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High School Math Courses - Common Core Curriculum

Discover comprehensive Mathematics III coursework aligned with Common Core standards. Explore advanced algebra, trigonometry, and statistics to prepare for college-level mathematics and real-world applications.

Common Core High School Math Curriculum - Mathematics III

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Common Core ID
Standard
StudyPug Topic
CC.HSA.SSE.A.1
Interpret expressions that represent a quantity in terms of its context.
What is a polynomial?
Applications of linear equations
CC.HSA.SSE.A.2
Use 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.3
Choose 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.7
Solve 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.2
Know 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.4
Prove 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.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.
Pascal's triangle
Binomial theorem
Determining the equation of a polynomial function
CC.HSA.APR.D.6
Rewrite simple rational expressions in different forms.
Applications of polynomial functions
Solving polynomial inequalities
Fundamental theorem of algebra
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.
Negative exponent rule
Multiplying rational expressions
Dividing rational expressions
Descartes' rule of signs
CC.HSA.REI.A.2
Solve 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.4
Rearrange 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.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.
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.4
For 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
Evaluating logarithms using logarithm rules
CC.HSF.LE.B.5
Interpret 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.4
Find inverse functions.
Finding the quadratic functions for given parabolas
Inverse functions
CC.HSF.BF.B.5
Understand 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.1
Understand 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.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.
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.
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.5
Choose 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.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.
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.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.
Evaluating inverse trigonometric functions
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.
Pythagorean identities
CC.HSF.TF.C.9
Prove 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.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.
Area of triangles: 1/2 a*b sin(C)
CC.HSG.SRT.D.10
Prove the Laws of Sines and Cosines and use them to solve problems.
Law of sines
Law of cosines
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.
Applications of the sine law and cosine law
CC.HSG.GPE.A.2
Derive the equation of a parabola given a focus and directrix.
Conics - Parabola
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.
Conics - Ellipse
Conics - Hyperbola
CC.HSG.GMD.A.1
Give 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.2
Give 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.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Surface area and volume of pyramids
CC.HSG.GMD.B.4
Identify 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.1
Use geometric shapes, their measures, and their properties to describe objects.
Scale diagrams
CC.HSG.MG.A.2
Apply concepts of density based on area and volume in modeling situations.
Word problems of polynomials
CC.HSS.ID.A.4
Use 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.
Organizing data
Introduction to normal distribution
Normal distribution and continuous random variable
Z-scores and random continuous variables
CC.HSS.ID.B.5
Summarize 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.1
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Sampling methods
CC.HSS.IC.A.2
Decide 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.3
Recognize 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.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.
Margin of error
Confidence intervals to estimate population mean
Making a confidence interval
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.
Traditional hypothesis testing
P-value hypothesis testing
Analysis of variance (ANOVA)
CC.HSS.IC.B.6
Evaluate reports based on data.
Influencing factors in data collection
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.
Probability distribution - histogram, mean, variance & standard deviation
CC.HSS.MD.A.2
Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
Properties of expectation
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.
Binomial distribution
Mean and standard deviation of binomial distribution
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).
Type 1 and type 2 errors
CC.HSN.CN.A.1
Know 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.2
Use 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.3
Find 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.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.
Polar form of complex numbers
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.
Operations on complex numbers in polar form
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.
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
CC.HSN.CN.C.7
Solve 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.8
Extend 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 "b" from ax^2 + bx + c
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.9
Know 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.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.
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.2
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Scalar multiplication of vectors
Equivalent vectors
CC.HSN.VM.A.3
Solve 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.4
Add and subtract vectors.
Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Adding and subtracting vectors in component form
Operations on vectors in magnitude and direction form
CC.HSN.VM.B.5
Multiply a vector by a scalar.
Slope intercept form: y = mx + b
Unit vector
CC.HSN.VM.C.6
Use 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.7
Multiply 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.8
Add, subtract, and multiply matrices of appropriate dimensions.
Matrix multiplication
The three types of matrix row operations
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.
Properties of matrix multiplication
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.
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.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.
Transforming vectors with matrices
Transforming shapes with matrices
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.
Finding the transformation matrix
CC.HSA.REI.C.5
Prove 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.8
Represent 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.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).
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.4
Derive 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: x2−y2x^2 - y^2x2−y2

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