Will this help with my child's Integrated Math 3 homework?

Yes. StudyPug covers every Integrated Math 3 strand taught in Minnesota high schools, from polynomial identities and logarithms to the Law of Sines and probability distributions, so your child can find help for whatever homework problem they are stuck on.

How long are the video lessons?

Most video lessons run between 5 and 15 minutes, focusing on one concept at a time. Students can pause, rewind, and rewatch as many times as they need, making it easy to fit a lesson into a busy after-school schedule.

Is there a state test for Integrated Math 3 in Minnesota?

Minnesota administers the MCA for math in grades 3 through 8 and in 11th grade. If your student is in 11th grade, StudyPug practice on algebra, functions, and statistics can support preparation for the Grade 11 MCA assessment.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and computers, so your child can watch lessons and complete practice problems at home, at school, or anywhere else they have an internet connection.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can see the content before committing. If you subscribe and decide it is not the right fit, the 30-day money-back guarantee means you can get a full refund with no hassle.

MN High School Integrated Math 3 Curriculum

Give your high schooler the support they need in Integrated Math 3. Our lessons and practice problems follow what Minnesota schools actually teach, covering everything from trigonometry to statistics and complex numbers.

MN High School Integrated Math 3 Curriculum

IDStandardStudyPug Topic

CC.HSA.SSE.A.1Interpret expressions that represent a quantity in terms of its context.
- What is a polynomial?
- Applications of linear equations
CC.HSA.SSE.A.2Use the structure of an expression to identify ways to rewrite it.
- Polynomial components
- Simplifying rational expressions and restrictions
- Applications of polynomials
- Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
CC.HSA.SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- Common factors of polynomials
- Adding and subtracting rational expressions
- Evaluating polynomials
- Using algebra tiles to factor polynomials
- Solving polynomial equations
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.APR.B.2Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
- Greatest common factors (GCF)
- Remainder theorem
- Polynomial long division
- Polynomial synthetic division
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.6Rewrite simple rational expressions in different forms.
- Applications of polynomial functions
- Solving polynomial inequalities
- Fundamental theorem of algebra
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.HSA.REI.A.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- Evaluating and simplifying radicals
- Solving radical equations
- Square and square roots
- Cubic and cube roots
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.LE.A.4For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
- Quotient rule of logarithms
- Combining product rule and quotient rule in logarithms
- Power rule of logarithms
- Evaluating logarithms using logarithm rules
CC.HSF.LE.B.5Interpret the parameters in a linear or exponential function in terms of a context.
- Exponential growth and decay by a factor
- Finance: Compound interest
- Continuous growth and decay
- Logarithmic scale: Richter scale (earthquake)
- Logarithmic scale: pH scale
- Logarithmic scale: dB scale
- Finance: Future value and present value
CC.HSF.BF.B.4Find inverse functions.
- Finding the quadratic functions for given parabolas
- Inverse functions
CC.HSF.BF.B.5Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
- Product rule of logarithms
- Solving exponential equations with logarithms
- What is a logarithm?
- Converting from logarithmic form to exponential form
- Evaluating logarithms without a calculator
- Common logarithms
- Natural log: ln
- Evaluating logarithms using change-of-base formula
- Converting from exponential form to logarithmic form
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.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.HSG.GMD.A.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
- Surface area and volume of cylinders
- Surface area and volume of cones
- Surface area and volume of prisms
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
CC.HSG.GMD.A.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- Surface area and volume of pyramids
CC.HSG.GMD.B.4Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
- Surface area of 3-dimensional shapes
- Introduction to surface area of 3-dimensional shapes
- Nets of 3-dimensional shapes
CC.HSG.MG.A.1Use geometric shapes, their measures, and their properties to describe objects.
- Scale diagrams
CC.HSG.MG.A.2Apply concepts of density based on area and volume in modeling situations.
- Word problems of polynomials
CC.HSS.ID.A.4Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
- Introduction to normal distribution
- Normal distribution and continuous random variable
- Z-scores and random continuous variables
CC.HSS.ID.B.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
- Reading and drawing Venn diagrams
- Probability with Venn diagrams
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.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.HSN.CN.A.1Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real.
- Understanding the number systems
- Introduction to imaginary numbers
CC.HSN.CN.A.2Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- Combining the exponent rules
- Complex numbers and complex planes
- Adding and subtracting complex numbers
- Multiplying and dividing complex numbers
CC.HSN.CN.A.3Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- Complex conjugates
- Distance and midpoint of complex numbers
- Angle and absolute value of complex numbers
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.HSN.CN.C.7Solve quadratic equations with real coefficients that have complex solutions.
- Nature of roots of quadratic equations: The discriminant
- Using quadratic formula to solve quadratic equations
- Applications of quadratic equations
CC.HSN.CN.C.8Extend polynomial identities to the complex numbers.
- Solving polynomials with unknown coefficients
- Factoring polynomials: x^2 + bx + c
- Applications of polynomials: x^2 + bx + c
- Solving polynomials with the unknown
- Factoring polynomials: ax^2 + bx + c
- Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
- Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
CC.HSN.CN.C.9Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
- Word problems of polynomials
- Fundamental theorem of algebra
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.5Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
- Shortcut: Vertex formula
- Graphing quadratic functions: General form VS. Vertex form
- Finding the quadratic functions for given parabolas
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.HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
- Geometric series
- Factor by taking out the greatest common factor
- Factor by grouping
- Factoring difference of squares: $x^2 - y^2$

