Calculus 1 · Worksheets

Calculus 1 Worksheets

166 worksheets · pick a grade and topic, practice on screen, or print a worksheet and work it on paper.

Grade-by-grade topicsPrintable practice

Accumulation Function Behavior

1 worksheet

Calculus 1: Accumulation Function Behavior worksheets

Accumulation Function BehaviorCalculus · Interpret the behavior of accumulation functions by analyzing how signed area under a rate function determines increasing/decreasing intervals, extrema, and concavity of F(x) = ∫ₐˣ f(t) dt.Practice

Accumulation Functions in Context

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Calculus 1: Accumulation Functions in Context worksheets

Accumulation Functions in ContextCalculus · Practice using accumulation functions and definite integrals in applied, real-world contexts to build fluency with interpreting and evaluating integrals as net change.Practice

Accumulations of Change

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Calculus 1: Accumulations of Change worksheets

Accumulations of Change: Integration & the FTCCalculus · Build fluency with accumulation functions, net change via definite integrals, and the Fundamental Theorem of Calculus through varied practice.Practice

Area Between Multiple Intersections

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Calculus 1: Area Between Multiple Intersections worksheets

Area Between Curves with Multiple IntersectionsCalculus · Find the area between curves that intersect at more than two points by identifying all intersection points, determining which curve is on top in each subinterval, and summing the absolute values of the integrals over each subinterval.Practice

Area Between Curves (y-functions)

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Calculus 1: Area Between Curves (y-functions) worksheets

Area Between Curves: Functions of yCalculus · Find the area between two curves expressed as functions of y by integrating with respect to y.Practice

Average & Instantaneous Rates

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Calculus 1: Average & Instantaneous Rates worksheets

Average & Instantaneous Rates of ChangeCalculus · Define and compute average and instantaneous rates of change at a point using the difference quotient and limits.Practice

Basic Derivative Rules

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Calculus 1: Basic Derivative Rules worksheets

Basic Derivative Rules: Constant, Sum, Difference & Constant MultipleCalculus · Build fluency with the Constant Rule, Sum Rule, Difference Rule, and Constant Multiple Rule for differentiation.Practice

Basic Trig Integrals

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Calculus 1: Basic Trig Integrals worksheets

Basic Trigonometric IntegralsCalculus · Build fluency evaluating indefinite and definite integrals of the six basic trigonometric functions (sin, cos, tan, cot, sec, csc and their squares) using standard antiderivative formulas.Practice

Connecting f, f', and f''

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Calculus 1: Connecting f, f', and f'' worksheets

Connecting f, f′, and f″Calculus · Build fluency connecting a function, its first derivative, and its second derivative by analyzing sign charts, interpreting critical and inflection points, and reasoning about increasing/decreasing behavior and concavity.Practice

Continuity at a Point

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Calculus 1: Continuity at a Point worksheets

Continuity at a PointCalculus · Define and verify continuity at a point using the three conditions: f(a) is defined, lim x→a f(x) exists, and lim x→a f(x) = f(a).Practice

Derivative Definition & Notation

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Calculus 1: Derivative Definition & Notation worksheets

Derivative Definition & NotationCalculus · Define the derivative of a function using the limit definition and interpret standard derivative notation (Leibniz, Lagrange, and Newton).Practice

Derivative Meaning in Context

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Calculus 1: Derivative Meaning in Context worksheets

Derivative Meaning in ContextCalculus · Interpret the meaning of the derivative in real-world contextual situations, including units, sign, and magnitude.Practice

Derivatives of cos, sin, e^x, ln x

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Calculus 1: Derivatives of cos, sin, e^x, ln x worksheets

Derivatives of cos x, sin x, eˣ, and ln xCalculus · Build fluency differentiating cos x, sin x, eˣ, and ln x — including with the chain rule, product rule, and quotient rule — through varied practice.Practice

Derivatives of sin & cos

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Calculus 1: Derivatives of sin & cos worksheets

Derivatives of Sine & CosineCalculus · Build fluency in computing and recognizing derivatives of sin(x) and cos(x), including chain-rule compositions, and apply these rules in real-world rate-of-change contexts.Practice

Derivatives of tan, cot, sec, csc

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Calculus 1: Derivatives of tan, cot, sec, csc worksheets

Derivatives of tan, cot, sec, cscCalculus · Find the derivatives of tangent, cotangent, secant, and cosecant functions, including compositions via the chain rule.Practice

