High School — Number and Quantity

Other Delaware Common Core Mathematics sets

• Grade K
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grades 9, 10, 11, 12
• High School — Algebra
• High School — Functions
• High School — Geometry
• High School — Statistics and Probability

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.CCSS.Math.Content.HSN-RN.A.1

Rewrite expressions involving radicals and rational exponents using the properties of exponents.CCSS.Math.Content.HSN-RN.A.2

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.CCSS.Math.Content.HSN-RN.B.3

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.CCSS.Math.Content.HSN-Q.A.1

Define appropriate quantities for the purpose of descriptive modeling.CCSS.Math.Content.HSN-Q.A.2

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.CCSS.Math.Content.HSN-Q.A.3

Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.CCSS.Math.Content.HSN-CN.A.1

Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.CCSS.Math.Content.HSN-CN.A.2

(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.CCSS.Math.Content.HSN-CN.A.3

(+) 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.CCSS.Math.Content.HSN-CN.B.4

(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.CCSS.Math.Content.HSN-CN.B.5

(+) 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.CCSS.Math.Content.HSN-CN.B.6

Solve quadratic equations with real coefficients that have complex solutions.CCSS.Math.Content.HSN-CN.C.7

(+) Extend polynomial identities to the complex numbers.CCSS.Math.Content.HSN-CN.C.8

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.CCSS.Math.Content.HSN-CN.C.9

(+) 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 (e.g., v, |v|, ||v||, v).CCSS.Math.Content.HSN-VM.A.1

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.CCSS.Math.Content.HSN-VM.A.2

(+) Solve problems involving velocity and other quantities that can be represented by vectors.CCSS.Math.Content.HSN-VM.A.3

(+) Add and subtract vectors.CCSS.Math.Content.HSN-VM.B.4

(+) Multiply a vector by a scalar.CCSS.Math.Content.HSN-VM.B.5

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.CCSS.Math.Content.HSN-VM.C.6

(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.CCSS.Math.Content.HSN-VM.C.7

(+) Add, subtract, and multiply matrices of appropriate dimensions.CCSS.Math.Content.HSN-VM.C.8

(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.CCSS.Math.Content.HSN-VM.C.9

(+) 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.CCSS.Math.Content.HSN-VM.C.10

(+) 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.CCSS.Math.Content.HSN-VM.C.11

(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.CCSS.Math.Content.HSN-VM.C.12