Algebra Fundamentals Quiz
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Questions and Answers

What is a missing number in algebra?

In algebra, it can appear many times.

Which of the following are operations in mathematics?

  • Addition (correct)
  • Multiplication (correct)
  • Subtraction (correct)
  • Division (correct)

What are variables used for in algebra?

Variables are used instead of a question mark when representing missing numbers.

What defines an equation?

<p>Two groups of numbers with an equal sign in between them.</p> Signup and view all the answers

What is an expression in algebra?

<p>A group of numbers and x's.</p> Signup and view all the answers

What is a solution?

<p>The answer to an equation.</p> Signup and view all the answers

What are equivalent equations?

<p>Equations that look different but have the same solution.</p> Signup and view all the answers

What is the golden rule of algebra?

<p>If you change the value of one side of an equation, you must change the other by the same amount.</p> Signup and view all the answers

What are inverse operations?

<p>When two operations undo each other (multiplication/division, addition/subtraction).</p> Signup and view all the answers

What does the commutative property state for addition and multiplication?

<p>a + b = b + a (A), a x b = b x a (B)</p> Signup and view all the answers

What are equivalent expressions?

<p>Two expressions that have the same value.</p> Signup and view all the answers

What is interest as defined in banking?

<p>What a bank pays people to keep their money.</p> Signup and view all the answers

What is the rate of change?

<p>The speed with which something changes as time passes.</p> Signup and view all the answers

What defines a negative number?

<p>A number that is less than zero.</p> Signup and view all the answers

What defines a positive number?

<p>A number that is more than zero.</p> Signup and view all the answers

What is a number line?

<p>A line that shows a list of numbers in order.</p> Signup and view all the answers

What is an opposite number?

<p>A number that is the same except having the opposite sign.</p> Signup and view all the answers

The order of operations is ______.

<p>parentheses, exponents, multiplication, division, addition, subtraction.</p> Signup and view all the answers

What does 'undo in reverse order' refer to?

<p>Order of operations backwards.</p> Signup and view all the answers

What is the associative property?

<p>(a + b) + c = a + (b + c), (ab)c = a(bc).</p> Signup and view all the answers

What are terms in algebra?

<p>Products, quotients, individual numbers, and x's.</p> Signup and view all the answers

What does simplifying mean?

<p>Rewriting an expression in a simpler form.</p> Signup and view all the answers

What does combining coefficients involve?

<p>Simplifying to get a single term.</p> Signup and view all the answers

Rate is defined as ______.

<p>rate = amount/time.</p> Signup and view all the answers

What is the distributive property?

<p>a(b + c) = ab + ac.</p> Signup and view all the answers

What is a false equation?

<p>An equation with no solution.</p> Signup and view all the answers

What is an identity in algebra?

<p>When every number can make two sides equal.</p> Signup and view all the answers

What is the numerator?

<p>The top part of a fraction.</p> Signup and view all the answers

What is the denominator?

<p>The bottom part of a fraction.</p> Signup and view all the answers

What does factoring refer to?

<p>Rewriting a number as a multiplication.</p> Signup and view all the answers

What are prime numbers?

<p>Numbers that cannot be broken down into any more multiplications, only the number itself times one.</p> Signup and view all the answers

What is a rational expression?

<p>Fractions with x's.</p> Signup and view all the answers

What is a proportion?

<p>Two ratios set equal to each other.</p> Signup and view all the answers

What is a ratio?

<p>A comparison between two numbers.</p> Signup and view all the answers

What is an exponent?

<p>The superscript of a number.</p> Signup and view all the answers

What is the base in exponentiation?

<p>The number below the superscript (exponent).</p> Signup and view all the answers

What are like terms?

<p>Terms raised to the same power.</p> Signup and view all the answers

What is advanced distributing?

<p>FOIL method: First, Outer, Inner, Last.</p> Signup and view all the answers

What is a monomial?

<p>A polynomial with one term.</p> Signup and view all the answers

What is a binomial?

