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Calculus I and II · Focused practice

Calculus worksheets

Follow a course path, choose a skill, or edit a review packet with separate answer editions.

Calculus I review packet →Calculus II review packet →
Jump to a calculus topic

Course path 01

Calculus I: limits, derivatives and integrals

Build from limits to rates of change, then connect accumulation to antiderivatives.

Start with: Begin with algebraic manipulation, functions, graph reading and radians. Use the Precalculus collection if these skills need attention.

Worked review and teaching notes for Calculus I

Start with limits and continuity, derive local rates of change, and apply derivatives before connecting accumulation to antiderivatives. Calculus I and Calculus 1 refer to this same path.

Worked review and check

For f(x) = x², the derivative definition gives ((x + h)² − x²)/h = 2x + h for h ≠ 0; taking h → 0 gives f′(x) = 2x. At x = 3 the tangent slope is 6. Conversely, ∫₀³ 2x dx = [x²]₀³ = 9, the net change of x².

For teachers and tutors

Assign one section at a time. Ask for a theorem hypothesis or a unit interpretation alongside each calculation; use the packet as a diagnostic, then remove topics not yet taught.

Move from a limit and the derivative definition through composite derivatives and optimization to accumulation and substitution. Start with 6 complete worksheets. Edit the order and selection, then choose Letter or A4 and student or teacher editions.

Course path 02

Calculus II: integration methods and series

Choose integration methods, justify convergence, and explore parametric and polar curves.

Start with: Begin after derivative rules, the fundamental theorem and elementary substitution. Review algebraic fractions and trigonometric identities before advanced integration.

Topic 04 · 6 worksheets

Sequences, infinite series and approximations

A vanishing term is necessary but not sufficient for series convergence. Check endpoints and justify the error bound used for an approximation.

Worked review and teaching notes for Calculus II

Choose integration methods, interpret improper limits, and justify convergence and approximation before moving into parametric and polar calculus. Calculus II and Calculus 2 refer to this same path.

Worked review and check

The geometric series Σ from n = 0 to infinity of (1/2)ⁿ has sum 1/(1 − 1/2) = 2 because |1/2| < 1. Stopping at n = 3 gives 15/8; the exact omitted tail is (1/2)⁴/(1 − 1/2) = 1/8. A small term alone would not establish convergence for an arbitrary series.

For teachers and tutors

Use the review packet in its displayed order or split it into integration and series sessions. Require a method choice, convergence justification and derivative or remainder check. Area, differential equations and other topics may fall in different courses locally.

Review integration methods and improper integrals before convergence tests, Taylor polynomials and parametric calculus. Start with 6 complete worksheets. Edit the order and selection, then choose Letter or A4 and student or teacher editions.

Before you start

Full collection

All calculus worksheets

Browse every worksheet below, including additional practice beyond the course-path selections. Reproducible Letter and A4 worksheets include separate answers.

Practice finite change, symbolic Delta y, derivative definitions, exact derivative limits, instantaneous change, point slopes and lines, area estimates, Riemann sums, substitution, and the Chain Rule.

Core differentiation and integration

First page preview: Delta y formula worksheets

Calculus

Delta y formula worksheets

Find the symbolic change in y for polynomial, rational, composite and trigonometric functions.

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First page preview: Derivative by definition worksheets

Calculus

Derivative by definition worksheets

Differentiate polynomial, rational, signed-power composite and trigonometric functions from the limit definition.

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First page preview: Instantaneous and average rate worksheets

Calculus

Instantaneous and average rate worksheets

Compare finite-interval and lower-endpoint rates for polynomial, rational and radian trigonometric functions with blank and keyed graphs.

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First page preview: Chain Rule worksheets

Calculus

Chain Rule worksheets

Differentiate exact powers of polynomial binomials and square roots of odd polynomial powers, keeping each answer in concise factored form.

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First page preview: Slope at a Point worksheets

Calculus

Slope at a Point worksheets

Find exact curve slopes at rational and standard-unit-circle points across four function families.

