N-RN: The Real Number System

N-RN.A: Extend the properties of exponents to rational exponents.

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

Operations with Radical Expressions
Simplifying Radical Expressions

N-Q: Quantities

N-Q.A: Reason quantitatively and use units to solve problems.

N-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.

Density
Distance-Time Graphs
Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs
Distance-Time and Velocity-Time Graphs - Metric
Household Energy Usage

N-Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

N-Q.A.3.a: Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. Identify significant figures in recorded measures and computed values based on the context given and the precision of the tools used to measure.

Unit Conversions 2 - Scientific Notation and Significant Digits

N-CN: The Complex Number System

N-CN.A: Perform arithmetic operations with complex numbers.

N-CN.A.1: 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.

Points in the Complex Plane
Roots of a Quadratic

N-CN.A.2: Use the relation i² = –1 and the Commutative, Associative, and Distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

N-CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane
Roots of a Quadratic

N-CN.B: Represent complex numbers and their operations on the complex plane.

N-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.

Points in the Complex Plane

N-CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

Points in the Complex Plane

N-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.

Points in the Complex Plane

N-CN.C: Use complex numbers in polynomial identities and equations.

N-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.

Roots of a Quadratic

N-CN.C.8: Extend polynomial identities to the complex numbers.

Points in the Complex Plane

N-VM: Vector and Matrix Quantities

N-VM.A: Represent and model with vector quantities.

N-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 (e.g., v, |v|, || v ||, v).

Adding Vectors
Vectors

N-VM.A.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Adding Vectors

N-VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions
Adding Vectors
Golf Range
Vectors

N-VM.B: Perform operations on vectors.

N-VM.B.4: Add and subtract vectors.

N-VM.B.4.a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

Adding Vectors
Vectors

N-VM.C: Perform operations on matrices and use matrices in applications.

N-VM.C.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

Dilations

N-VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.

Translations

N-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.

Solving Linear Systems (Matrices and Special Solutions)

N-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.

Translations