<p>A polynomial with two terms.</p> Signup and view all the answers

What is a trinomial?

<p>A polynomial with three terms.</p> Signup and view all the answers

What is a polynomial?

<p>An expression with x's that only have whole number exponents.</p> Signup and view all the answers

What does the radical sign indicate?

<p>Indicates the square roots.</p> Signup and view all the answers

What is a root in mathematics?

<p>The inverse of a power; also called taking a root.</p> Signup and view all the answers

What are radical equations?

<p>Equations with roots of x.</p> Signup and view all the answers

What is an irrational number?

<p>Numbers that cannot be written as a ratio of whole numbers.</p> Signup and view all the answers

What is a rational number?

<p>Numbers that can be written as a whole number.</p> Signup and view all the answers

What defines a real number?

<p>Rationals and irrationals, whole numbers, fractions, and decimals.</p> Signup and view all the answers

What is a right triangle?

<p>A triangle that has one angle equal to 90 degrees.</p> Signup and view all the answers

What is the Pythagorean Theorem?

<p>Relation between the lengths of the sides of a right triangle, usually expressed as $a^2 + b^2 = c^2$.</p> Signup and view all the answers

Study Notes

Algebra Fundamentals

  • Missing Number: Represents unknown values in algebra, appearing multiple times.
  • Operations: Key arithmetic functions: addition, multiplication, subtraction, division.
  • Variables: Symbols used in place of numerical values to denote missing numbers.

Equations and Expressions

  • Equation: Consists of two sides with an equal sign, indicating equivalence.
  • Expression: Combination of numbers and variables without an equal sign.
  • Solution: The value that satisfies an equation.

Properties of Equations

  • Equivalent Equations: Different forms of equations that yield the same solution.
  • Golden Rule of Algebra: Altering one side of an equation necessitates a corresponding change on the other side.
  • Inverse Operations: Pairs of operations that cancel each other (e.g., multiplication vs. division).

Mathematical Properties

  • Commutative Property: The order of addition or multiplication does not affect the result (a+b = b+a, ab = ba).
  • Associative Property: The way numbers are grouped in addition or multiplication does not change the outcome ((a+b)+c = a+(b+c)).
  • Distributive Property: Distributing multiplication over addition (a(b+c) = ab + ac).

Numbers and Operations

  • Negative Number: A number less than zero.
  • Positive Number: A number greater than zero.
  • Terms: Components of expressions, including individual numbers and variables.

Fractions and Ratios

  • Numerator and Denominator: The top and bottom parts of a fraction, respectively.
  • Rational Numbers: Numbers expressible as a fraction of whole numbers.
  • Irrational Numbers: Cannot be expressed as fractions; have non-repeating, non-terminating decimal expansions.

Advanced Mathematics

  • Polynomial Types: Monomial (one term), binomial (two terms), trinomial (three terms).
  • Factoring: The process of expressing a number or expression as a product of its factors.
  • Radical Equations: Equations that include square roots or other roots.

Graphs and Geometry

  • Number Line: A visual representation of numbers in a linear format.
  • Rate of Change: Measurement of how a quantity changes relative to another variable, often time.

Special Concepts

  • Pythagorean Theorem: Fundamental relationship in right triangles; states that the square of the hypotenuse equals the sum of the squares of the other two sides.
  • Like Terms: Terms in an expression that have the same variable raised to the same power; can be combined.
  • Exponent: Indicates how many times a number is multiplied by itself; represented as a superscript.

Summary of Process

  • Order of Operations: The rules that dictate the sequence in which operations are performed (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, abbreviated as PEMDAS).
  • Simplifying Expressions: The act of rewriting expressions in a more manageable or concise form by combining like terms or performing operations.

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Test your understanding of algebra fundamentals including missing numbers, operations, and the properties of equations. This quiz will cover key concepts and definitions important for mastering algebraic equations and expressions. Sharpen your skills with practical examples and problem-solving techniques.

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