Basic Math Concepts Quiz

Numbers
- Natural Numbers: 1, 2, 3, ...
- Whole Numbers: 0, 1, 2, 3, ...
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational Numbers: Numbers that can be expressed as a fraction (e.g., 1/2, 3/4).
- Irrational Numbers: Cannot be expressed as a fraction (e.g., √2, π).
Arithmetic Operations
- Addition (+)
- Subtraction (−)
- Multiplication (×)
- Division (÷)

Variables & Expressions
- Variables: Symbols representing numbers (e.g., x, y)
- Expressions: Combinations of numbers and variables (e.g., 2x + 3)
Equations
- Solving equations involves finding the value of the variable that makes the equation true.
- Example: 2x + 3 = 11; solve for x.

Shapes
- 2D: Circle, Triangle, Square, Rectangle, etc.
- 3D: Sphere, Cube, Cylinder, Cone, etc.
Properties
- Area: Measure of space inside a shape (e.g., Area of a rectangle = length × width).
- Perimeter: Total distance around a shape (e.g., Perimeter of rectangle = 2(length + width)).
- Volume: Measure of space inside a 3D object (e.g., Volume of a cube = side³).

Basics
- Studies relationships between angles and sides of triangles.
- Key functions: Sine (sin), Cosine (cos), Tangent (tan).
Right Triangle Relationships
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent

Differentiation
- Process of finding the derivative (rate of change) of a function.
- Notation: f'(x) or dy/dx.
Integration
- Process of finding the integral (area under the curve) of a function.
- Notation: ∫f(x)dx.

Data Types
- Qualitative: Categorical data (e.g., colors, names).
- Quantitative: Numerical data (e.g., age, height).
Descriptive Statistics
- Mean: Average value.
- Median: Middle value when data is ordered.
- Mode: Most frequently occurring value.
Probability
- Likelihood of an event occurring.
- Ranges from 0 (impossible) to 1 (certain).

Logic
- Understanding valid arguments and reasoning patterns.
- Example: If P, then Q (Conditional statements).
Proof Techniques
- Direct Proof: Establishes truth directly.
- Indirect Proof: Assumes the negation to show contradiction.
- Mathematical Induction: Proving a base case and an inductive step.

Pythagorean Theorem: a² + b² = c² (for right-angled triangles).
Quadratic Formula: x = (-b ± √(b²-4ac)) / 2a (for solving ax² + bx + c = 0).
Circle Area: A = πr² (where r is the radius).
Circle Circumference: C = 2πr.

Natural numbers are positive whole numbers starting from 1 (1, 2, 3...).
Whole numbers include zero and all natural numbers (0, 1, 2, 3...).
Integers encompass all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3...)
Rational numbers can be expressed as a fraction, where the numerator and denominator are integers (e.g., 1/2, 3/4).
Irrational numbers cannot be expressed as a fraction and have infinite non-repeating decimal representations (e.g., √2, π).
Arithmetic operations are fundamental mathematical operations: addition (+), subtraction (−), multiplication (×), and division (÷).

Variables are symbols like x or y that represent unknown numerical values.
Expressions are combinations of variables, numbers, and mathematical operations (e.g., 2x + 3).
Equations express equality between two expressions, and solving them involves finding the values of variables that satisfy the equation.

Two-dimensional shapes (2D) include circles, triangles, squares, and rectangles, and exist within a plane.
Three-dimensional shapes (3D) have volume and include spheres, cubes, cylinders, and cones.
Area measures the space enclosed within a 2D shape.
Perimeter represents the total distance around the outside of a 2D shape.
Volume quantifies the space occupied by a 3D object.

Trigonometry explores the relationships between angles and sides of triangles.
Key trigonometric functions include sine (sin), cosine (cos), and tangent (tan).
Right triangles have one angle measuring 90 degrees.
Sine, cosine, and tangent are defined in terms of the sides of a right triangle in relation to a specific angle.

Differentiation determines the derivative of a function, which represents its rate of change.
Integration finds the integral of a function, which represents the area under its curve.

Data types are broadly categorized as qualitative (categorical) and quantitative (numerical).
Descriptive statistics summarize data using measures like mean, median, and mode.
Probability measures the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).

Logic involves understanding valid arguments and reasoning patterns, such as conditional statements ("If P, then Q").
Proof techniques are methods for demonstrating the truth of mathematical statements.
Direct proof directly shows the truth of a statement.
Indirect proof assumes the negation of a statement, aiming to reach a contradiction.
Mathematical induction proves a statement for all natural numbers through a base case and an inductive step.

Pythagorean Theorem: a² + b² = c² applies to right-angled triangles, where a and b are the lengths of the legs and c is the length of the hypotenuse.
Quadratic Formula: x = (-b ± √(b²-4ac)) / 2a is used to solve quadratic equations of the form ax² + bx + c = 0.
Circle Area Formula: A = πr² calculates the area of a circle with radius r.
Circle Circumference Formula: C = 2πr calculates the circumference (perimeter) of a circle with radius r.