Derivatives of tan & Other Trig

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Calculus 1: Derivatives of tan & Other Trig worksheets

Derivatives of Tangent & Other Trig FunctionsCalculus · Practice computing and recognizing derivatives of tan(x), cot(x), sec(x), and csc(x) using standard differentiation rules.Practice

Determining Concavity

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Calculus 1: Determining Concavity worksheets

Determining Concavity of FunctionsCalculus · Determine the concavity of functions over their domains using the second derivative test and inflection point analysis.Practice

Differentiability & Continuity

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Calculus 1: Differentiability & Continuity worksheets

Differentiability & Continuity: When Derivatives ExistCalculus · Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not ExistPractice

Disc Method: Other Axes

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Calculus 1: Disc Method: Other Axes worksheets

Disc Method: Revolving Around Other AxesCalculus · Practice setting up and evaluating integrals for volumes of revolution using the disc method when revolving around axes other than the x-axis or y-axis (e.g., y = k, x = k).Practice

Disc Method: x- or y-Axis

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Calculus 1: Disc Method: x- or y-Axis worksheets

Disc Method: Volumes of Revolution about the x- or y-AxisCalculus · Students will set up and evaluate definite integrals using the disc method to find volumes of solids of revolution about the x-axis or y-axis.Practice

Estimating Derivatives

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Calculus 1: Estimating Derivatives worksheets

Estimating Derivatives at a PointCalculus · Students will estimate the derivative of a function at a given point using difference quotients, secant-line slopes, tables of values, and graphical reasoning.Practice

Estimating Limits from Tables

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Calculus 1: Estimating Limits from Tables worksheets

Estimating Limits from TablesCalculus · Students will estimate the value of a limit by analyzing function values in a table as x approaches a given value from both sides.Practice

EVT, Extrema & Critical Points

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Calculus 1: EVT, Extrema & Critical Points worksheets

EVT, Extrema & Critical PointsCalculus · Practice identifying critical points, classifying local and global extrema, and applying the Extreme Value Theorem on closed intervals.Practice

Exponential DE Models

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Calculus 1: Exponential DE Models worksheets

Exponential Models with Differential EquationsCalculus · Build fluency in setting up, solving, and interpreting exponential differential equation models of the form dy/dt = ky, including growth and decay contexts.Practice

FTC & Definite Integrals

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Calculus 1: FTC & Definite Integrals worksheets

FTC & Definite IntegralsCalculus · Practice evaluating definite integrals using the Fundamental Theorem of Calculus, interpreting accumulation functions, and connecting antiderivatives to net area.Practice

General Solutions: Separation of Variables

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Calculus 1: General Solutions: Separation of Variables worksheets

General Solutions: Separation of VariablesCalculus · Build fluency in finding general solutions to differential equations using separation of variables, including separating dy and dx terms, integrating both sides, and expressing the solution with an arbitrary constant.Practice

Graphing Functions & Derivatives

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Calculus 1: Graphing Functions & Derivatives worksheets

Graphing Functions & Their DerivativesCalculus · Sketch and analyze graphs of functions and their derivatives, identifying critical points, intervals of increase/decrease, concavity, and inflection points from analytical information.Practice

Higher-Order Derivatives

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Calculus 1: Higher-Order Derivatives worksheets

Higher-Order Derivatives: Mastery PracticeCalculus · Calculate higher-order derivatives of polynomial, trigonometric, exponential, logarithmic, and composite functions using standard differentiation rules applied iteratively.Practice

Implicit Relation Behaviors

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Calculus 1: Implicit Relation Behaviors worksheets

Implicit Relation BehaviorsCalculus · Explore and analyze behaviors of implicit relations including tangent lines, regions of increasing/decreasing behavior, concavity, and singular points using implicit differentiation.Practice

Infinite Limits & Vertical Asymptotes

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Calculus 1: Infinite Limits & Vertical Asymptotes worksheets

Infinite Limits & Vertical AsymptotesCalculus · Build fluency connecting infinite limits to vertical asymptotes — determine when one-sided limits approach ±∞, identify vertical asymptotes from algebraic expressions, and reason about sign behavior near discontinuities.Practice

Integration: Long Division & Completing Square

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Calculus 1: Integration: Long Division & Completing Square worksheets

Integration: Long Division & Completing the SquareCalculus · Integrate rational functions and quadratic expressions using polynomial long division and completing the square techniques.Practice