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First page preview: Differentiation Tables worksheets

Calculus

Differentiation Tables worksheets

Apply sum, difference, product, quotient, scalar and Chain Rules to exact function and derivative values in one shared lookup table.

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First page preview: Riemann Sum Tables worksheets

Calculus

Riemann Sum Tables worksheets

Calculate exact left-endpoint, right-endpoint and midpoint Riemann-sum area estimates from complete tables on uniform intervals.

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First page preview: Approximating Area under a Curve worksheets

Calculus

Approximating Area under a Curve worksheets

Draw and calculate left-endpoint, right-endpoint and midpoint rectangle estimates for explicit polynomial, trigonometric, exponential and natural-log functions.

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First page preview: First Fundamental Theorem worksheets

Calculus

First Fundamental Theorem worksheets

Evaluate polynomial, reciprocal-power, trigonometric and exponential definite integrals with exact endpoint values.

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First page preview: Second Fundamental Theorem worksheets

Calculus

Second Fundamental Theorem worksheets

Differentiate polynomial accumulation functions with constant, variable, and polynomial bounds using exact chain-rule contributions.

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First page preview: Trigonometric Integration worksheets

Calculus

Trigonometric Integration worksheets

Practice six direct trigonometric antiderivative patterns with exact constant coefficients and unit or affine arguments in radians.

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First page preview: Integration by Parts worksheets

Calculus

Integration by Parts worksheets

Practice exact integration by parts with polynomial-exponential, polynomial-trigonometric, logarithmic and inverse-trigonometric integrands.

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First page preview: Power, Constant, and Sum Rules worksheets

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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First page preview: Product Rule worksheets

Calculus

Product Rule worksheets

Differentiate products of two nonzero polynomials with selectable factor size and degree ceilings, then combine like terms exactly.

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First page preview: Quotient Rule worksheets

Calculus

Quotient Rule worksheets

Differentiate exact polynomial quotients in both degree orientations and retain every restriction from the original denominator.

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First page preview: Power Rule Integration worksheets

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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Limits, continuity, area and volume

First page preview: Evaluating Limits at Infinity with Graphs

Calculus

Evaluating Limits at Infinity with Graphs

Use equations with blank or completed coordinate graphs to evaluate exact polynomial, rational, exponential, and logarithmic limits at infinity.

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First page preview: Evaluating Limits at Infinity

Calculus

Evaluating Limits at Infinity

Practice exact positive- and negative-infinity limits for polynomial, rational, trigonometric, exponential, and logarithmic functions.

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First page preview: Determining Continuity

Calculus

Determining Continuity

Practice exact continuity intervals and one-sided-limit reasoning for piecewise, absolute-value, kinked-polynomial, and rational functions.

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First page preview: Determining Continuity from Graphs

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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First page preview: Area Under a Curve

Calculus

Area Under a Curve

Practice exact total geometric area for polynomial, trigonometric, and exponential functions across supplied intervals.

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First page preview: Area Between Curves worksheets

Calculus

Area Between Curves worksheets

Practice exact area between polynomial curves with intersection-derived or supplied limits, x or y integration, and every order-changing crossing split correctly.

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First page preview: Volume Using Cross Sections

Calculus

Volume Using Cross Sections

Practice exact volumes whose square, rectangular, or right-triangular cross sections stand on widths through semicircular, semi-oval, and elliptical bases.

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First page preview: Volumes Using Cylindrical Shells

Calculus

Volumes Using Cylindrical Shells

Practice exact shell-method volumes from quadratic and cubic regions rotated about vertical or horizontal axes.

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First page preview: Volumes of Washers and Disks

Calculus

Volumes of Washers and Disks

Practice exact disk and washer volumes for regions between intersecting polynomial curves, including shifted axes.

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Derivative applications and differential equations

First page preview: Linear Approximation worksheets

Calculus

Linear Approximation worksheets

Construct exact linearizations for polynomial, exponential and trigonometric functions, then estimate nearby values to four decimal places.

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First page preview: Higher Order Derivatives worksheets

Calculus

Higher Order Derivatives worksheets

Differentiate exact sparse power sums through the second, third, fourth or fifth derivative using prime or Leibniz notation.

