Will this help with my child's high school pre-calculus homework?

Yes. StudyPug covers the Kansas Standards for Mathematics topics your student sees in class - complex numbers, trigonometry, vectors, matrices, and probability - so they can find help for specific homework problems any night of the week.

How long are the video lessons for pre-calculus?

Most video lessons run between five and fifteen minutes, focusing on one concept at a time. Students can pause, rewind, and rewatch as often as they need, making it easy to fit practice into a busy schedule.

Is there a Kansas state test for high school pre-calculus?

Kansas uses the Kansas Assessment Program (KAP) for math, but KAP testing targets specific grade levels and does not include a dedicated pre-calculus assessment. Your student's school may use end-of-course exams separately.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, laptops, and desktop computers. Your student can switch between devices and pick up right where they left off, whether they are at home or on the go.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can see how the content works before committing. Every paid plan also comes with a 30-day money-back guarantee, so there is no risk in getting started.

KS High School Pre-calculus Curriculum

Give your student the support they need to keep up with Kansas high school pre-calculus. Lessons and practice problems follow what local schools actually teach, from trigonometry to matrices and beyond.

KS High School Pre-calculus Curriculum

IDStandardStudyPug Topic

CC.HSN.CN.B.4Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
- Polar form of complex numbers
CC.HSN.CN.B.5Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
- Operations on complex numbers in polar form
CC.HSN.CN.B.6Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
- Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
CC.HSA.CED.A.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- Point-slope form: y - y_1 = m(x - x_1)
- Graphing quadratic inequalities in two variables
- Graphing systems of quadratic inequalities
CC.HSA.REI.D.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
- Graphing linear functions using table of values
- Graphing exponential functions
- Graphing logarithmic functions
- The inverse of 3 x 3 matrices with matrix row operations
- The inverse of 3 x 3 matrix with determinants and adjugate
CC.HSF.TF.A.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- Converting between degrees and radians
- Trigonometric ratios of angles in radians
- Radian measure and arc length
CC.HSF.TF.A.2Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
- Unit circle
CC.HSF.TF.A.3Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
- Find the exact value of trigonometric ratios
- Solving expressions using 45-45-90 special right triangles
- Solving expressions using 30-60-90 special right triangles
CC.HSF.TF.B.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
- Graphing transformations of trigonometric functions
- Determining trigonometric functions given their graphs
CC.HSF.TF.B.6Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- Finding inverse trigonometric function from its graph
- Finding inverse reciprocal trigonometric function from its graph
- Inverse reciprocal trigonometric function: finding the exact value
CC.HSF.TF.B.7Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
- Evaluating inverse trigonometric functions
CC.HSF.TF.C.8Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
- Pythagorean identities
CC.HSF.TF.C.9Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
- Sum and difference identities
- Double-angle identities
- Cofunction identities
CC.HSG.SRT.D.9Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
- Area of triangles: 1/2 a*b sin(C)
CC.HSG.SRT.D.10Prove the Laws of Sines and Cosines and use them to solve problems.
- Law of sines
- Law of cosines
CC.HSG.SRT.D.11Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
- Applications of the sine law and cosine law
CC.HSA.APR.C.4Prove polynomial identities and use them to describe numerical relationships.
- Solving polynomials with unknown coefficients
- Multiplicities of polynomials
- Imaginary zeros of polynomials
CC.HSA.APR.C.5Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
- Pascal's triangle
- Binomial theorem
- Determining the equation of a polynomial function
CC.HSA.APR.D.7Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
- Negative exponent rule
- Multiplying rational expressions
- Dividing rational expressions
- Descartes' rule of signs
CC.HSN.VM.A.1Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
- Use sine ratio to calculate angles and sides (Sin = o / h)
- Introduction to vectors
- Magnitude of a vector
- Direction angle of a vector
CC.HSN.VM.A.2Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
- Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- Scalar multiplication of vectors
- Equivalent vectors
CC.HSN.VM.A.3Solve problems involving velocity and other quantities that can be represented by vectors.
- Word problems relating guy wire in trigonometry
- Word problems on vectors
CC.HSN.VM.B.4Add and subtract vectors.
- Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- Adding and subtracting vectors in component form
- Operations on vectors in magnitude and direction form
CC.HSN.VM.B.5Multiply a vector by a scalar.
- Slope intercept form: y = mx + b
- Unit vector
CC.HSN.VM.C.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- Notation of matrices
- Adding and subtracting matrices
CC.HSN.VM.C.7Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- Scalar multiplication of matrices
CC.HSN.VM.C.8Add, subtract, and multiply matrices of appropriate dimensions.
- Matrix multiplication
- The three types of matrix row operations
CC.HSN.VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
- Properties of matrix multiplication
CC.HSN.VM.C.10Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
- Zero matrix
- Identity matrix
- The determinant of a 2 x 2 matrix
- The determinant of a 3 x 3 matrix (General & Shortcut Method)
- The Inverse of a 2 x 2 matrix
CC.HSN.VM.C.11Multiply 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.
- Transforming vectors with matrices
- Transforming shapes with matrices
CC.HSN.VM.C.12Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
- Finding the transformation matrix
CC.HSA.REI.C.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- System of linear-quadratic equations
- Nature of roots of quadratic equations: The discriminant
- Applications of quadratic equations
- Solving quadratic inequalities
CC.HSA.REI.C.8Represent a system of linear equations as a single matrix equation in a vector variable.
- Representing a linear system as a matrix
- Notation of matrices
- Adding and subtracting matrices
- Scalar multiplication of matrices
CC.HSA.REI.C.9Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
- The Inverse of a 2 x 2 matrix
- Solving linear systems using 2 x 2 inverse matrices
- Matrix multiplication
- The three types of matrix row operations
CC.HSG.C.A.4Construct a tangent line from a point outside a given circle to the circle.
- Tangent properties
CC.HSG.GPE.A.2Derive the equation of a parabola given a focus and directrix.
- Conics - Parabola
CC.HSG.GPE.A.3Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
- Conics - Ellipse
- Conics - Hyperbola
CC.HSN.RN.B.3Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
- Rational vs. Irrational numbers
- Solving radical equations
- Converting repeating decimals to fractions
CC.HSN.Q.A.1Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
- Metric systems
- Imperial systems
- Scale diagrams
- Conversions involving squares and cubic
CC.HSN.Q.A.2Define appropriate quantities for the purpose of descriptive modeling.
- Conversions between metric and imperial systems
- Squares and square roots
- Pythagorean theorem
- Estimating square roots
- Using the pythagorean relationship
- Applications of pythagorean theorem
CC.HSN.Q.A.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Upper and lower bound
- Cubic and cube roots
- Ratios
- Rates
- Proportions
- Percents, fractions, and decimals
CC.HSS.IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
- Sampling methods
CC.HSS.IC.A.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
- Sampling distributions
- Rare event rule
CC.HSS.IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
- Census and bias
CC.HSS.IC.B.4Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
- Margin of error
- Confidence intervals to estimate population mean
- Making a confidence interval
CC.HSS.IC.B.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
- Traditional hypothesis testing
- P-value hypothesis testing
- Analysis of variance (ANOVA)
CC.HSS.IC.B.6Evaluate reports based on data.
- Influencing factors in data collection
CC.HSS.CP.A.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
- Comparing experimental and theoretical probability
CC.HSS.CP.B.7Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
- Addition rule for
CC.HSS.MD.A.1Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
- Probability distribution - histogram, mean, variance & standard deviation
CC.HSS.MD.A.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
- Properties of expectation
CC.HSS.MD.A.3Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
- Binomial distribution
- Mean and standard deviation of binomial distribution
CC.HSS.MD.B.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
- Type 1 and type 2 errors
CC.HSG.GMD.A.2Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
- Surface area and volume of spheres

