Basic Arithmetic and Number Systems Quiz

Basic Arithmetic Operations

• Addition: Combining two or more numbers to find a total.
• Subtraction: Finding the difference between two numbers.
• Multiplication: Repeated addition of a number.
• Division: Separating a number into equal parts.

Number Systems

• Natural numbers (N): Counting numbers (1, 2, 3,...).
• Whole numbers (W): Natural numbers plus zero (0, 1, 2, 3,...).
• Integers (Z): Whole numbers and their opposites (..., -3, -2, -1, 0, 1, 2, 3,...).
• Rational numbers (Q): Numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
• Irrational numbers: Numbers that cannot be expressed as a fraction. Examples include π and √2.
• Real numbers (R): The set of all rational and irrational numbers.
• Complex numbers: Numbers that include real and imaginary parts (a + bi), where 'a' and 'b' are real numbers and 'i' is the imaginary unit (√-1).

Algebra

• Variables: Symbols (like x, y, z) that represent unknown values.
• Expressions: Combinations of numbers, variables, and operations.
• Equations: Statements that show two expressions are equal.
• Inequalities: Statements that show one expression is greater than or less than another.
• Solving equations: Finding the values of variables that make an equation true.
• Polynomials: Expressions with variables and coefficients, involving sums of terms with positive integer powers of variables.

Geometry

• Points: Locations in space.
• Lines: Straight paths extending infinitely in both directions.
• Angles: Formed by two rays meeting at a common endpoint.
• Triangles: Three-sided polygons.
• Quadrilaterals: Four-sided polygons.
• Circles: Sets of points equidistant from a center point.
• Area: The measure of a two-dimensional region.
• Volume: The measure of a three-dimensional space.

Measurement

• Units of length: Millimeters, centimeters, meters, kilometers.
• Units of area: Square meters, square centimeters.
• Units of volume: Cubic meters, cubic centimeters.
• Units of mass: Grams, kilograms.
• Units of time: Seconds, minutes, hours, days.

Data Analysis and Probability

• Data: Collections of information.
• Statistics: Methods for collecting, organizing, analyzing, and interpreting data.
• Measures of central tendency: Mean, median, mode.
• Measures of dispersion: Range, standard deviation.
• Probability: The likelihood of an event occurring.

Sets

• Sets: Collections of elements.
• Intersection of sets: Elements common to both sets.
• Union of sets: All elements in either (or both) sets.
• Subsets: One set completely contained within another.

Functions

• Functions: Relationships where each input has exactly one output.
• Domain: Set of all possible input values.
• Range: Set of all possible output values.
• Linear functions: Functions that form a straight line on a graph.
• Quadratic functions: Functions involving a variable squared.

Trigonometry

• Right-angled triangles: Triangles with a 90-degree angle.
• Trigonometric ratios: Sine, cosine, tangent, relating the sides and angles of a right-angled triangle.
• Applications of trigonometry: Solving for unknown sides and angles in triangles.

Calculus (Elementary Level)

• Limits: Approaching a value as something gets closer to a specific number.
• Derivatives: Rate of change of a function.
• Integrals: Accumulation of a function.