Practice

Math Practice Problems

Practice problems for every topic in our lessons, from arithmetic to calculus limits and derivatives. Every answer can be checked instantly, and every set is printable.

There are two kinds of practice here. Generator sets, which include all of the basic math and algebra preliminaries topics, produce a fresh set of problems every time you choose a difficulty, so you can keep practising one skill until it sticks. Most other topics are fixed sets of problems written to match a lesson, and every problem comes with a full worked solution you can open after you answer.

Most fixed sets end with the mistakes students make most often on that topic and link back to the lesson that teaches it. If you get stuck on a problem, read the worked solution first, then try the next problem without looking; that is usually faster than rereading the whole lesson.

Basic Math and Arithmetic 11 sets

Number fluency — the four operations, integers, fractions, decimals, percentages and ratios.

➕

Addition Practice Problems and Printable Worksheets

Generate unlimited addition problems at three difficulty levels. Practice on screen with instant answer checking, or print clean worksheets and answer keys.

Start practicing 🔢

Decimal Practice Problems

Generate unlimited decimal arithmetic worksheets with Easy, Medium, and Hard difficulty — addition, subtraction, multiplication, and division.

Start practicing ➗

Division Practice Problems and Long Division Worksheets

Generate unlimited division problems with or without remainders. Choose easy, medium, or hard, check answers instantly, or print a free division worksheet.

Start practicing 🍰

Fraction Practice Problems

Generate unlimited fraction practice problems — same denominators, unlike denominators, and mixed numbers — with instant, simplified answers.

Start practicing ±

Integer Practice Problems

Unlimited integer practice problems across three difficulty levels. Master negative-number sign rules with instant checking and printable worksheets.

Start practicing ✖️

Multiplication Practice Problems

Generate unlimited multiplication worksheets with Easy, Medium, and Hard difficulty — instant answers, printable, no sign-up.

Start practicing 🧮

Order of Operations Practice Problems

Generate unlimited PEMDAS/BODMAS practice problems with parentheses and mixed operations — instant, verified-correct answers.

Start practicing ％

Percentage Practice Problems

Generate unlimited percentage word problems — percent of a number, percent change, and reverse percentages — with instant checking.

Start practicing 🎲

Random Math Practice Problems

Unlimited random math practice problems across 11 topics — fractions, decimals, percentages, algebra and more. Pick a difficulty and get instant grading.

Start practicing ⚖️

Ratio Practice Problems and Printable Worksheets

Unlimited ratio practice problems: simplifying ratios, finding missing values in equivalent ratios, and sharing a quantity in a given ratio.

Start practicing ➖

Subtraction Practice Problems

Generate unlimited subtraction worksheets with Easy, Medium, and Hard difficulty — instant answers, printable, no sign-up.

Start practicing

Algebra Preliminaries 20 sets

The manipulation toolkit: exponents, radicals, polynomials, factoring and rational expressions.

P+Q

Adding Polynomials Practice Problems

Generate unlimited practice problems adding two or three polynomials, evaluated at a chosen x, with instant checking.

Start practicing a+bi

Complex Number Arithmetic Practice Problems

Unlimited practice problems adding, subtracting, multiplying, and dividing complex numbers, plus powers of i and conjugate products.

Start practicing a+bi

Complex Numbers Practice Problems

Unlimited complex number practice problems across three levels — adding, multiplying, dividing, conjugates, and powers of i.

Start practicing aᵐ⁺ⁿ

Exponent Rules Practice Problems

Unlimited practice problems chaining two or more exponent rules in one expression — product, quotient, power, and rational exponents.

Start practicing a·b

Factoring by Grouping Practice Problems

Generate unlimited practice problems factoring a four-term polynomial by grouping, plus the ac method for trinomials, with instant checking.

Start practicing xⁿ±1

Factoring Higher-Degree Polynomials Practice Problems

Unlimited practice problems factoring degree-3 and degree-4 polynomials — sum and difference of cubes, GCF-first cases, and quadratic-in-form quartics.

