Mathematics Fundamentals
Public flashcard deck about Mathematics Fundamentals. 8 cards.
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What is the difference between a rational and an irrational number?
A rational number can be expressed as a fraction p/q, where p and q are integers and q is not zero. Its decimal representation either terminates or repeats. An irrational number cannot be expressed as a simple fraction, and its decimal representation neither terminates nor repeats.
Explain the order of operations (PEMDAS/BODMAS) and why it's important.
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS is similar (Brackets, Orders, Division and Multiplication, Addition and Subtraction). It's crucial for ensuring that mathematical expressions have a single, consistent interpretation.
What is the distributive property of multiplication over addition?
The distributive property states that for any numbers a, b, and c, a * (b + c) = (a * b) + (a * c). It means you can distribute the multiplication to each term inside the parentheses.
Define 'variable' and 'constant' in algebra.
A variable is a symbol (usually a letter) that represents an unknown or changing value. A constant is a value that does not change; it's fixed.
What is the Pythagorean theorem, and what type of triangle does it apply to?
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). Mathematically, it's a² + b² = c², where c is the hypotenuse.
What is the concept of 'absolute value'?
The absolute value of a number is its distance from zero on the number line, regardless of direction. It's always non-negative. Mathematically, |x| = x if x ≥ 0, and |x| = -x if x < 0.