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# Math: Numbers and Operations

Created by
@ExaltedIvy

### What is the set of input values in a function?

• Range
• Output Value
• Domain (correct)
• Function Notation
• ### What is the property of real numbers that states a + b = b + a?

• Distributive Property
• Commutative Property (correct)
• Associative Property
• Order of Operations
• ### What is the process of combining like terms in an algebraic expression?

• Solving
• Distributing
• Simplifying (correct)
• Factoring
• ### What type of function has the general form f(x) = mx + b?

<p>Linear Function</p> Signup and view all the answers

### What is the trigonometric ratio of the opposite side to the hypotenuse?

<p>Sine</p> Signup and view all the answers

### What is the equation for the Pythagorean Identity?

<p>sin^2(A) + cos^2(A) = 1</p> Signup and view all the answers

### What is the first step in solving a linear equation?

<p>Add the same value to both sides</p> Signup and view all the answers

### What is the x-intercept of a linear function?

<p>The point where the graph crosses the x-axis</p> Signup and view all the answers

### What is the trigonometric ratio of the adjacent side to the hypotenuse?

<p>Cosine</p> Signup and view all the answers

### What is the correct order of operations?

<p>Parentheses, Exponents, Multiplication, Division, Addition, Subtraction</p> Signup and view all the answers

## Study Notes

### Numbers and Operations

• Real Numbers: Include all rational and irrational numbers, can be represented on the number line
• Properties of Real Numbers:
• Commutative Property: a + b = b + a, ab = ba
• Associative Property: (a + b) + c = a + (b + c), (ab)c = a(bc)
• Distributive Property: a(b + c) = ab + ac
• Order of Operations: Follow the order of parentheses, exponents, multiplication and division, and addition and subtraction

### Algebraic Expressions and Equations

• Expressions: A collection of variables, constants, and algebraic operations
• Equations: Two expressions equal to each other
• Simplifying Expressions:
• Combine like terms
• Use the distributive property
• Use the properties of real numbers
• Solving Linear Equations:
• Add, subtract, multiply, or divide both sides by the same value
• Use inverse operations to isolate the variable

### Functions

• Domain and Range: Domain is the set of input values, range is the set of output values
• Function Notation: f(x) = output value, where x is the input value
• Types of Functions:
• Linear Functions: f(x) = mx + b, where m is the slope and b is the y-intercept
• Quadratic Functions: f(x) = ax^2 + bx + c, where a, b, and c are constants
• Graphing Functions:
• Use the x-axis for the domain and the y-axis for the range
• Identify the x-intercept(s) and y-intercept

### Trigonometry

• Angles and Triangles:
• Degrees, minutes, and seconds
• Right triangles, acute angles, and obtuse angles
• Trigonometric Ratios:
• Sine (sin), cosine (cos), and tangent (tan)
• sin(A) = opposite side / hypotenuse, cos(A) = adjacent side / hypotenuse, tan(A) = opposite side / adjacent side
• Identities and Formulas:
• Pythagorean Identity: sin^2(A) + cos^2(A) = 1
• Sum and Difference Formulas: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), etc.

### Analytic Geometry

• Coordinate Plane:
• Quadrants, x-axis, y-axis, and origin
• Plotting points and graphing equations
• Circle Equations:
• Standard form: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius
• General form: x^2 + y^2 + Dx + Ey + F = 0
• Conic Sections:
• Parabolas, ellipses, and hyperbolas
• Equations and graphs of each

### Numbers and Operations

• Real numbers include all rational and irrational numbers and can be represented on the number line.
• The Commutative Property of Real Numbers states that the order of numbers does not change the result: a + b = b + a, ab = ba.
• The Associative Property of Real Numbers states that the order in which numbers are grouped does not change the result: (a + b) + c = a + (b + c), (ab)c = a(bc).
• The Distributive Property of Real Numbers states that multiplication can be distributed over addition: a(b + c) = ab + ac.
• The Order of Operations follows the order of parentheses, exponents, multiplication and division, and addition and subtraction.

### Algebraic Expressions and Equations

• An algebraic expression is a collection of variables, constants, and algebraic operations.
• An equation is two expressions equal to each other.
• To simplify expressions, combine like terms, use the distributive property, and use the properties of real numbers.
• To solve linear equations, add, subtract, multiply, or divide both sides by the same value, and use inverse operations to isolate the variable.

### Functions

• The domain of a function is the set of input values, and the range is the set of output values.
• Function notation is f(x) = output value, where x is the input value.
• Linear functions have the form f(x) = mx + b, where m is the slope and b is the y-intercept.
• Quadratic functions have the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
• To graph functions, use the x-axis for the domain and the y-axis for the range, and identify the x-intercept(s) and y-intercept.

### Trigonometry

• Angles can be measured in degrees, minutes, and seconds.
• Right triangles have acute angles and obtuse angles.
• The sine, cosine, and tangent ratios are defined as sin(A) = opposite side / hypotenuse, cos(A) = adjacent side / hypotenuse, and tan(A) = opposite side / adjacent side.
• The Pythagorean Identity states that sin^2(A) + cos^2(A) = 1.
• The Sum and Difference Formulas include sin(A + B) = sin(A)cos(B) + cos(A)sin(B), etc.

### Analytic Geometry

• The coordinate plane has four quadrants, an x-axis, a y-axis, and an origin.
• Points can be plotted and equations can be graphed on the coordinate plane.
• Circle equations can be written in standard form: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
• Circle equations can also be written in general form: x^2 + y^2 + Dx + Ey + F = 0.
• Conic sections include parabolas, ellipses, and hyperbolas, each with its own equation and graph.

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## Description

Understand real numbers, properties of real numbers, and order of operations. Also, learn about algebraic expressions and equations.

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