Algebra I: Core Concepts & Formulas
A comprehensive review of high school Algebra I, covering 41 essential definitions and formulas. Topics include variables and expressions, linear equations and their graphs, the quadratic formula and discriminant, exponent rules, factoring techniques, polynomials, functions, systems of equations, and inequalities. Ideal for exam revision or building a solid algebra foundation before tackling more advanced math.
This is a free, public flashcard deck on Memor More containing 43 cards about Science & Engineering, covering mathematics, math, algebra for learning English from English. Estimated study time: 20 min. Designed for spaced repetition — review with the Memor More iOS app for optimized recall.
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Cards in this deck
- Q:What is a variable?
- A:A symbol (usually a letter) that represents an unknown or changeable value.
- Q:What is a constant?
- A:A fixed value that does not change.
- Q:What is a coefficient?
- A:The numerical factor that multiplies a variable in a term.
- Q:What is a term in algebra?
- A:A single number, variable, or the product of numbers and variables.
- Q:What is an algebraic expression?
- A:A combination of variables, numbers, and operations without an equals sign.
- Q:What is an equation?
- A:A mathematical statement that two expressions are equal, shown with an "=" sign.
- Q:What order of operations does PEMDAS describe?
- A:Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (left to right).
- Q:What is the Distributive Property?
- A:a(b + c) = ab + ac
- Q:What are "like terms"?
- A:Terms that have the same variable(s) raised to the same power.
- Q:What is a linear equation?
- A:An equation whose graph is a straight line, e.g. y = mx + b.
- Q:What is the slope-intercept form of a line?
- A:y = mx + b, where m is the slope and b is the y-intercept.
- Q:What is the formula for the slope between two points?
- A:m = (y2 - y1) / (x2 - x1)
- Q:What is the point-slope form of a line?
- A:y - y1 = m(x - x1)
- Q:What is the standard form of a linear equation?
- A:Ax + By = C
- Q:What is the Distance Formula?
- A:d = √[(x2 - x1)² + (y2 - y1)²]
- Q:What is the Midpoint Formula?
- A:M = ((x1 + x2)/2, (y1 + y2)/2)
- Q:What is a quadratic equation?
- A:An equation of the form ax² + bx + c = 0, where a ≠ 0.
- Q:What is the Quadratic Formula?
- A:x = (-b ± √(b² - 4ac)) / 2a
- Q:What is the discriminant of a quadratic equation?
- A:b² - 4ac; it tells you how many real solutions the equation has.
- Q:What does a positive discriminant tell you?
- A:The equation has two distinct real solutions.
- Q:What does a discriminant of zero tell you?
- A:The equation has exactly one repeated real solution.
- Q:What does a negative discriminant tell you?
- A:The equation has no real solutions (two complex solutions).
- Q:What is the Product Rule of exponents?
- A:aᵐ × aⁿ = aᵐ⁺ⁿ
- Q:What is the Quotient Rule of exponents?
- A:aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- Q:What is the Power Rule of exponents?
- A:(aᵐ)ⁿ = aᵐⁿ
- Q:What is any nonzero number raised to the power of 0?
- A:1 (a⁰ = 1)
- Q:What does a negative exponent mean?
- A:a⁻ⁿ = 1/aⁿ
- Q:What does the FOIL method help you do?
- A:Multiply two binomials: First, Outer, Inner, Last.
- Q:What is the Difference of Squares formula?
- A:a² - b² = (a + b)(a - b)
- Q:What is a Perfect Square Trinomial?
- A:a² + 2ab + b² = (a + b)²
- Q:What is factoring?
- A:Rewriting an expression as a product of its factors.
- Q:What is a monomial?
- A:A polynomial with exactly one term.
- Q:What is a binomial?
- A:A polynomial with exactly two terms.
- Q:What is a trinomial?
- A:A polynomial with exactly three terms.
- Q:What is the degree of a polynomial?
- A:The highest exponent of the variable in the polynomial.
- Q:What is a function?
- A:A relation in which each input has exactly one output.
- Q:What is the domain of a function?
- A:The set of all possible input (x) values.
- Q:What is the range of a function?
- A:The set of all possible output (y) values.
- Q:How do you solve a system of equations by substitution?
- A:Solve one equation for a variable, then substitute that expression into the other equation.
- Q:How do you solve a system of equations by elimination?
- A:Add or subtract the equations so that one variable cancels out.
- Q:What is an inequality?
- A:A mathematical statement comparing two expressions using <, >, ≤, ≥, or ≠.
- Q:What happens to an inequality when you multiply or divide both sides by a negative number?
- A:The inequality sign flips direction.
- Q:What is the absolute value of a number?
- A:Its distance from zero on the number line, which is always non-negative.
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