Start practicing ( )

Factoring Polynomials Practice Problems

Unlimited factoring practice problems across three difficulty levels — trinomials, the GCF, special patterns, and the ac method.

Start practicing x²+

Factoring Quadratics Practice Problems

Unlimited practice problems factoring quadratic trinomials — leading coefficient of 1, difference of squares, perfect squares, and the ac method.

Start practicing GCF

Greatest Common Factor

Generate unlimited practice problems finding the greatest common factor of numbers, monomial exponents, and negative-GCF cases, with instant checking.

Start practicing xⁿ

Integer Exponents Practice Problems

Unlimited integer exponent practice problems across three levels — product, quotient, power, zero, and negative exponent rules.

Start practicing P·Q

Multiplying Polynomials Practice Problems

Unlimited practice problems multiplying polynomials — monomial times polynomial, FOIL, the box method, and special product patterns.

Start practicing x⁻ⁿ

Negative Exponents Practice Problems

Unlimited negative exponent practice problems across three levels: numeric bases, negative powers of products and quotients, and variable expressions.

Start practicing P(x)

Polynomials Practice Problems

Unlimited polynomial practice problems across three levels — evaluating, adding, subtracting, multiplying, and dividing by a monomial.

Start practicing √x

Radicals Practice Problems

Unlimited radical practice problems across three levels — perfect roots, multiplying radicals, conjugates, and decimal approximations.

Start practicing ⁿ√x

Rational Exponents Practice Problems

Unlimited rational (fractional) exponent practice problems across three difficulty levels — evaluating roots and powers together.

Start practicing a/b

Rational Expressions Practice Problems

Generate unlimited rational expression practice problems across three difficulty levels — evaluating fractions built from polynomials — with instant checking.

Start practicing 1/√x

Rationalizing Denominators Practice Problems

Unlimited practice problems rationalizing denominators — monomial radicals, conjugate binomials, and higher-index roots — with instant checking.

Start practicing √

Simplifying Radicals Practice Problems

Generate unlimited practice problems extracting the coefficient from a radical, across square roots, cube roots, and variable exponents, with instant checking.

Start practicing a/b

Simplifying Rational Expressions Practice Problems

Generate unlimited practice problems finding the excluded values of a rational expression, plus a cancel-then-evaluate check, with instant checking.

Start practicing P−Q

Subtracting Polynomials Practice Problems

Unlimited practice problems subtracting polynomials, evaluated at a chosen x, including reversed order to drill that subtraction is not commutative.

Start practicing

Solving Equations and Inequalities 24 sets

Linear and quadratic equations, inequalities, interval answers and applied word problems.

|x|

Absolute Value Equations Practice Problems

Unlimited practice solving absolute value equations by isolating and splitting into two cases, with instant checking. Enter the larger solution.

Start practicing 📏

Absolute Value Inequalities Practice Problems

Twelve absolute value inequalities — "less than" as one interval, "greater than" as two pieces — plus the always- and never-true cases.

Start practicing 🔤

Algebra Equations Practice Problems

Generate unlimited algebra equations — one-step, two-step, multi-step, and variables on both sides — with instant checking.

Start practicing 📝

Algebra Word Problems Practice

Fifteen worked algebra word problems — number, age, consecutive-integer, and part-of-a-whole — each with a full step-by-step solution.

Start practicing □²

Completing the Square Practice Problems

Unlimited practice finding the constant that completes the square for x² + bx, with integer and fractional results and instant checking.

Start practicing <x<

Compound Inequalities Practice Problems

Twelve compound inequalities joined by "and" or "or", including the three-part form, each solved and written in interval notation.

Start practicing y=kx

Direct Variation Practice Problems

Twelve direct variation practice problems with answers: finding k, writing y = kx, tables, word problems and variation with a square.

