Algebra Flashcards
- What is a variable?
- A variable is a symbol (x, y, n) representing an unknown or changing value in an algebraic expression or equation.
- What is a linear equation?
- A linear equation has the form ax + b = c. The highest power of the variable is 1. Its graph is a straight line.
- What is the quadratic formula?
- x = (−b ± √(b²−4ac)) / 2a — solves ax² + bx + c = 0. The discriminant (b²−4ac) determines the number of real roots.
- What is factorisation?
- Factorisation rewrites an expression as a product of factors. Example: x²−9 = (x+3)(x−3). Simplifies solving equations.
- What are simultaneous equations?
- Two or more equations with the same unknowns solved together. Methods: substitution and elimination.
- What is an inequality?
- An inequality compares two expressions using <, >, ≤, ≥. When multiplying/dividing by a negative, the sign flips.
- What is BODMAS?
- BODMAS is the order of operations: Brackets → Orders (powers) → Division → Multiplication → Addition → Subtraction.
- What is an arithmetic progression?
- An AP is a sequence where each term increases by a constant (common difference d). Formula: aₙ = a + (n−1)d.
- What is a geometric progression?
- A GP is a sequence where each term is multiplied by a constant ratio r. Formula: aₙ = a·rⁿ⁻¹.
- What are indices (exponents)?
- Indices represent repeated multiplication. Key rules: aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1.
- What is the decimal (base-10) system?
- The decimal system uses 10 digits (0–9). Each digit position represents a power of 10. It is the standard system for everyday use.
- Convert 0.5₁₀ to Binary
- Multiply by 2 repeatedly: 0.5×2=1.0 → stop. Answer: 0.1₂
- What is a prime number?
- A prime number is a natural number greater than 1 with exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
- What are divisibility rules?
- Div by 2: even last digit. Div by 3: digit sum divisible by 3. Div by 5: ends in 0 or 5. Div by 9: digit sum divisible by 9.
- What is HCF (GCD)?
- HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. Found by prime factorisation or Euclidean algorithm.
- What is LCM?
- LCM (Least Common Multiple) is the smallest number divisible by two or more given numbers. LCM × HCF = product of two numbers.