How does High School Math differ from Middle School Math in Common Core?

High School Math in Common Core introduces more advanced concepts, emphasizes abstract thinking, and focuses on applying mathematical skills to real-world scenarios and problem-solving.

What support is available for students struggling with High School Math?

Support includes online tutoring, video lessons, practice problems, study groups, and additional resources provided by schools. Many districts also offer after-school math help programs.

How challenging is the High School Algebra course in Common Core?

The Algebra course can be challenging as it introduces abstract concepts. It covers linear equations, quadratic functions, and systems of equations. With consistent practice and support, most students can succeed.

What career paths benefit from strong High School Math skills?

Strong math skills are valuable in STEM fields, finance, economics, data analysis, engineering, computer science, and many other careers. Math develops critical thinking applicable to various professions.

How does the Common Core Statistics and Probability course prepare students for college?

This course introduces data analysis, probability theory, and statistical inference, preparing students for college-level statistics courses and research methods across various disciplines.

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High School Math Courses - Common Core Curriculum

Explore comprehensive High School math courses aligned with Common Core standards. From Number and Quantity to Statistics, our curriculum guides students through essential mathematical concepts and problem-solving skills.

Common Core High School Math Curriculum Topics

Common Core ID	Standard	StudyPug Topic
HSN.RN.A.1	CC.HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.	Convert between radicals and rational exponents Exponents: Product rule (a^x)(a^y) = a^(x+y) Exponents: Division rule: a^x / a^y = a^(x-y) Exponents: Power rule: (a^x)^y = a^(xy) Exponents: Negative exponents Exponents: Zero exponent: a^0 = 1 Exponents: Rational exponents

HSN.RN.A.2

CC.HSN.RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solving for exponents

Operations with radicals

Conversion between entire radicals and mixed radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Evaluating and simplifying radicals

HSN.RN.B.3

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.

Rational vs. Irrational numbers

Solving radical equations

Converting repeating decimals to fractions

HSN.Q.A.1

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.

Metric systems

Imperial systems

Scale diagrams

Conversions involving squares and cubic

HSN.Q.A.2

CC.HSN.Q.A.2: Define 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

HSN.Q.A.3

CC.HSN.Q.A.3: Choose 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

HSN.CN.A.1

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

HSN.CN.A.2

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

HSN.CN.A.3

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

HSN.CN.B.4

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

HSN.CN.B.5

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

HSN.CN.B.6

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: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

HSN.CN.C.7

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

HSN.CN.C.8

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)

HSN.CN.C.9

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

HSN.VM.A.1

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

HSN.VM.A.2

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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Scalar multiplication of vectors

Equivalent vectors

HSN.VM.A.3

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

HSN.VM.B.4

CC.HSN.VM.B.4: Add 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

HSN.VM.B.5

CC.HSN.VM.B.5: Multiply a vector by a scalar.

Slope intercept form: y = mx + b

Unit vector

HSN.VM.C.6

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

HSN.VM.C.7

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

HSN.VM.C.8

CC.HSN.VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.

Matrix multiplication

The three types of matrix row operations

HSN.VM.C.9

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

HSN.VM.C.10

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

HSN.VM.C.11

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

HSN.VM.C.12

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

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