Algebra Chapter 1 Flashcards

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Questions and Answers

What are inverse operations?

Operations that do not affect each other

Operations that always produce a larger number

Operations that can only be used in pairs

Operations that 'undo' one another (correct)

What does the Addition Property of Equality state?

Adding the same number to each side of an equation produces an equivalent equation.

What does the Subtraction Property of Equality state?

Subtracting the same number from each side of an equation produces an equivalent equation.

What does the Multiplication Property of Equality state?

Multiplying the same number to each side of an equation produces an equivalent equation. Signup and view all the answers

What does the Division Property of Equality state?

Dividing the same number to each side of an equation produces an equivalent equation. Signup and view all the answers

What is an Absolute Value Equation?

An equation that contains an absolute value expression. Signup and view all the answers

What is the definition of Absolute Value?

The distance away from 0. Signup and view all the answers

What is the formula for the Area of a Triangle?

A = 0.5bh Signup and view all the answers

What is the formula for the Area of a Trapezoid?

A = 0.5(b1 + b2)h Signup and view all the answers

What is Perimeter?

The distance around a figure. Signup and view all the answers

What is the formula for the Circumference of a circle?

C = 2πr or C = πd Signup and view all the answers

What is the formula for the Area of a Parallelogram?

A = bh Signup and view all the answers

What is the formula for the Volume of a Prism?

V = lwh Signup and view all the answers

What is the formula for the Volume of a Pyramid?

V = 1/3Bh Signup and view all the answers

What is the formula for the Volume of a Cylinder?

V = πr²h Signup and view all the answers

What is the formula for the Volume of a Cone?

V = 1/3πr²h Signup and view all the answers

What is a Literal Equation?

An equation that has two or more variables. Signup and view all the answers

What is the formula for the Surface Area of a Cone?

S = πr² + πrℓ Signup and view all the answers

What is the Power of a Quotient Property?

To find a power of a quotient, find the power of the numerator and the power of the denominator and divide. Signup and view all the answers

Study Notes

Inverse Operations

Inverse operations are actions that reverse each other, aiding in solving equations.
Key pairs include: addition and subtraction, multiplication and division.

Properties of Equality

Addition Property of Equality: Adding the same number to both sides maintains equivalence.
Subtraction Property of Equality: Subtracting the same number from both sides maintains equivalence.
Multiplication Property of Equality: Multiplying both sides by the same number maintains equivalence.
Division Property of Equality: Dividing both sides by the same number maintains equivalence.

Absolute Value

Absolute Value Equation: An equation featuring an absolute value expression, indicating distance from zero.
Absolute Value: Represents the distance of a number from 0 on the number line.

Geometric Formulas

Area of a Triangle: A = 0.5 * b * h (where b is base and h is height).
Area of a Trapezoid: A = 0.5 * (b1 + b2) * h.
Perimeter: Total distance around a figure, calculated by adding all side lengths.
Circumference of a Circle: C = 2𝛑r or C = 𝛑d (where r is radius and d is diameter).
Area of a Parallelogram: A = b * h (base times height at a right angle to the base).
Volume of a Prism: V = l * w * h (length times width times height).
Volume of a Pyramid: V = (1/3) * B * h (where B is the base area).
Volume of a Cylinder: V = 𝛑 * r² * h (where r is radius and h is height).
Volume of a Cone: V = (1/3) * 𝛑 * r² * h (where r is radius and h is height).
Surface Area of a Cone: S = 𝛑r² + 𝛑rℓ (includes base and lateral surface area, where ℓ is slant height).

Literal Equations

A literal equation contains two or more variables, used to express relationships between quantities.

Power of a Quotient Property

The power of a quotient is calculated by individually raising the numerator and denominator to the power before dividing them.

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Description

Explore the fundamentals of solving linear equations with these flashcards from Algebra Chapter 1. Each card presents key concepts, such as inverse operations and the properties of equality, essential for mastering algebra. Perfect for quick revisions and enhancing your problem-solving skills.