Start practicing 🚗

Distance, Rate, and Time Practice Problems

Twelve worked motion word problems — meeting, catch-up, round trips, and current or wind — each solved with a distance-rate-time chart.

Start practicing u²

Equations Reducible to Quadratic Form Practice Problems

Twelve equations that become quadratic after a substitution — quartics, fractional exponents, and √x — each solved by u-substitution.

Start practicing [ )

Interval Notation Practice Problems

Fifteen conversion problems between inequalities, number-line graphs, and interval notation, each fully worked.

Start practicing y=k/x

Inverse Variation Practice Problems

Twelve inverse variation practice problems with answers: finding k = xy, speed and time, workers and days, Boyle’s law and inverse squares.

Start practicing kxz

Joint Variation Practice Problems

Joint variation practice problems with answers: find the constant k, use y = kxz, variation with squares, combined variation and word problems.

Start practicing x/a

Linear Equations with Fractions Practice Problems

Unlimited practice solving linear equations that contain fractions by clearing the denominator with the LCD, with instant answer checking.

Start practicing x<

Linear Inequalities Practice Problems

Unlimited practice solving one-variable linear inequalities, including the flip when dividing by a negative, with instant checking.

Start practicing 🧪

Mixture Word Problems Practice

Twelve worked mixture problems — percent solutions, dilutions, priced blends, coins, and split investments — each with a full solution.

Start practicing >0

Polynomial Inequalities Practice Problems

Twelve polynomial inequalities solved with the sign-chart method — quadratics, cubics, and repeated factors — each with an interval answer.

Start practicing ax²

Quadratic Equations Practice Problems

Unlimited practice solving quadratic equations by factoring and the zero-product property, with instant checking. Enter the larger solution.

Start practicing ±√

Quadratic Formula Practice Problems

Fifteen quadratic equations solved with the quadratic formula — rational, irrational, repeated, and complex roots — each fully worked.

Start practicing 📐

Quadratic Word Problems Practice

Twelve quadratic word problems — area, borders, projectiles, integer products, and revenue — each solved with impossible roots rejected.

Start practicing √x

Radical Equations Practice Problems

Twelve radical equations — one root, two roots, and cube roots — each solved by isolating and squaring, with the extraneous check shown.

Start practicing p/q

Rational Equations Practice Problems

Twelve solving rational equations practice problems with answers, including cross-multiplying, quadratic results and extraneous solutions.

Start practicing p/q

Rational Inequalities Practice Problems

Twelve rational inequalities solved with the sign-chart method, combining into one fraction and excluding denominator zeros.

Start practicing 🔧

Solving for a Variable Practice Problems

Fifteen worked literal-equation problems: rearranging formulas to isolate one variable, including variables in a power or a root.

Start practicing ⏱️

Work Rate Practice Problems

Twelve worked "working together" rate problems — two and three workers, a worker leaving early, and fill-and-drain tanks — fully solved.

Start practicing

Graphing and Functions 17 sets

Lines in every form, circles, and functions — notation, domain and range, composition and inverses.

Δy/Δx

Average Rate of Change Practice Problems

Twelve average rate of change practice problems with answers: from formulas, tables and real-world data, including negative rates.

Start practicing Δ/h

Difference Quotient Practice Problems

Twelve difference quotient practice problems with answers: linear, quadratic, cubic, rational and square root functions, simplified step by step.

Start practicing ↔↕

Domain and Range Practice Problems

Fifteen problems on finding the domain of rational and radical functions and the range of lines, parabolas, roots and absolute values.

Start practicing ○

Equation of a Circle Practice Problems

Fourteen problems on reading centre and radius, writing a circle's equation, completing the square, and the degenerate cases.

Start practicing f(x)

Function Notation Practice Problems

Fourteen problems on evaluating f(x) at numbers and expressions, working backwards from an output, and telling f(x+1) from f(x)+1.

Start practicing f∘g

Function Operations and Composition Practice Problems

Fifteen problems on adding, subtracting, multiplying and dividing functions, and on composing them with f(g(x)).

