Mathematics Concepts: PEMDAS and Prime Numbers

PEMDAS

• Acronym for the order of operations in mathematics: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
• Operations inside Parentheses are performed first.
• Exponents indicate powers, where ( a^b ) means ( a ) multiplied by itself ( b ) times.
• Multiplication and Division are performed from left to right.
• Addition and Subtraction are also performed from left to right.

Prime Numbers

• Defined as whole numbers greater than 1 that cannot be divided evenly by any number other than themselves and 1.
• The first few prime numbers include: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

Lines

• Standard Form: Expressed as ( Ax + By = C ).
• Slope-Intercept Form: Written as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
• Point-Slope Form: Formulated as ( y - y_1 = m(x - x_1) ), used when a point and a slope are known.
• Example equations illustrate how the same line can be represented in different forms.

Difference of Squares

• Formulated as ( a^2 - b^2 = (a + b)(a - b) ).
• Example conversion: ( (x^2 - 16) = 0 ) simplifies to ( (x - 4)(x + 4) = 0 ).

Quadratic Formula

• Used to solve quadratic equations of the form ( ax^2 + bx + c = 0 ).
• The formula is ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
• Example: For the equation ( x^2 + 2x - 3 = 0 ), substituting values provides the solutions ( x = 1 ) and ( x = -3 ).

Divisibility Rules

• 2: A number is divisible if its last digit is 0, 2, 4, 6, or 8.
• 3: A number is divisible if the sum of its digits is divisible by 3 (e.g., 27 → 2 + 7 = 9).
• 4: A two-digit number is divisible if the number formed by its last two digits is divisible by 4 (e.g., 2308 → 08 divided by 4 equals 2).
• 5: A number is divisible if its last digit is 0 or 5.
• 6: A number is divisible if it is divisible by both 2 and 3 (e.g., 18 is divisible by 2 and 3).
• 8: A three-digit number is divisible if the number formed by the last three digits is divisible by 8 (e.g., 2434 → 434 divided by 8 equals 54.25).
• 9: A number is divisible if the sum of its digits is divisible by 9.

This quiz covers essential mathematical concepts including the order of operations (PEMDAS) and the characteristics of prime numbers. Test your understanding of how to approach calculations and identify prime numbers. Perfect for reinforcing fundamental math skills for students.