Integrated Math 3

About High School Minnesota Integrated Math 3

Minnesota follows the Minnesota Academic Standards for mathematics, and Integrated Math 3 brings together advanced algebra, trigonometry, geometry, statistics, and number systems into one course. Students work through polynomial and rational expressions, logarithmic and exponential functions, trigonometric functions and identities, conic sections, probability distributions, complex numbers, vectors, and matrices. StudyPug provides video lessons and practice problems matched to every strand so students can get unstuck and build confidence at their own pace.

Strands: algebra and expressions, trigonometry and functions, geometry and modeling, statistics and probability, complex numbers, vectors, and matrices
Video lessons taught step-by-step for every Integrated Math 3 topic
Practice problems with worked examples aligned to Minnesota Academic Standards
Unlimited access across all topics so students can review any concept at any time

Curriculum topics by strand

Find lessons and practice for every Integrated Math 3 topic, organized by strand and aligned to Minnesota Academic Standards.

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Minnesota High School Integrated Math 3 Topics

Algebra and Expressions: Interpreting and rewriting polynomial, rational, and exponential expressions; solving systems of linear and quadratic equations; working with the Remainder Theorem, polynomial identities, and the Binomial Theorem; simplifying and operating on rational expressions; solving rational and radical equations.
Functions and Equations: Finding inverse functions; understanding the relationship between exponents and logarithms; solving exponential equations using logarithms; interpreting parameters in linear and exponential models; graphing and solving equations involving polynomial, rational, absolute value, exponential, and logarithmic functions.
Trigonometry: Radian measure and the unit circle; values of sine, cosine, and tangent for special angles; symmetry and periodicity of trigonometric functions; modeling periodic phenomena; inverse trigonometric functions; the Pythagorean identity; addition and subtraction formulas; the Laws of Sines and Cosines; area of a triangle using trigonometry.
Geometry and Modeling: Deriving equations of parabolas, ellipses, and hyperbolas; volume formulas for cylinders, pyramids, cones, and spheres; cross-sections of three-dimensional objects; density in modeling situations; applying geometric methods to design problems.
Statistics and Probability: Normal distributions and standard deviation; two-way frequency tables; statistical inference and random sampling; sample surveys, experiments, and observational studies; margin of error; comparing treatments with simulations; random variables and expected value; probability distributions; analyzing decisions using probability.
Complex Numbers: Defining and operating on complex numbers; the complex plane in rectangular and polar form; solving quadratic equations with complex solutions; the Fundamental Theorem of Algebra.
Vectors and Matrices: Representing vector quantities; adding, subtracting, and scalar-multiplying vectors; matrix operations; matrix multiplication and its properties; matrices as transformations; using matrices to solve systems of linear equations; geometric series formulas.

How StudyPug Helps Minnesota High School Integrated Math 3 Students

When a student hits a wall on a topic like logarithmic equations or the Law of Cosines, StudyPug lets them go straight to that concept, watch a clear step-by-step lesson, and work through practice problems with full solutions. There is no need to wait for the next class or search through a textbook for an explanation that makes sense.

Because Integrated Math 3 pulls together content from algebra, geometry, trigonometry, and statistics all at once, students often need to revisit earlier ideas mid-unit. StudyPug gives unlimited access to every strand so a student can review rational expressions one evening and jump to probability distributions the next, following whatever their class requires.

Aligned to Minnesota High School Integrated Math 3 Curriculum

Every lesson and practice set on StudyPug is built around the Minnesota Academic Standards for mathematics, which means the content your child studies here matches what their teacher covers in class. From interpreting expressions and proving polynomial identities to modeling with trigonometric functions and analyzing data with the normal distribution, the scope and sequence follows the Integrated Math 3 course as taught in Minnesota high schools.

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Last updated June 5, 2026

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