Start practicing y≥

Graphing Linear Inequalities Practice Problems

Twelve graphing linear inequalities practice problems with answers: solid or dashed lines, which side to shade, test points, and inequalities that flip.

Start practicing ↗↘

Increasing and Decreasing Intervals Practice Problems

Twelve practice problems on increasing, decreasing and constant intervals with answers, for lines, parabolas, absolute value and cubic graphs.

Start practicing f⁻¹

Inverse Functions Practice Problems

Fourteen problems on deciding whether a function is one-to-one, finding its inverse by swapping and solving, and swapping domain and range.

Start practicing ∥ ⊥

Parallel and Perpendicular Lines Practice Problems

Fifteen problems on equal slopes and negative reciprocals: classifying pairs of lines, writing new lines through a point, and perpendicular bisectors.

Start practicing f(x)

Parent Functions Practice Problems

Parent functions practice problems with answers: identify the parent of an equation, give domains and ranges, and track points after a shift.

Start practicing { }

Piecewise Functions Practice Problems

Thirteen problems on evaluating piecewise functions, handling the boundary value, and finding the domain and range of a multi-rule definition.

Start practicing y−y₁

Point-Slope Form Practice Problems

Fourteen problems on building a line from a slope and a point, from two points, and converting the result into the other two forms.

Start practicing Δy/Δx

Slope Practice Problems

Fifteen problems on finding slope from two points, from an equation, and from a rate, including the zero and undefined cases.

Start practicing mx+b

Slope-Intercept Form Practice Problems

Fourteen problems on reading slope and intercept, rearranging any linear equation into y = mx + b, and using m and b in real models.

Start practicing Ax+By

Standard Form of a Line Practice Problems

Thirteen problems on converting to and from Ax + By = C, clearing fractions, reducing coefficients, and finding intercepts fast.

Start practicing (a,0)

x- and y-Intercepts Practice Problems

Fifteen problems on finding intercepts from lines, parabolas and standard form, including the cases where an intercept does not exist.

Start practicing

Polynomial Functions 13 sets

Dividing polynomials, the remainder and factor theorems, finding zeros, end behavior, sketching graphs and partial fractions.

a±bi

Complex Zeros Practice Problems

Twelve complex zeros practice problems: count zeros, use conjugate pairs, solve for imaginary zeros, and find the rest from one given complex zero.

Start practicing aₙxⁿ

Degree and Leading Coefficient Practice Problems

Twelve practice problems on the degree, leading coefficient, leading term and constant term of a polynomial, in order, out of order and factored.

Start practicing +−+

Descartes' Rule of Signs Practice Problems

Twelve Descartes' rule of signs practice problems: count sign changes, form P(−x), and list the possible numbers of positive and negative real zeros.

Start practicing ↗↘

End Behavior Practice Problems

Twelve worked problems on polynomial end behavior — degree, leading coefficient, which way each tail goes, and reading the leading term off a factored form.

Start practicing ∿

Graphing Polynomials Practice Problems

Practice sketching polynomial graphs: y-intercepts, cross or touch at each zero, turning points, and writing a function from its graph.

Start practicing A/B

Partial Fractions Practice Problems

Unlimited partial fractions practice: distinct linear, repeated linear and irreducible quadratic factors, solving for A, B and C with instant checking.

Start practicing ÷x

Polynomial Division Practice Problems

Unlimited polynomial long division practice — divide by a linear or quadratic divisor and find the remainder or a quotient coefficient, with instant checking.

Start practicing x⁵→x⁰

Polynomial in Standard Form Practice Problems

Practice writing polynomials in standard form: reorder terms, combine like terms, expand brackets and distribute a minus sign, with worked solutions.

Start practicing x₀

Polynomial Zeros Practice Problems

Practice finding the zeros of a polynomial and their multiplicity: factored forms, grouping, difference of squares and quadratic substitution.

