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Pre-calculus

Oregon Pre-Calculus Curriculum

Video lessons and practice for every pre-calculus topic. Aligned to Oregon Mathematics Standards so Oregon high school students stay on track.

Oregon Pre-Calculus Curriculum | StudyPugHelp

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Standard

StudyPug Topic

CC.HSN.CN.B.4

Represent 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.

CC.HSN.CN.B.5

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

CC.HSN.CN.B.6

Calculate 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.

CC.HSA.CED.A.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

CC.HSA.REI.D.11

Explain 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.

CC.HSF.TF.A.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

CC.HSF.TF.A.2

Explain 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.

CC.HSF.TF.A.3

Use 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.

CC.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

CC.HSF.TF.B.6

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

CC.HSF.TF.B.7

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

CC.HSF.TF.C.8

Prove 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.

CC.HSF.TF.C.9

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

CC.HSG.SRT.D.9

Derive 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.

CC.HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

CC.HSG.SRT.D.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

CC.HSA.APR.C.4

Prove polynomial identities and use them to describe numerical relationships.

CC.HSA.APR.C.5

Know 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.

CC.HSA.APR.D.7

Understand 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.

CC.HSN.VM.A.1

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.

CC.HSN.VM.A.2

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

CC.HSN.VM.A.3

Solve problems involving velocity and other quantities that can be represented by vectors.

CC.HSN.VM.B.5

Multiply a vector by a scalar.

CC.HSN.VM.C.6

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

CC.HSN.VM.C.7

Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

CC.HSN.VM.C.8

Add, subtract, and multiply matrices of appropriate dimensions.

CC.HSN.VM.C.9

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

CC.HSN.VM.C.10

Understand 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.

CC.HSN.VM.C.11

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.

CC.HSN.VM.C.12

Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

CC.HSA.REI.C.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

CC.HSA.REI.C.8

Represent a system of linear equations as a single matrix equation in a vector variable.

CC.HSA.REI.C.9

Find 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).

CC.HSG.C.A.4

Construct a tangent line from a point outside a given circle to the circle.

CC.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

CC.HSG.GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

CC.HSN.RN.B.3

Explain 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.

CC.HSN.Q.A.1

Use 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.

CC.HSN.Q.A.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

CC.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

CC.HSS.IC.A.2

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

CC.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

CC.HSS.IC.B.4

Use 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.

CC.HSS.IC.B.5

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

CC.HSS.IC.B.6

Evaluate reports based on data.

CC.HSS.CP.A.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

CC.HSS.CP.B.7

Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

CC.HSS.MD.A.1

Define 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.

CC.HSS.MD.A.2

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

CC.HSS.MD.A.3

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

CC.HSS.MD.B.7

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

CC.HSG.GMD.A.2

Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

Oregon Pre-Calculus: What Students Learn

Pre-calculus is a pivotal course for Oregon high school students preparing for college-level mathematics. The course is built around the Oregon Mathematics Standards and covers a wide range of topics that bridge algebra, geometry, and introductory calculus concepts.

Complex Numbers and the Complex Plane

Students learn to represent complex numbers in both rectangular and polar form, perform arithmetic operations geometrically on the complex plane, and calculate distances and midpoints using the modulus. These skills form a foundation for understanding advanced algebra and engineering mathematics.

Trigonometry and the Unit Circle

A large portion of Oregon pre-calculus is devoted to trigonometry. Students explore radian measure, the unit circle, special triangle values, and the properties of sine, cosine, and tangent functions. They also study inverse trigonometric functions, the Pythagorean identity, addition and subtraction formulas, and the Laws of Sines and Cosines to solve real-world triangle problems.

Vectors and Matrices

Students represent vector quantities with directed line segments, add and subtract vectors, multiply by scalars, and apply vectors to solve problems involving velocity and other real-world quantities. Matrix topics include scalar multiplication, matrix addition and multiplication, determinants, inverse matrices, and using matrices to solve systems of linear equations. Students also explore 2×2 matrices as transformations of the plane.

Conic Sections and Polynomial Identities

Pre-calculus introduces conic sections, including parabolas, ellipses, and hyperbolas, derived from their geometric definitions involving foci and directrices. Students also prove polynomial identities, apply the Binomial Theorem, and work with rational expressions as a closed system under arithmetic operations.

Statistics and Probability

The course concludes with data analysis and probability. Students interpret sample surveys and experiments, use simulation to estimate population parameters, construct two-way frequency tables, and apply the Addition and Multiplication Rules for probability. Random variables, expected value, and probability distributions round out the statistics strand.

  • Complex numbers and the complex plane
  • Trigonometric functions, identities, and inverse functions
  • Laws of Sines and Cosines
  • Vectors and matrix operations
  • Conic sections: parabolas, ellipses, hyperbolas
  • Polynomial identities and the Binomial Theorem
  • Statistics, probability, and expected value

StudyPug covers every one of these topics with pre-calculus video lessons and practice problems aligned to Oregon Mathematics Standards.