Real Numbers and Basic Algebra Terms

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Questions and Answers

Which of the following accurately describes a rational number?

A number that cannot be expressed as a fraction.

A number that is the result of a square root operation.

A number that can only be a whole number or zero.

A number that can be expressed as a fraction of two integers. (correct)

What is the absolute value of -7?

7 (correct)

-7

In a system of equations, what does it mean if the equations have no solution?

The lines representing the equations intersect at multiple points.

The lines representing the equations are the same line.

The lines representing the equations are parallel. (correct)

The lines representing the equations intersect at one point.

Which of the following is a prime number?

2 Signup and view all the answers

What term describes the bottom of a geometric figure?

Base Signup and view all the answers

What is the diameter of a circle?

A line segment connecting two points on the circle and passing through the center. Signup and view all the answers

What is an improper fraction?

A fraction where the numerator is taller than its denominator. Signup and view all the answers

In a coordinate plane, what does the horizontal line represent?

The x-axis. Signup and view all the answers

What does a system of equations consist of?

Two or more equations containing common variable(s). Signup and view all the answers

Which of the following describes relatively prime numbers?

Two numbers that have a greatest common factor of 1. Signup and view all the answers

What is a cube root?

A number that must be multiplied by itself three times to equal a given number. Signup and view all the answers

What is the least common multiple (LCM) of 4 and 6?

12 Signup and view all the answers

Which term best describes two angles that lie on different parallel lines and on opposite sides of a transversal?

Alternate Interior Angles Signup and view all the answers

Which of the following is a prime number?

13 Signup and view all the answers

What is the radical symbol used for?

To indicate square roots or nth roots of a number. Signup and view all the answers

If two angles are adjacent, what characteristic do they share?

They must have a common vertex and a common side but do not overlap. Signup and view all the answers

What defines a proper fraction?

A fraction with a smaller numerator than denominator. Signup and view all the answers

Which statement accurately describes a polygon?

A polygon must have at least three sides. Signup and view all the answers

What is the perimeter of a rectangle with side lengths 4 units and 6 units?

20 units Signup and view all the answers

How is the radius defined in relation to a circle?

It is the line segment from the center to any point on the circle. Signup and view all the answers

Which of the following describes a square?

A quadrilateral with four sides of equal length and four right angles. Signup and view all the answers

What does it mean to simplify a fraction?

To cancel out all common factors in the numerator and denominator. Signup and view all the answers

Which of the following correctly defines a vertex in geometry?

The common endpoint of two rays or line segments. Signup and view all the answers

What is the relationship between the sides of a regular polygon?

All sides are equal and all angles are equal. Signup and view all the answers

Study Notes

Real Numbers

Real numbers encompass all numbers on the number line, including positive and negative integers, rational numbers, and irrational numbers like π.
Zero signifies no quantity and is the additive identity, meaning it does not alter the value of other numbers when added.

Basic Terminology in Mathematics

Algebra: The field of mathematics focused on variables and their relationships.
Base: The bottom part of geometric figures in both plane and solid geometry.
Brackets: Denoted by [ and ], used to group or enclose elements.
Circumference: The total distance around a circle, forming a complete circular arc.
Coordinate Plane: A two-dimensional space defined by a horizontal (x-axis) and vertical axis (y-axis).
Compute: To evaluate or calculate a numerical expression.
Constant: A fixed value in mathematics; does not change over time.
Curly Brackets: Represented by { and }, used to group related items.
Denominator: The bottom component of a fraction, indicating how many parts the whole is divided into.
Diameter of a Circle: The straight line segment passing through the center and connecting two points on the circle.
Diagonal of a Polygon: A line segment that connects non-adjacent vertices within a polygon.
Equation: A mathematical statement asserting the equality of two expressions, marked by an equals sign (=).
Evaluate: The process of computing the value of an expression.
Expression: A combination of numbers, symbols, and operators representing a value.
Formula: A mathematical relation or rule expressed in symbols.
Fraction: Represents a ratio of two numbers or variables.
Height (Altitude): The shortest distance from the base of a geometric figure to its highest point.
Horizontal: Represents a perfectly flat and level line.
Improper Fraction: A fraction where the numerator is larger than the denominator, such as 5/3.
Inequality: A mathematical expression displaying a relationship of less than, greater than, or equal to.
Mixed Fraction: A whole number combined with a proper fraction.
Numerator: The top part of a fraction, representing how many parts are being considered.
Origin: The point of intersection (0, 0) on a coordinate plane.
Parentheses: Symbols ( and ) used to indicate that operations within them should be performed first.
Perimeter: The total length around a two-dimensional shape, calculated by summing the lengths of its sides.
Polygon: A closed plane figure with sides made of line segments, named by the number of sides.
Proper Fraction: A fraction with a numerator smaller than its denominator.
Radius: A segment connecting the center of a circle to a point on its circumference, also representing its length.
Rectangle: A quadrilateral with four right angles (90°) and opposite sides equal.
Reduce a Fraction: Simplifying a fraction by eliminating common factors in the numerator and denominator.
Side of a Polygon: Each line segment forming the polygon.
Square: A specific type of rectangle with all sides equal in length.
Triple: To multiply a value by three.
Variable: A symbol representing an unknown or changing quantity.
Vertex: The point where two or more lines meet; important in polygons and systems of equations.
Solve: To determine all possible solutions for an equation or system of equations/inequalities.
System of Equations: Multiple equations that share common variables.
System of Inequalities: Multiple inequalities that share common variables.

Prime Numbers and Factors

Greatest Common Factor (GCF): The largest integer that can evenly divide each member of a set of numbers.
Least Common Multiple (LCM): The smallest positive integer divisible by two or more integers.
Prime Factorization: Expressing an integer as a product of its prime numbers.
Relatively Prime: Two numbers with a GCF of 1, meaning they have no common factors other than 1.

Radicals and Roots

Cube Root: A value that, when multiplied by itself three times, equals a given number, denoted as ∛x.
Radical Symbol: The symbol √ used to indicate square and nth roots.
Radicand: The number under the radical sign.
Root of a Number: Refers to both square roots and nth roots.
Square Root: A nonnegative number that when multiplied by itself results in a given number, indicated as √x. For example, √9 = 3.

Basic Geometry

Acute Angle: An angle measuring less than 90°.
Adjacent Angles: Two angles sharing a vertex and a side, but do not overlap.
Alternate Interior Angles: Angles located between two parallel lines and on opposite sides of a transversal.

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Description

Explore the world of real numbers including positives, negatives, integers, and rational numbers. This quiz also covers fundamental algebra terminology and concepts such as zero, bases in geometry, and more. Test your knowledge and understanding of these essential mathematical elements.