Start practicing p/q

Rational Root Theorem Practice Problems

Twelve worked problems on the rational root theorem — listing p over q candidates, counting them, and testing down to the actual rational roots.

Start practicing P(a)

Remainder and Factor Theorem Practice Problems

Unlimited practice on the remainder and factor theorems — evaluate P(a) to get a remainder, and solve for the coefficient that makes x minus a a factor.

Start practicing ⌐

Synthetic Division Practice Problems

Unlimited synthetic division practice — divide by x minus a and read the quotient coefficients and remainder straight off the bottom row, with instant checking.

Start practicing (x−r)

Writing a Polynomial From Its Zeros Practice Problems

Twelve practice problems on writing a polynomial from its zeros: one factor per zero, repeated zeros, conjugate pairs, and fitting a point.

Start practicing

Exponential & Logarithmic Functions 15 sets

Exponential functions and their graphs, growth and decay, logarithms and log rules, change of base, and solving exponential and log equations.

logₐ

Change of Base Practice Problems

Twelve change of base practice problems — evaluating logs in any base with ln or log, exact answers by switching to a common base, and a first equation.

Start practicing ln

Common and Natural Log Practice Problems

Twelve practice problems on log (base 10) and ln (base e) — evaluating, the natural log rules with e, undoing ln, and solving simple ln equations.

Start practicing Peʳᵗ

Continuous Compound Interest Practice Problems

Twelve continuous compound interest practice problems with answers: final amount, interest earned, effective annual rate, doubling time, rate and time.

Start practicing ⇄

Exponential and Logarithmic Functions Practice Problems

Twelve mixed practice problems on exponential and logarithmic functions — inverses, identifying data, domains, and real models such as pH and decibels.

Start practicing 2ˣ

Exponential Function Practice Problems

Twelve exponential function practice problems with answers — evaluating a·bˣ, negative and fractional inputs, e, and telling exponential data from linear.

Start practicing %

Exponential Growth and Decay Practice Problems

Twelve exponential growth and decay word problems with answers — growth factors, depreciation, doubling time, half-life and compound interest.

Start practicing S

Exponential vs Logistic Growth Practice Problems

Twelve exponential vs logistic growth practice problems with answers: classifying models, carrying capacity, evaluating P(t) and solving for time.

Start practicing ⤴

Graphing Exponential Functions Practice Problems

Twelve practice problems on graphs of exponential functions — asymptotes, intercepts, domain and range, growth or decay, and transformations.

Start practicing ⤳

Graphing Logarithmic Functions Practice Problems

Twelve practice problems on graphs of logarithmic functions — domain, vertical asymptote, intercepts, transformations and finding the base.

Start practicing log

Logarithm Practice Problems

Twelve logarithm practice problems with answers — evaluating logs by hand, negative and fractional values, fractional bases and simple log equations.

Start practicing log(ab)

Logarithm Rules Practice Problems

Twelve practice problems on the product, quotient and power rules of logarithms, including expanding and condensing logs and evaluating by combining.

Start practicing M

Richter Scale Practice Problems

Twelve Richter scale practice problems with answers: magnitude from amplitude, comparing shaking and energy, and finding magnitudes from ratios.

Start practicing bˣ=c

Solving Exponential Equations Practice Problems

Twelve practice problems on solving exponential equations — common bases, taking logs of both sides, different bases, quadratic form and doubling time.

Start practicing log=c

Solving Logarithmic Equations Practice Problems

Twelve practice problems on solving logarithmic equations — converting to exponential form, the one-to-one property, condensing logs and extraneous roots.

Start practicing a·bˣ

Writing Exponential Functions Practice Problems

Twelve practice problems on writing an exponential function y = a·bˣ from two points, a table or a graph with a shifted asymptote, with full solutions.

Start practicing

Systems of Equations 11 sets

Substitution, elimination and graphing, three-variable and matrix methods, nonlinear systems, systems of inequalities and word problems.

