Basic Algebra Concepts and Properties
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Questions and Answers

What is the branch of mathematics that uses symbols to represent numbers and quantities?

Algebra

What are symbols used to represent unknown values in algebra called?

Variables

Constants are fixed values that do not change.

True (A)

If 'a' equals 'b', what happens when we add 'c' to both sides of the equation?

<p>The equation remains equal.</p> Signup and view all the answers

What is the name of the property that allows us to multiply both sides of an equation by the same value without changing its equality?

<p>Multiplication Property of Equality</p> Signup and view all the answers

What is the general form of a linear equation?

<p>ax + b = c</p> Signup and view all the answers

What is the process involved in solving linear equations?

<p>Isolating the variable 'x' by using the properties of equality.</p> Signup and view all the answers

When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be flipped.

<p>True (A)</p> Signup and view all the answers

What are equations that have more than one variable called?

<p>Equations with several variables</p> Signup and view all the answers

The graph of a linear equation in two variables is always a straight line.

<p>True (A)</p> Signup and view all the answers

What does an exponent represent?

<p>Repeated multiplication</p> Signup and view all the answers

What is the general form of a quadratic equation?

<p>ax² + bx + c = 0</p> Signup and view all the answers

What are the solutions to a quadratic equation called?

<p>Roots or solutions</p> Signup and view all the answers

What is a relationship where each input value has only one output value called?

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

What is the notation used to represent a function?

<p>f(x)</p> Signup and view all the answers

The graph of a quadratic function is always a straight line.

<p>False (B)</p> Signup and view all the answers

What is the set of all possible input values for a function called?

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

What is the process called when solving systems of equations by finding points common to all equations?

<p>Finding solutions or points of intersection</p> Signup and view all the answers

What are square roots, cube roots, and other roots referred to as?

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

It is possible to convert between radical and exponential forms of expressions.

<p>True (A)</p> Signup and view all the answers

What is the name of the coordinate system used in coordinate geometry?

<p>Cartesian coordinate system</p> Signup and view all the answers

What does the slope of a line represent?

<p>Rate of change</p> Signup and view all the answers

What kind of sequences have a constant difference between consecutive terms?

<p>Arithmetic sequences</p> Signup and view all the answers

What kind of sequences involve multiplying consecutive terms by a constant value?

<p>Geometric sequences</p> Signup and view all the answers

Flashcards

Algebra

Branch of math using symbols (variables) to represent numbers and quantities.

Variable

A symbol (usually a letter) representing an unknown value.

Constant

A fixed value that doesn't change.

Addition Property of Equality

Adding the same value to both sides of an equation maintains equality.

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Subtraction Property of Equality

Subtracting the same value from both sides of an equation maintains equality.

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Multiplication Property of Equality

Multiplying both sides of an equation by the same value maintains equality.

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Division Property of Equality

Dividing both sides of an equation by the same non-zero value maintains equality.

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Linear Equation

Equation of the form ax + b = c, where x is the variable.

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Linear Inequality

Inequality of the form ax + b > c. (or <, ≥, ≤).

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Solving Equations

Finding the value(s) of the variable(s) that make the equation true.

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Solving Inequalities

Finding the set of values for the variable that makes the inequality true.

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Function

A relation where each input has only one output.

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Function Notation

Using f(x) to represent the output of a function for a given input.

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Quadratic Equation

An equation in the form ax² + bx + c = 0.

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Systems of Equations

Two or more equations considered together.

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Coordinate Geometry

Study of geometry using coordinates in a plane.

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Slope

The steepness of a line.

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x-intercept

The point where a line crosses the x-axis.

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y-intercept

The point where a line crosses the y-axis.

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Polynomial

Expression of variables and constants combined by addition, subtraction, and multiplication.

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Arithmetic Sequence

Sequence where the difference between consecutive terms is constant.

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Geometric Sequence

Sequence where the ratio between consecutive terms is constant.

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Study Notes

Basic Algebra Concepts

  • Algebra is a branch of mathematics that uses symbols (variables) to represent numbers and quantities.
  • Variables allow for the generalization of mathematical relationships and the solution of equations.
  • Variables are typically represented by letters of the alphabet (e.g., x, y, z).
  • Constants are fixed values, not variables.

Properties of Equality

  • Addition Property of Equality: If a = b, then a + c = b + c. (Adding the same value to both sides of an equation maintains equality).
  • Subtraction Property of Equality: If a = b, then a – c = b – c. (Subtracting the same value from both sides maintains equality).
  • Multiplication Property of Equality: If a = b, then ac = bc. (Multiplying both sides by the same value maintains equality).
  • Division Property of Equality: If a = b and c ≠ 0, then a/c = b/c. (Dividing both sides by the same non-zero value maintains equality).

Solving Linear Equations

  • Linear equations have the form ax + b = c, where 'a', 'b', and 'c' are constants and 'x' is the variable.
  • Solve for 'x' by using the properties of equality to isolate the variable.
  • Combine like terms on each side of the equation.
  • Add or subtract constants to move them to the opposite side of the equation.
  • Multiply or divide by constants to isolate the variable.

Solving Linear Inequalities

  • Linear inequalities have the form ax + b > c, ax + b < c, ax + b ≥ c, or ax + b ≤ c.
  • The process for solving inequalities is similar to solving equations but with a crucial difference.
  • When multiplying or dividing by a negative number, flip the inequality sign.

Linear Equations with Several Variables

  • Equations can have more than one variable.
  • Systems of equations.
  • Solve for a specific variable in terms of the other variables.
  • Use substitution or elimination methods to solve systems of equations and inequalities.
  • Graphing linear equations in two variables.
  • The graph of a linear equation in two variables is a straight line.
  • Finding x and y intercepts.

Exponents and Polynomials

  • Exponents represent repeated multiplication.
  • Polynomials are expressions consisting of variables and constants, combined with operations like addition, subtraction, and multiplication.
  • Basic operations with polynomials (addition, subtraction, multiplication).
  • Factoring quadratic expressions: Finding factors of quadratic equations

Quadratic Equations

  • Quadratic equations have the form ax² + bx + c = 0, where 'a', 'b', and 'c' are constants and 'x' is the variable.
  • Solving quadratic equations using factoring, completing the square, and the quadratic formula.
  • Finding roots or solutions (the 'x' values that make the equation true).

Functions

  • A function is a relation where each input value has only one output value.
  • Function notation (f(x)).
  • Different types of functions (linear, quadratic, etc.).
  • Graphing functions on a coordinate plane.
  • Finding the domain and range of a function.

Systems of Equations

  • Two or more equations considered together.
  • Solutions are points in common on the graph for all equations.
  • Solving systems by graphing, substitution, and elimination methods.
  • Special cases (infinite solutions, no solutions).

Radicals and Rational Exponents

  • Square roots, cube roots, and other roots.
  • Simplifying radical expressions.
  • Operations with radicals.
  • Converting between radical and exponential forms.

Coordinate Geometry

  • Cartesian coordinate system (x-y plane)
  • Graphing points, lines, and other geometric shapes.
  • Finding the distance between two points.
  • Finding the midpoint of a line segment.
  • Understanding slope and its applications in linear equations and lines.

Sequences and Series

  • Understand the concepts of arithmetic sequences and geometric sequences.
  • Calculate terms in a sequence.
  • Calculate sums of sequences.

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Description

This quiz covers fundamental concepts of algebra, including variables, constants, and the properties of equality essential for solving equations. Test your understanding of linear equations and the manipulation of algebraic expressions. Ideal for students in algebra classes or those revisiting basic math principles.

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