Real numbers
Classifying real numbers worksheets
Classify fourteen values into every applicable number set. Compare integers, reducible and irreducible signed fractions, square roots and pi with a separate answer key.
Preview and downloadBuild on what the learner knows
Algebra 2 worksheets
Check the basics with real number sets and signed arithmetic, then explore functions, matrices and complex numbers. Choose the skill that matches the lesson and review a prerequisite when a specific step needs work.
Choose a practice worksheetCheck the foundations
Real numbers and signed arithmetic
Classify a value before calculating with it. These fourteen-question worksheets separate number-set reasoning, sums and differences, and multiplication or division notation.
Real numbers
Adding and subtracting rational numbers worksheets
Create fourteen signed sums and differences with integers, decimals, fractions or a mixture. Each question has two or three operands and an exact answer.
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Real numbers
Multiplying and dividing integers worksheets
Practice fourteen signed integer products and exact quotients. Choose fraction-bar division, ÷, × or parentheses, with factor magnitudes from 2 to 20.
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Real numbers
Multiplying and dividing rational numbers worksheets
Create fourteen signed products and quotients with any combination of integers, decimal tenths and fractions. Exact answers use terminating decimals or simplest fractions.
Preview and downloadPredict and solve roots
Work with quadratic roots
Use the discriminant to classify roots, or isolate a squared variable and take both square roots. Practice exact radicals, rounded real roots and imaginary roots.
Equations
Working with the discriminant worksheets
Calculate the discriminant for twelve quadratic equations, then use its sign and square status to count and classify distinct roots. Choose monic, signed nonmonic or mixed leading coefficients.
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Equations
Solving quadratics by taking square roots worksheets
Solve ten quadratic equations by isolating a squared variable and taking both square roots. Choose direct, offset, scaled, multi-step or mixed equations with rounded real, exact real, no-real or imaginary results.
Preview and downloadFrom a pattern to an explicit rule
Sequences and series
Classify sequences from lists or formulas, calculate specified terms, insert arithmetic or geometric means, write explicit or recursive rules from patterns and find finite polynomial, exponential and arithmetic sums or finite and infinite geometric sums. Read each series’ stated lower and upper limits.
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
Comparing arithmetic and geometric sequences worksheets
Classify sequences from four terms or a formula as arithmetic, geometric or neither, with twelve questions and a separate answer key.
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Sequences and series
Arithmetic series worksheets
Sum finite arithmetic lists, evaluate sigma notation and find the number of terms from a first term, last term and total. Choose integers or tenths.
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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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Sequences and series
General series worksheets
Expand sigma notation into finite sums, evaluate polynomial and exponential series, and rewrite sums in sigma notation. Combine the three problem types in twelve-question worksheets.
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Sequences and series
Arithmetic and geometric means worksheets
Insert one, two or three missing terms between endpoints of arithmetic and geometric sequences. Choose positive, negative or mixed numbers with twelve questions and separate answer keys.
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Sequences and series
General sequences worksheets
Continue number patterns, write explicit and recursive sequence formulas, and find the first four terms from a given rule. Practice linear, quadratic and exponential patterns.
Preview and downloadReduce, combine and solve exact algebraic fractions
Rational expressions and equations
Simplify, multiply, divide, add and subtract rational expressions, then solve rational equations and check each candidate against the original domain. Every activity retains the conditions that keep the original expressions defined.
Rational expressions
Simplifying rational expressions worksheets
Practice ten exact single-quotient reductions with monomial, binomial or trinomial inputs, complete cancellation and retained original denominator restrictions.
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Rational expressions
Multiplying rational expressions worksheets
Practice ten exact products using monomials, binomial factors and factorable polynomials, with reduced answers and retained original denominator restrictions.
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Rational expressions
Dividing rational expressions worksheets
Practice ten exact quotients with expanded monomials, linear binomials and factorable quadratics, fully reduced answers and all original domain restrictions.
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Rational expressions
Adding and subtracting rational expressions worksheets
Practice ten exact sums and differences with common or unlike polynomial denominators, including multivariable monomials, higher-degree binomials and retained domain restrictions.
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Rational expressions
Solving rational equations worksheets
Practice ten exact rational equations with monomial or binomial expressions, original-domain restrictions and checked rational solutions.
Preview and downloadConnect exact equations with geometry
Conic sections
Find exact circle, ellipse, parabola and hyperbola properties, construct equations, graph conics, classify standard or general equations and compare exact eccentricities.
