Subjects
Shows
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For [...]
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using [...]
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the [...]
(+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that [...]
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role [...]
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another [...]
(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant [...]
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are [...]
(+) Add, subtract, and multiply matrices of appropriate dimensions.
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies [...]
Interpret expressions that represent a quantity in terms of its context.*
Interpret parts of an expression, such as terms, factors, and coefficients.*
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as [...]
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 [...]
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the [...]
Factor a quadratic expression to reveal the zeros of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Use the properties of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 [...]
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use [...]
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, [...]
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x [...]
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the [...]
Define appropriate quantities for the purpose of descriptive modeling.*
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*
Know there is a complex number i such that i^2 = −1, and every complex number has the form a [...]
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain [...]
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation [...]
(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of [...]
Solve quadratic equations with real coefficients that have complex solutions.
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate [...]
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a [...]
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
(+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors [...]
(+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
(+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with [...]
(+) Perform operations on vectors. Multiply a vector by a scalar.
(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v(sub [...]
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those [...]
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an [...]
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units [...]
Evaluate licenses that limit or restrict use of computational artifacts when using resources such as libraries.
Subjects
Shows
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For [...]
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using [...]
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the [...]
(+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that [...]
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role [...]
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another [...]
(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant [...]
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are [...]
(+) Add, subtract, and multiply matrices of appropriate dimensions.
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies [...]
Interpret expressions that represent a quantity in terms of its context.*
Interpret parts of an expression, such as terms, factors, and coefficients.*
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as [...]
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 [...]
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the [...]
Factor a quadratic expression to reveal the zeros of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Use the properties of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 [...]
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use [...]
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, [...]
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x [...]
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the [...]
Define appropriate quantities for the purpose of descriptive modeling.*
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*
Know there is a complex number i such that i^2 = −1, and every complex number has the form a [...]
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain [...]
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation [...]
(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of [...]
Solve quadratic equations with real coefficients that have complex solutions.
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate [...]
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a [...]
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
(+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors [...]
(+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
(+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with [...]
(+) Perform operations on vectors. Multiply a vector by a scalar.
(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v(sub [...]
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those [...]
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an [...]
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units [...]
Evaluate licenses that limit or restrict use of computational artifacts when using resources such as libraries.