Intro to Calculus: Instantaneous Change

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Calculus 1: Intro to Calculus: Instantaneous Change worksheets

Intro to Calculus: Can Change Occur at an Instant?Calculus · Build fluency and conceptual understanding of instantaneous change, limits, and the transition from average rate of change to instantaneous rate of change.Practice

Intro to Related Rates

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Calculus 1: Intro to Related Rates worksheets

Introduction to Related RatesCalculus · Students will set up and solve introductory related rates problems by identifying relationships between quantities, implicitly differentiating with respect to time, and interpreting results in context.Practice

Inverse Trig Derivatives

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Calculus 1: Inverse Trig Derivatives worksheets

Inverse Trig DerivativesCalculus · Differentiate inverse trigonometric functions, including compositions with the chain rule.Practice

L'Hospital's Rule

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Calculus 1: L'Hospital's Rule worksheets

L'Hôpital's Rule: Mastering Indeterminate FormsCalculus · Apply L'Hôpital's Rule to evaluate limits involving indeterminate forms such as 0/0 and ∞/∞.Practice

Limit Definition & Notation

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Calculus 1: Limit Definition & Notation worksheets

Limit Definition & NotationCalculus · Define limits and use proper limit notation to describe the behavior of functions as the input approaches a given value.Practice

Limits at Infinity & Horizontal Asymptotes

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Calculus 1: Limits at Infinity & Horizontal Asymptotes worksheets

Limits at Infinity & Horizontal AsymptotesCalculus · Evaluate limits at infinity for rational and other functions, and identify horizontal asymptotes by connecting end-behavior limits to the geometric meaning of a horizontal asymptote.Practice

Limits via Algebraic Manipulation

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Calculus 1: Limits via Algebraic Manipulation worksheets

Limits via Algebraic ManipulationCalculus · Determine limits of functions using algebraic techniques such as factoring, rationalizing, multiplying by conjugates, and simplifying complex fractions.Practice

Linear Approximation

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Calculus 1: Linear Approximation worksheets

Linear Approximation & Local LinearityCalculus · Approximate values of a function using local linearity and linearizationPractice

Squeeze Theorem

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Calculus 1: Squeeze Theorem worksheets

Mastering the Squeeze TheoremCalculus · Determine limits of functions using the Squeeze Theorem by identifying bounding functions, verifying inequalities, and evaluating shared limits.Practice

u-Substitution

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Calculus 1: u-Substitution worksheets

Mastering u-SubstitutionCalculus · Practice u-substitution for simple composite functions to build fluency in recognizing inner functions, computing du, and rewriting integrals for evaluation.Practice

Modeling with Differential Equations

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Calculus 1: Modeling with Differential Equations worksheets

Modeling with Differential EquationsCalculus · Students will translate real-world situations into differential equations, identify appropriate models, and verify that proposed differential equations correctly capture given relationships involving rates of change.Practice

Motion: Position, Velocity, Acceleration

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Calculus 1: Motion: Position, Velocity, Acceleration worksheets

Motion: Position, Velocity, & AccelerationCalculus · Practice connecting position, velocity, and acceleration functions for straight-line motion using derivatives and antiderivatives.Practice

Multiple Limit Representations

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Calculus 1: Multiple Limit Representations worksheets

Multiple Limit RepresentationsCalculus · Connect and translate between algebraic, numerical (table), graphical, and verbal representations of limits to deepen conceptual understanding of limit behavior.Practice

Non-Motion Rates of Change

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Calculus 1: Non-Motion Rates of Change worksheets

Non-Motion Rates of ChangeCalculus · Practice interpreting and computing rates of change in applied contexts other than motion, including population growth, temperature change, cost functions, chemical reactions, and other real-world scenarios.Practice

Position, Velocity, Acceleration via Integrals

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Calculus 1: Position, Velocity, Acceleration via Integrals worksheets

Position, Velocity & Acceleration via IntegralsCalculus · Connect position, velocity, and acceleration functions using integrals to solve motion problems.Practice

Reasoning with Slope Fields

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Calculus 1: Reasoning with Slope Fields worksheets

Reasoning with Slope FieldsCalculus · Interpret and analyze slope fields to reason about the behavior of solutions to differential equations, including identifying equilibrium solutions, matching slope fields to differential equations, and sketching solution curves.Practice

Related Rates with Geometry

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Calculus 1: Related Rates with Geometry worksheets