Pre-calculus

About High School Kansas pre-calculus

Kansas high school pre-calculus follows the Kansas Standards for Mathematics, organized around connected strands of algebraic reasoning, functions, and data. This course works through complex numbers and the complex plane, trigonometric functions and identities, vectors, matrices, conic sections, polynomial and rational expressions, and probability and statistics. StudyPug provides video lessons and step-by-step practice problems covering each of these strands so students can get help whenever they need it.

Strands: complex numbers, trigonometry, vectors, matrices, conic sections, polynomial and rational expressions, and probability
Video lessons for every pre-calculus topic, taught step by step
Practice problems and worked examples aligned to Kansas Standards for Mathematics
Lessons available anytime on any device, so students can review at their own pace

Curriculum topics by strand

Find lessons and practice problems for every strand, aligned to the Kansas Standards for Mathematics.

Topic includes:

Practice

Video

Quiz

Standard

StudyPug Topic

Kansas High School Pre-calculus Topics

Complex numbers and the complex plane: Rectangular and polar forms, addition, subtraction, multiplication, conjugation, modulus, and midpoints on the complex plane.
Trigonometric functions and identities: Radian measure, the unit circle, special triangles, inverse trig functions, the Pythagorean identity, addition and subtraction formulas, and modeling periodic phenomena.
Laws of Sines and Cosines: Proving and applying both laws to find unknown measurements in right and non-right triangles, including area formulas.
Vectors: Magnitude and direction, components, addition, subtraction, scalar multiplication, and applications to velocity and other real-world quantities.
Matrices: Matrix operations, scalar multiplication, matrix multiplication properties, determinants, inverse matrices, and matrices as transformations of the plane.
Polynomial, rational, and conic section algebra: Polynomial identities, the Binomial Theorem, rational expressions, systems of equations, parabolas, ellipses, and hyperbolas.
Probability and statistics: Conditional probability, independence, two-way frequency tables, random variables, expected value, probability distributions, and evaluating statistical reports.

How StudyPug Helps Kansas High School Pre-calculus Students

When a student gets stuck on a concept like polar form of complex numbers or the Law of Cosines, they can go straight to the relevant lesson, watch a step-by-step video, and then work through practice problems with guided solutions. There is no need to wait until the next class or hope the textbook explanation clicks.

Students who fall behind or want to get ahead can move through strands at their own pace, revisiting any lesson as many times as they need. Every topic is organized to match the Kansas Standards for Mathematics, so nothing studied here is out of place for what the class requires.

Aligned to Kansas High School Pre-calculus Curriculum

All StudyPug pre-calculus content is built around the Kansas Standards for Mathematics, covering the same strands - from complex numbers and trigonometry through vectors, matrices, conic sections, and probability - that Kansas high school students are expected to master. Families can trust that the lessons reinforce exactly what is being taught in the classroom.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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