Precalculus · Worksheets

Precalculus Worksheets

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

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Using 2x2 Matrices for Plane Transformations

1 worksheet

Precalculus: Using 2x2 Matrices for Plane Transformations worksheets

2×2 Matrices as Plane TransformationsPrecalculus · Work with 2×2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.Practice

Applying Laws of Sines and Cosines

1 worksheet

Precalculus: Applying Laws of Sines and Cosines worksheets

Applying the Laws of Sines and CosinesPrecalculus · Use the Law of Sines and the Law of Cosines to solve problems involving general (non-right) triangles, including finding unknown sides, angles, and applying these laws to real-world contexts.Practice

Constructing Inverse Trigonometric Functions

1 worksheet

Precalculus: Constructing Inverse Trigonometric Functions worksheets

Constructing Inverse Trigonometric FunctionsPrecalculus · Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed (CCSS.F-TF.6).Practice

Constructing Tangents to Circles

1 worksheet

Precalculus: Constructing Tangents to Circles worksheets

Constructing Tangents to CirclesPrecalculus · Construct a tangent line from a point outside a given circle to the circle, applying theorems about tangent-radius perpendicularity and tangent-segment congruence.Practice

Extending Trigonometric Functions with Unit Circle

1 worksheet

Precalculus: Extending Trigonometric Functions with Unit Circle worksheets

Extending Trigonometric Functions with the Unit CirclePrecalculus · Explain how the unit circle enables the extension of trigonometric functions to all real numbers interpreted as radian measures of angles traversed counterclockwise around the unit circle.Practice

Finding Components of Vectors

1 worksheet

Precalculus: Finding Components of Vectors worksheets

Finding Components of VectorsPrecalculus · Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point (CCSS.N-VM.2).Practice

Find Sum of Two Vectors

1 worksheet

Precalculus: Find Sum of Two Vectors worksheets

Finding the Sum of Two VectorsPrecalculus · Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum using the law of cosines and the law of sines.Practice

All Circles Are Similar

1 worksheet

Precalculus: All Circles Are Similar worksheets

Law of Sines & Law of Cosines PracticePrecalculus · Apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.Practice

Matrix Addition, Subtraction, and Multiplication

1 worksheet

Precalculus: Matrix Addition, Subtraction, and Multiplication worksheets

Matrix Addition, Subtraction, and MultiplicationPrecalculus · Add, subtract, and multiply matrices of appropriate dimensions (CCSS.N-VM.8)Practice

Matrix Transformations of Vectors

1 worksheet

Precalculus: Matrix Transformations of Vectors worksheets

Matrix Transformations of VectorsPrecalculus · Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.Practice

Modeling Periodic Phenomena with Trigonometric Functions

1 worksheet

Precalculus: Modeling Periodic Phenomena with Trigonometric Functions worksheets

Modeling Periodic Phenomena with Trigonometric FunctionsPrecalculus · Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline (CCSS.F-TF.5)Practice

Properties of Matrix Operations

1 worksheet

Precalculus: Properties of Matrix Operations worksheets

Properties of Matrix OperationsPrecalculus · Understand that matrix multiplication is not commutative but satisfies the associative and distributive properties (CCSS.N-VM.9).Practice

Proving Angle Addition/Subtraction Formulas

1 worksheet

Precalculus: Proving Angle Addition/Subtraction Formulas worksheets

Proving & Applying Angle Addition and Subtraction FormulasPrecalculus · Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems (CCSS.F-TF.9).Practice

Proving the Pythagorean Identity

1 worksheet

Precalculus: Proving the Pythagorean Identity worksheets

Proving & Applying the Pythagorean IdentityPrecalculus · Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given one trig value and the quadrant of the angle.Practice

Radian Measure and Arc Length

1 worksheet

Precalculus: Radian Measure and Arc Length worksheets

Radian Measure, Arc Length & Sector AreaPrecalculus · Derive and apply the relationship between arc length, radius, and radian measure; compute sector areas using s = rθ and A = ½r²θ.Practice

Representing Linear Systems with Matrices

1 worksheet

Precalculus: Representing Linear Systems with Matrices worksheets

Representing Linear Systems with MatricesPrecalculus · Represent a system of linear equations as a single matrix equation in a vector variable (CCSS A-REI.8).Practice

Show Scalar Multiplication Visually

1 worksheet

Precalculus: Show Scalar Multiplication Visually worksheets

Scalar Multiplication of Vectors: Visual & Component-WisePrecalculus · Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).Practice

Solving Right Triangles: Pythagorean Theorem, Trigonometry

1 worksheet

Precalculus: Solving Right Triangles: Pythagorean Theorem, Trigonometry worksheets

Sine & Cosine of Complementary AnglesPrecalculus · Explain and use the relationship between the sine and cosine of complementary angles (sin θ = cos(90° − θ) and cos θ = sin(90° − θ)) in right-triangle contexts.Practice

Sine and Cosine of Complementary Angles

1 worksheet

Precalculus: Sine and Cosine of Complementary Angles worksheets

Sine and Cosine of Complementary AnglesPrecalculus · Understand and apply the cofunction identity sin(θ) = cos(90° − θ) using properties of similar right triangles and trigonometric ratio definitions.Practice

Solving Problems with Vectors and Velocity

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Precalculus: Solving Problems with Vectors and Velocity worksheets

Solving Problems with Vectors & VelocityPrecalculus · Solve problems involving velocity and other quantities that can be represented by vectors (CCSS N-VM.3).Practice

Solving Trigonometric Equations in Context

1 worksheet

Precalculus: Solving Trigonometric Equations in Context worksheets

Solving Trigonometric Equations in ContextPrecalculus · Use inverse trigonometric functions to solve equations arising from periodic modeling contexts, evaluate solutions using technology, and interpret them in terms of the real-world scenario.Practice