Conic sections
Properties of circles worksheets
Find exact circle centers and positive radii from standard and rearranged general equations using whole numbers, fractions and radicals.
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Conic sections
Writing equations of circles worksheets
Write exact standard-form circle equations from centers, radii, points, diameters, translations, area, circumference and tangent lines.
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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
Writing equations of ellipses worksheets
Construct exact standard-form ellipse equations from vertices, co-vertices, foci, centers and horizontal widths.
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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 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
Writing equations of parabolas worksheets
Write exact vertical or horizontal vertex-form equations from foci, directrices, intercepts, points or three-point interpolation.
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Conic sections
Graphing parabolas worksheets
Graph unit-coefficient vertical parabolas in vertex form on equal-scale coordinate grids with exact vertices.
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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
Writing equations of hyperbolas worksheets
Construct exact standard-form hyperbola equations from general equations, vertices, foci, conjugate-axis data and asymptotes.
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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
Classifying conic sections worksheets
Classify circles, ellipses, parabolas and hyperbolas from standard or general equations, then convert and graph general equations.
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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.
Preview and downloadRead a function through its values
Function values, inverses and average rates
Substitute numbers or expressions into functions, combine two polynomials with arithmetic or composition, or calculate an average rate from a table, a graph or a symbolic difference quotient. Find inverse formulas, restrict quadratic domains and reflect graphs across y = x. Each activity includes a separate worked key.
General functions
Average rate of change from tables worksheets
Find average rates from six function tables. Choose 6 or 12 questions, print Letter or A4, and check each result with a separate worked answer key.
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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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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
Average rate of change from graphs worksheets
Read four function graphs and estimate their average rates of change. Choose linear, quadratic, cubic, sine or exponential curves, with secants and 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 quadratic functions worksheets
Graph four quadratic functions in vertex form on blank coordinate grids. Each sheet includes every leading coefficient from −2, −1, 1 and 2, with a separate completed graph key.
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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
Logarithmic function inverses worksheets
Find inverses in logarithmic, exponential or mixed directions across six exact forms. Every problem prints the real domain needed for a single-valued inverse, with separate exact answer keys.
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General functions
Graphing quadratic inequalities worksheets
Graph four expanded quadratic inequalities on blank coordinate grids. Compare unit and nonunit leading coefficients, both opening directions and all four strict or inclusive relations.
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General functions
Determining functions from mapping diagrams worksheets
Classify eight mapping diagrams as functions or nonfunctions. Choose two to five numeric or letter values on each side, with four of each classification and a separate answer key.
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General functions
Domain and range from ordered pairs worksheets
Find the domain and range of ten five-pair relations. Choose negative or nonnegative coordinates, control repeats independently and optionally classify each relation as a function.
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General functions
Identifying functions from graphs worksheets
Apply the vertical line test to eight finite graph relations. Choose lines, polynomials, special curves, horizontal parabolas or rotated curves, with balanced endpoints and a separate key.
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General functions
Domain and range from graphs worksheets
Read finite domain and range intervals from eight varied relation graphs. Practice open and closed extrema and optionally apply the vertical line test.
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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.
Preview and downloadConnect equations and coordinate graphs
Linear equations, inequalities and absolute value
Review slopes and equations, select strict or inclusive comparisons for half-plane graphs, then extend graph reading to the vertices and reflections of absolute value functions.
Linear functions
Mixed linear equation skills worksheets
Connect graphs, equations and line properties in ten tasks: four graph-to-slope questions, four equation-to-slope questions and two write-and-graph problems.
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Linear functions
Graphing two-variable inequalities worksheets
Graph eight linear inequalities on coordinate planes. Select any nonempty combination of <, ≤, > and ≥, then draw the boundaries and shade the solution regions with a separate graphical key.
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Linear functions
Graphing absolute value functions worksheets
Graph eight absolute value functions or write equations from eight V-shaped graphs. Practice translations and reflections of y = |x| with integer vertices and a separate worked graphical key.
Preview and downloadReason about sets of solutions
Compound inequalities
Combine two solved conditions with AND or OR. Practice addition/subtraction, multiplication/division or mixed operations with exact intervals and two-ray graphs.
Inequalities
Compound inequalities worksheets
Solve and graph ten compound inequalities. Choose addition and subtraction, multiplication and division, or mixed operations, then connect AND intervals and OR rays with a separate graphical answer key.