[ | ]

Augmented Matrix Practice Problems

Twelve augmented matrix practice problems with answers: writing matrices, row operations, Gauss-Jordan elimination and reading special cases.

Start practicing Dₓ/D

Cramer's Rule Practice Problems

Cramer's rule practice problems with answers: 2×2 and 3×3 determinants, solving systems with determinants, and systems with no unique solution.

Start practicing ±

Elimination Method Practice Problems

Twelve elimination method practice problems with answers: adding, subtracting and multiplying equations to cancel a variable.

Start practicing ⨯

Graphing Systems of Equations Practice Problems

Twelve solving systems of equations by graphing practice problems with answers: slope-intercept, intercepts, parallel lines and estimates.

Start practicing A⁻¹

Inverse of a Matrix Practice Problems

Twelve inverse matrix practice problems with answers: determinants, 2×2 inverses, singular matrices, and solving systems with X = A⁻¹B.

Start practicing ∩

Nonlinear Systems Practice Problems

Twelve nonlinear systems practice problems with answers: lines with parabolas and circles, counting solutions, and the discriminant.

Start practicing y=…

Substitution Method Practice Problems

Twelve substitution method practice problems with answers, from systems with a variable already alone to no-solution and infinite cases.

Start practicing {x,y}

Systems of Equations Practice Problems

Twelve systems of equations practice problems with answers: checking solutions, counting solutions, and solving simple linear systems.

Start practicing 2×2

Systems of Equations Word Problems Practice

Twelve systems of equations word problems with answers: tickets, coins, investments, mixtures, wind and current, break-even and geometry.

Start practicing ≤

Systems of Inequalities Practice Problems

Twelve systems of inequalities practice problems with answers: testing points, solid vs dashed lines, shading, vertices and budgets.

Start practicing xyz

Systems With Three Variables Practice Problems

Twelve practice problems on systems of equations with 3 variables, with answers: checking triples, triangular systems and full 3x3 elimination.

Start practicing

Sequences and Series 8 sets

Arithmetic and geometric sequences, sigma notation, arithmetic and geometric series, and the binomial theorem.

a+d

Arithmetic Sequences Practice Problems

Twelve arithmetic sequence practice problems with answers: common difference, the nth term, explicit formulas, recursive rules and word problems.

Start practicing Σa

Arithmetic Series Practice Problems

Twelve arithmetic series practice problems with answers: sums of terms, counting terms, sigma sums, finding n from a total and word problems.

Start practicing d/r

Arithmetic vs Geometric Sequences Practice Problems

Twelve practice problems on telling arithmetic and geometric sequences apart, with answers: from lists, from formulas, and finding a missing middle term.

Start practicing nCk

Binomial Theorem Practice Problems

Twelve binomial theorem practice problems with answers: binomial coefficients, Pascal’s triangle, full expansions, specific terms and constant terms.

Start practicing a·r

Geometric Sequences Practice Problems

Twelve geometric sequence practice problems with answers: common ratio, the nth term, explicit formulas, negative ratios, growth and decay.

Start practicing Σar

Geometric Series Practice Problems

Twelve geometric series practice problems with answers: finite sums, infinite sums, convergence, repeating decimals, bouncing balls and salaries.

Start practicing aₙ₋₁

Recursive Formulas Practice Problems

Recursive formula practice problems with answers: find terms from a rule, write rules for sequences, and convert between recursive and explicit forms.

Start practicing Σ

Sigma Notation Practice Problems

Twelve sigma notation practice problems with answers: expanding and evaluating sums, counting terms, constant terms, squares and alternating signs.

Start practicing

Calculus 28 sets

Calculus 1: the trigonometry review, then limits — from graphs and algebra, one-sided and infinite limits, continuity, the squeeze theorem, epsilon-delta and L'Hôpital's rule — then derivatives, from the limit definition through the power, product, quotient and chain rules to implicit and logarithmic differentiation.

f′(g)·g′