Special Triangles, Unit Circle in Trigonometry

1 worksheet

Precalculus: Special Triangles, Unit Circle in Trigonometry worksheets

Special Triangles & Unit Circle TrigonometryPrecalculus · Use special triangles to determine exact values of sine, cosine, and tangent for π/3, π/4, and π/6, and use unit circle symmetry to express trig values for π−x, π+x, and 2π−x in terms of their values for x.Practice

Subtract and Represent Vectors Graphically

1 worksheet

Precalculus: Subtract and Represent Vectors Graphically worksheets

Subtract and Represent Vectors GraphicallyPrecalculus · Understand vector subtraction v – w as v + (–w), represent vector subtraction graphically by connecting tips, and perform vector subtraction component-wise.Practice

Symmetry and Periodicity of Trigonometric Functions

1 worksheet

Precalculus: Symmetry and Periodicity of Trigonometric Functions worksheets

Symmetry and Periodicity of Trigonometric FunctionsPrecalculus · Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions (CCSS.F-TF.4).Practice

Deriving the Triangle Area Formula

1 worksheet

Precalculus: Deriving the Triangle Area Formula worksheets

Triangle Area via Trigonometry & Right-Triangle Problem SolvingPrecalculus · Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including deriving and applying the triangle area formula A = ½ ab sin C.Practice

Understanding Radian Measure of Angles

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Precalculus: Understanding Radian Measure of Angles worksheets

Understanding Radian Measure of AnglesPrecalculus · Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle (F-TF.1).Practice

Understanding Vector Quantities and Representation

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Precalculus: Understanding Vector Quantities and Representation worksheets

Understanding Vector Quantities & RepresentationPrecalculus · Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes.Practice

Using Matrices to Represent, Manipulate Data

1 worksheet

Precalculus: Using Matrices to Represent, Manipulate Data worksheets

Using Matrices to Represent & Manipulate DataPrecalculus · Use matrices to represent and manipulate data, including payoff matrices, incidence matrices, and transition matrices (CCSS N-VM.6).Practice

Zero and Identity Matrices and Determinants

1 worksheet

Precalculus: Zero and Identity Matrices and Determinants worksheets

Zero & Identity Matrices and DeterminantsPrecalculus · Understand the roles of zero and identity matrices in matrix addition and multiplication, analogous to 0 and 1 for real numbers, and connect the nonzero determinant of a square matrix to the existence of a multiplicative inverse.Practice

Binomial and normal distributions

9 worksheets

Precalculus: Binomial and normal distributions worksheets

Binomial Distribution ProbabilitiesPrecalculus · Find probabilities using the binomial distribution.Practice Distributions of Sample MeansPrecalculus · Apply the Central Limit Theorem to find the mean and standard deviation of a sampling distribution, and reason about binomial and normal approximations.Practice Finding Values of Normal VariablesPrecalculus · Use z-scores and the standard normal model to find values, percentiles, and probabilities for normally distributed variables.Practice Finding z-Values in Normal DistributionsPrecalculus · Compute and interpret z-scores for values drawn from normal distributions.Practice Mean, Variance, and Standard Deviation of Binomial DistributionsPrecalculus · Compute and reason about the mean, variance, and standard deviation of binomial distributions.Practice Normal Approximation to the BinomialPrecalculus · Use normal distributions to approximate binomial distributions, including checking conditions, finding mean and standard deviation, and applying the continuity correction.Practice Probabilities with the Normal DistributionPrecalculus · Use z-scores, the empirical rule, and standard normal tables to find probabilities under a normal distribution.Practice Probabilities with the Normal Distribution IIPrecalculus · Use z-scores, the empirical rule, and the normal approximation to the binomial to compute probabilities.Practice The Central Limit Theorem: Binomial & Normal DistributionsPrecalculus · Apply the Central Limit Theorem and the normal approximation to the binomial distribution to compute means, standard deviations, and probabilities for sample means and proportions.Practice

Bivariate statistics

8 worksheets

Precalculus: Bivariate statistics worksheets

Analyzing Regression LinesPrecalculus · Interpret slope, intercept, residuals, and predictions from a least-squares regression line of a bivariate data set.Practice Analyzing Regression Lines from Data StatisticsPrecalculus · Use summary statistics (means, standard deviations, and correlation) of a bivariate data set to find, interpret, and evaluate a least-squares regression line.Practice Calculating Correlation CoefficientsPrecalculus · Compute and interpret the Pearson correlation coefficient r for bivariate data.Practice Exponential RegressionPrecalculus · Model bivariate data with exponential functions y = a·b^x, interpret growth/decay factors, and use the model to predict.Practice Finding the Equation of a Regression LinePrecalculus · Compute and interpret the least-squares regression line y = a + bx from bivariate data.Practice Interpreting Regression LinesPrecalculus · Interpret the slope, intercept, predictions, and residuals of a least-squares regression line in context.Practice Outliers in Scatter PlotsPrecalculus · Identify, interpret, and reason about outliers in bivariate scatter plots and their effect on correlation and regression.Practice Reading Correlation: Matching r to Scatter PlotsPrecalculus · Interpret the correlation coefficient r and match its value to the strength and direction of a scatter plot.Practice

Complex numbers

2 worksheets

Precalculus: Complex numbers worksheets

Absolute Values of Complex NumbersPrecalculus · Compute and reason about the modulus |a + bi| = sqrt(a^2 + b^2) of complex numbers.Practice Adding and Subtracting Complex NumbersPrecalculus · Add and subtract complex numbers by combining real and imaginary parts.Practice