Preview and downloadSolve a comparison about distance
Absolute value inequalities
Distinguish operations inside and outside the absolute-value bars. Find two exact boundaries, decide whether to keep the interior or exterior regions, and graph every real solution.
Inequalities
Absolute value inequalities worksheets
Solve and graph ten absolute value inequalities. Choose addition and subtraction, multiplication and division, or mixed operations, with shifts, negative inner coefficients and separate worked graphical answers.
Preview and downloadSolve both valid branches
Absolute value equations
Distinguish absolute-value bar placement, solve signed and fractional expressions, and keep values that make a denominator zero out of the solution set. Exact roots and separately marked decimal approximations support each check.
Equations
Absolute value equations worksheets
Solve ten absolute value equations from six selectable families. Practice signed interiors, outside coefficients, fractions and variable denominators, with exact solutions, clearly marked approximations and separate worked keys.
Preview and downloadReview a basic algebra skill
These activities keep their own skill pages and settings. Choose the one that matches the step the learner needs to practice.
Polynomials
Factoring polynomials with all techniques worksheets
Factor twelve expanded polynomials completely over the integers, mixing greatest common factors, quadratics, grouping, cube identities, substitution patterns, repeated factors and irreducible quadratic factors.
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Polynomials
Analyzing and solving polynomial equations worksheets
Analyze and solve six expanded monic polynomial equations of selected degrees two through six. Each exact key separates degree and Descartes possibilities from rational candidates and the complete roots with multiplicity.
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Polynomials
Polynomial graph identification worksheets
Match expanded linear, quadratic, cubic and quartic equations to one of four coordinate graphs drawn on the same −5 to 5 scale, with balanced answer positions and deliberately useful distractors.
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Polynomials
Irrational and imaginary root theorem worksheets
Use degree and conjugate pairing only—not polynomial solving—to list possible real and nonreal complex-root counts, counting multiplicity and including real roots in the complex total. Complete rational-coefficient root lists and construct least-degree monic integer 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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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
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
Factoring sums and differences of cubes worksheets
Factor twelve sums and differences of cubes completely. Choose common variable factors, displayed leading coefficients, or mixed practice with exact complete products.
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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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Algebraic expressions
Writing algebraic expressions worksheets
Translate words into algebra with ten questions per worksheet. Select easy, medium and hard phrases, including grouping, fractions and powers, and print an explained answer key.
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Algebraic expressions
Combining like terms worksheets
Print ten combining-like-terms questions and a separate worked key. Choose original one-variable practice or a progressive English lesson with two-variable grouping, distribution, error analysis, and perimeter.
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Algebraic expressions
Distributive property worksheets
Print 10 distributive property expressions. Choose grouped three- or four-term forms, signed factors and coefficient ranges, with worked answers.
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Equations
Multi-step integer equations worksheets
Choose from eleven equation structures for ten questions with integer operands. Practice like terms, grouped expressions and variables on either side, with exact worked solutions and separately rounded answers.
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Algebraic expressions
Evaluating two-variable expressions worksheets
Evaluate expressions using two distinct variable values. Select sums, grouped multiplication and exact-division forms with whole numbers or integers, plus an explained answer key.
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Order of operations
Basic order of operations worksheets
Evaluate ten expressions with all four arithmetic operations. Select easy or hard practice and five grouping/exponent formats, then print the questions and a separate worked key.
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Percent
Percentage calculations: part, whole and rate
Find a part, a whole or a percentage in ten configurable problems. Choose five equation forms, whole or decimal operands, word prompts and 1–3 decimal places.
Preview and downloadCheck structure before calculating
Matrix operations, determinants, inverses and systems
Add, subtract and multiply matrices, evaluate exact determinants, solve matrix equations without changing multiplication order, find 2 × 2 inverses, and use Cramer's rule to solve or classify systems.
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.
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Matrices
2 × 2 determinant worksheets
Evaluate twelve determinants of 2 × 2 matrices with numeric, algebraic or mixed entries. Algebraic questions supply one variable value for the final numeric answer.
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Matrices
3 × 3 determinant worksheets
Evaluate twelve determinants of 3 × 3 matrices with numeric, algebraic or mixed entries. Algebraic questions supply one variable value for the final numeric answer.
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Matrices
Matrix inverse worksheets
Decide whether six numeric 2 × 2 matrices have inverses, then find six exact inverses or state that no inverse exists.
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Matrices
Matrix equations worksheets
Solve six exact matrix equations by isolating a scalar multiple of X or multiplying by a 2 × 2 inverse on the left.