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First page preview: Symbolic Differentials worksheets

Calculus

Symbolic Differentials worksheets

Find exact symbolic differentials for polynomial, rational, composite, and trigonometric functions with fully worked rule-specific keys.

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First page preview: Horizontal Tangents worksheets

Calculus

Horizontal Tangents worksheets

Find every exact coordinate where polynomial, rational-polynomial, and trigonometric functions have horizontal tangent lines.

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First page preview: Critical Points worksheets

Calculus

Critical Points worksheets

Find, classify, and plot exact polynomial critical coordinates, then report complete increasing and decreasing intervals.

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First page preview: Concavity worksheets

Calculus

Concavity worksheets

Find exact polynomial inflection coordinates and complete concave-up and concave-down intervals with second-derivative sign analysis.

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First page preview: Absolute Extrema worksheets

Calculus

Absolute Extrema worksheets

Find exact absolute minimum and maximum values of quadratic, cubic, and quartic polynomials on the real line or a stated closed interval.

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First page preview: Mean Value Theorem worksheets

Calculus

Mean Value Theorem worksheets

Find every exact interior value where a derivative equals the secant slope for polynomial, trigonometric, exponential, and logarithmic functions.

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First page preview: Graphing Differentials worksheets

Calculus

Graphing Differentials worksheets

Compare the exact change on a polynomial or trigonometric curve with the tangent-line differential on an actual reference graph.

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First page preview: Solving Separable Equations worksheets

Calculus

Solving Separable Equations worksheets

Solve genuinely y-dependent first-order separable equations with exact implicit solutions, connected-domain restrictions, and restored equilibrium solutions.

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First page preview: Newton's Method worksheets

Calculus

Newton's Method worksheets

Approximate a real zero of polynomial and trigonometric functions through repeated Newton updates.

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First page preview: L'Hopital's Rule worksheets

Calculus

L'Hopital's Rule worksheets

Evaluate indeterminate quotient limits with justified, repeated applications of L'Hopital's Rule.

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First page preview: Optimization worksheets

Calculus

Optimization worksheets

Maximize area or volume under geometric constraints with a complete feasible-domain argument.

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First page preview: Related Rates worksheets

Calculus

Related Rates worksheets

Differentiate geometric constraints with respect to time and solve unit-aware instantaneous rates.

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First page preview: Understanding Motion worksheets

Calculus

Understanding Motion worksheets

Analyze polynomial position for velocity, direction changes, direction intervals, and displacement.

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First page preview: Horizontal Tangents on Graphs worksheets

Calculus

Horizontal Tangents on Graphs worksheets

Plot or inspect polynomial, rational, and trigonometric functions and identify every horizontal tangent coordinate in the displayed interval.

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First page preview: Graphing Derivatives worksheets

Calculus

Graphing Derivatives worksheets

Sketch derivative graphs from aligned polynomial, rational, and trigonometric function graphs, with an optional explicit equation.

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First page preview: Summation Properties worksheets

Calculus

Summation Properties worksheets

Evaluate finite sums with linearity, supplied sums, constant sums, and power-sum formulas through cubes.

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Integration methods, sequences, series and curves

Printable improper integrals worksheets preview

Calculus II

Improper Integrals worksheets

Classify and evaluate infinite-bound and singular integrals using one-sided limits, including interior splits.

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Printable work by integration worksheets preview

Calculus

Work by Integration worksheets

Model spring, cable-lifting, and tank-pumping work with force-distance integrals and exact units.

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Printable euler method worksheets preview

Calculus

Euler Method worksheets

Build explicit Euler recurrence tables with configurable step size, number of steps, and initial point.

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Printable parametric calculus worksheets preview

Calculus

Parametric Calculus worksheets

Differentiate bounded polynomial and trigonometric parametric curves, classify tangents, and calculate speed, arc length, and enclosed area.

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Printable polar calculus worksheets preview

Calculus

Polar Calculus worksheets

Find polar slopes and tangents, area over one trace, and bounded arc length for familiar circle, cardioid, rose, limacon, and spiral curves.

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