Basic Mathematics Concepts

Basic Mathematics Concepts

• Place Value: A digit's value is determined by its position in a number. Example: In 456, the 5 is in the tens place, representing 50.
• Comparing Numbers: Use symbols like = (equal to), < (less than), > (greater than), ≥ (greater than or equal to), ≤ (less than or equal to) to compare numbers.
• Rounding Numbers: Adjust a number to the nearest specified place value. Example: 64 rounded to the nearest ten is 60.
• Whole Numbers: Non-negative integers: {0, 1, 2, 3,...}
• Integers: Whole numbers and their negative counterparts including zero: {..., -3, -2, -1, 0, 1, 2, 3,...}
• Real Numbers: All numbers on the number line, including integers, fractions, decimals, irrational numbers (like √2 and π).
• Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
• Absolute Value: The distance of a number from zero on the number line (always non-negative). Example: |−22| = 22

Fractions, Decimals, and Percentages

• Fractions: Express a part of a whole. Examples: 1/2, 3/4
• Decimals: Fractions expressed using a base-10 system. Example: 1/2 = 0.5
• Percentages: Fractions of 100; indicated by the symbol %. Example: 50% = 50/100

Algebraic Expressions and Equations

• Variables: Symbols (often letters) representing unknown numbers. Example: In 2 + a, 'a' is a variable.
• Expressions: Combinations of numbers, variables, and operations. Example: addition (2 + a), subtraction (y - 3), multiplication (5a) division (4/x)
• Equations: Mathematical statements showing equality between two expressions. Example: ax + b = c
• Inequalities: Statements comparing the size of two values. Examples: a ≠ b, a < b, a > b, a ≥ b, a ≤ b.

Geometry: Lines, Angles, and Shapes

• Parallel Lines: Lines that never meet and stay the same distance apart.
• Perpendicular Lines: Lines that intersect to form right angles.
• Triangles: Shapes with three sides.
  • Right Triangle: Contains one 90-degree angle. Example: a 3-4-5 right triangle.
    • Area: Area = 1/2 * base * height
    • Sum of interior angles: 180 degrees
• Circles: Closed shapes.
  • Area: Area = πr²
  • Circumference: Circumference = 2πr
• Degrees in a circle: 360 degrees

Statistics and Probability

• Mean: The average of a set of numbers.
• Median: The middle value when a data set is ordered.
• Mode: The most frequent value in a data set.
• Range: The difference between the highest and lowest values in a dataset.

Advanced Concepts

• Exponents: Show how many times a number is multiplied by itself. Example: 2³ = 2 * 2 * 2 = 8
• Scientific Notation: A way of representing very large or very small numbers. Example: 5 × 10³
• Factorials: The product of a number and all the whole numbers below it. Example: 5! = 5 * 4 * 3 * 2 * 1 = 120