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Matrices
Cramer's rule 2 × 2 worksheets
Solve twelve two-variable systems with Cramer's rule. Practice unique, infinitely many and no-solution systems with exact determinant reasoning.
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Matrices
Cramer's rule 3 × 3 worksheets
Solve twelve three-variable systems with Cramer's rule. Use exact determinants and rank evidence for unique, infinitely many and no-solution systems.
Preview and downloadChoose the question you want a learner to answer
Where is the number?
Use the real and imaginary components as two signed coordinates. Plotting and identifying points connect notation with position.
Practice complex-plane graphs →How far is it from zero?
Use a right triangle to derive the modulus. Square both components and take the nonnegative square root of their sum.
Practice modulus →How does the expression simplify?
Use distribution, i² = −1 and conjugates to produce an exact result.
Practice complex arithmetic →Available now
Complex numbers practice
Each activity has ready-made PDFs, a customizable preview and separate answers. Choose a focused task before using a combined review.
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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Complex numbers
Graphing complex numbers worksheets
Plot complex numbers and read a + bi from points on the complex plane. Choose six plotting questions, six identification questions or a balanced mixture.
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Complex numbers
Complex number operations worksheets
Add, subtract and multiply complex numbers in ten-question sets. Select sums and differences, imaginary monomial products or binomial products and squares.
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Complex numbers
Rationalizing complex denominators worksheets
Rewrite ten complex quotients with real denominators. Select real-over-imaginary, binomial-over-imaginary or binomial-over-binomial questions and print worked answers.
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Complex numbers
Complex numbers review worksheets
Combine four modulus questions with four complex-plane questions. Choose plotting, identifying points or both, with a separate key for the same generated set.
Preview and downloadConnect powers and logarithms
Rewrite equations in exponential or logarithmic form and evaluate exact logarithms, including fractional and negative exponents. Apply product, quotient and power laws to expand or condense logarithms, solve exponential equations by matching bases or taking logarithms, solve logarithmic equations with domain checks, use supplied log values without a calculator, or use change of base for calculator evaluation.
Exponents and radicals
Meaning of logarithms worksheets
Rewrite exponential and logarithmic equations and evaluate exact logarithms. Choose numeric or symbolic forms, fractional exponents and reciprocal arguments, with separate answers.
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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
Change of base formula worksheets
Use a calculator to evaluate natural, common and other logarithms. Choose 12, 14 or 16 questions and round answers to two or three decimal places.
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Exponents and radicals
Writing logs in terms of others worksheets
Use three given logarithms to find another value without a calculator. Select nine forms and practice with numbers, letters or a mix of both.
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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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Exponents and radicals
Exponential equations without logarithms worksheets
Solve nine types of exponential equations by rewriting to a common base. Choose 12 or 14 questions with exact fraction answers and worked keys.
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Exponents and radicals
Exponential equations requiring logarithms worksheets
Solve six types of exponential equations using logarithms, including natural-base equations. Choose 12, 14 or 16 questions with worked keys and four-place answers.
Preview and downloadReview the prerequisite that matches the difficulty
A lost negative sign and an unfamiliar conjugate need different follow-up practice. These foundation resources retain their own skill pages and are not additional complex number generators.
Distribution and polynomial products
Recall how each term multiplies every term in the other factor. This same structure appears in complex multiplication.
Review polynomial operations →Powers and exact roots
Separate a power from its principal root. Simplifying roots helps keep a complex modulus exact.
Review powers and radicals →Coordinates and linear relationships
Read signed coordinates, follow a scale and connect an equation with a graph before introducing a different kind of plane.
Review linear functions →Equations and checking solutions
Keep equivalent steps visible. Substitution and checking a result are useful habits before more advanced equation work.
Review linear equations →Teach conjugates as a useful relationship
Begin with (2 + 3i)(2 − 3i). Distribution produces 4 − 9i² because the imaginary cross terms cancel. The product is 13.
Generalize the same calculation to (a + bi)(a − bi) = a² + b². Then use it to explain why multiplying both parts of a complex fraction by the conjugate gives an equivalent fraction with a real denominator.
Plan, print and check
Begin with a diagnostic
Ask the learner to plot one number, find one modulus and expand one product. Choose the next sheet from the step that needs attention.
Change one setting
Use plot-only or identify-only questions first. Keep sums and differences separate from multiplication until the real and imaginary terms are secure.
Keep answers separate
Download the student edition or include the key after the student pages. A settings link preserves the same seed when you need to revisit a set.