Questions and Answers
What is the Quadratic Formula?
x= [-b±√(b²-4ac)] / 2a
What is the formula for the Difference of Two Squares?
a²-b²= (a+b)(a-b)
What defines a Perfect Square Trinomial?
a²+2ab+b² : (a +b)² or (a-b)²
What is the formula for Permutations in Probability?
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What is the formula for Combinations in Probability?
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What is the formula for Standard Deviation?
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What is the Pythagorean Theorem?
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What is the Law of Sines?
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What is the Law of Cosines?
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What is the formula for Arc Length?
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What is the formula for Slope?
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What is the Slope-Intercept Form of a Line?
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What is the Point-Slope Form of a Line?
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What is the equation for a circle on a coordinated plane?
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Study Notes
Quadratic Equation
- The Quadratic Formula is used to find the roots of quadratic equations.
- The formula is expressed as x = [-b ± √(b² - 4ac)] / 2a, where a, b, and c are coefficients from the equation ax² + bx + c = 0.
Algebraic Identities
- Difference of Two Squares states that a² - b² can be factored into (a + b)(a - b).
- This identity is useful for simplifying expressions and solving equations.
- A Perfect Square Trinomial follows the form a² + 2ab + b², which factors to (a + b)² or (a - b)².
Combinatorics
- Permutations (P(n,r)) calculate the number of ways to arrange r items from n distinct items, using the formula P(n, r) = n! / (n - r)!, where order matters.
- Combinations (C(n,r)) calculate the number of ways to select r items from n distinct items, given by C(n, r) = n! / [(n - r)!r!], where order does not matter.
Statistics
- Standard Deviation is a measure of how much individual data points differ from the mean.
- The formula is δ = √[(X₁ - x)² + (X₂ - x)² + ... + (X₇ - x)²] / n, where x is the mean and n is the number of data points.
Geometry
- Pythagorean Theorem relates the sides of a right triangle, expressed as a² + b² = c², where c is the hypotenuse.
- The Law of Sines states that the ratios of the sides of a triangle to the sine of their opposite angles are equal: sinA/a = sinB/b = sinC/c.
- The Law of Cosines generalizes the Pythagorean theorem for any triangle: a² = b² + c² - 2bcCosA.
Circular Geometry
- Arc Length is a portion of the circumference of a circle, calculated with the formula l = (n/360) x 2Πr, where n is the central angle in degrees and r is the radius.
Linear Functions
- Slope (m) measures the steepness of a line and is calculated as m = (y₂ - y₁) / (x₂ - x₁).
- Slope-Intercept Form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.
- Point-Slope Form of a line is expressed as y - y₁ = m(x - x₁), useful for writing the equation of a line given a point and slope.
Circle Equation
- The equation for a circle on a coordinate plane is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
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Test your knowledge of essential Algebra 1 formulas with these flashcards. Each card features a key term along with its definition, helping you master concepts like the Quadratic Formula and different types of polynomials. Perfect for review and study!