distinguish a constant difference from a constant ratio, then connect the terms to a finite sum.
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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Sequences and series
Infinite geometric series worksheets
Decide convergence or divergence, find infinite geometric sums and determine common ratios from terms, sigma notation or first-term and total givens. Choose fractions or decimals.
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Counting and conditional probability
Decide whether order matters before counting. Then distinguish a conditional probability from a joint event, using two-way tables and draws without replacement.
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.
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Rational functions and conic graphs
Organize a graph using its restrictions, zeros and asymptotes. For conics, connect an equation to its center, vertex or radius.
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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Conic sections
Properties of ellipses worksheets
Find exact centers, vertices, co-vertices, foci, axis lengths and eccentricity from standard-form ellipse equations.
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Conic sections
Graphing ellipses worksheets
Graph standard-form ellipses on equal-scale coordinate grids using exact centers and axial extrema.
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Conic sections
Properties of hyperbolas worksheets
Find exact vertices, foci and opening directions from horizontal and vertical standard-form hyperbola equations.
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Conic sections
Graphing hyperbolas worksheets
Graph both visible branches, vertices, construction rectangles and asymptotes on equal-scale coordinate grids.
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Conic sections
Eccentricity of conic sections worksheets
Find exact eccentricities for circles, ellipses, parabolas and hyperbolas from standard or general equations.
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Parametric and polar curves
Connect equations to coordinates and inherited domains. Follow one complete trace, preserve signed radii and distinguish ordinary polar curves from focus/directrix conics.
Precalculus
Parametric Equations worksheets
Trace oriented parametric curves, eliminate parameters without losing domains, create parameterizations, and interpret projectile motion.
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Precalculus
Polar Coordinate Conversions worksheets
Convert exact points and bounded line or circle equations between rectangular and polar forms, including negative-radius equivalents.
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Precalculus
Polar Function Graphs worksheets
Build key-value tables, test symmetry, graph full polar curves, and identify circle, cardioid, limacon, rose, and lemniscate families.
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Precalculus
Polar Conic Sections
Normalize, classify, graph, and write focus-at-pole polar conics from eccentricity and an axis-parallel directrix.
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Complex numbers in polar form
Start from modulus and rectangular coordinates, then use arguments to multiply, divide, take powers and list every root.
Complex numbers
Absolute value of complex numbers worksheets
Find the modulus of ten complex numbers. Connect real and imaginary components with distance from the origin, then check exact, simplified radical answers.
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Precalculus
Complex Numbers in Polar Form
Convert polar and rectangular forms, multiply and divide, apply De Moivre's theorem, and list all roots through fourth degree.
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Vectors and matrix operations
Keep vector components, magnitude and direction distinct. For matrix operations, check dimensions and order before calculating.
Precalculus
Vectors in the Plane worksheets
Find components, magnitude, direction, unit vectors, operations, displacement resultants, and dot products in two dimensions.
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Matrices
Basic matrix operations worksheets
Practice six matrix addition, subtraction and scalar multiplication questions with numeric, algebraic or mixed entries. Undefined cases make dimension checks part of the work.
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Matrices
Matrix multiplication worksheets
Complete six matrix products with exact numeric, algebraic or mixed entries, and identify products that are undefined because the inner dimensions differ.
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Matrices
Mixed matrix operations worksheets
Work through six questions that mix addition, subtraction or scalar multiplication with separate matrix products. Exact entries and dimension-aware answers distinguish valid expressions from undefined ones.
Preview and downloadWhen the prerequisites are secure
Continue to limits and derivatives when algebra, function graphs and trigonometry are comfortable. Calculus is a separate next step.
Grade 11 practice · Grade 12 practice · Focused trigonometry practice