Podcast
Questions and Answers
Quo es le forma general pro un sequenza arithmetica?
Quo es le forma general pro un sequenza arithmetica?
- an = a1 * rn-1
- an = √(a + b)
- an = (n/2) * (a1 + an)
- an = a1 + (n-1)d (correct)
Quo es le valore numerique de P(2) pro le polynomial x³ + 4x² + x - 2?
Quo es le valore numerique de P(2) pro le polynomial x³ + 4x² + x - 2?
- 15
- 10
- 30
- 23 (correct)
Quo es le producte de (x² + 2x + 1) e (x)?
Quo es le producte de (x² + 2x + 1) e (x)?
- x³ + 2x + 1
- x² + 2x + 1
- x³ + 3x² + 1
- x³ + 2x² + x (correct)
Quo es le ratio comun pro un sequenza geometric?
Quo es le ratio comun pro un sequenza geometric?
Quo es le expression correcte pro le sum de 15x²y - 20x²z?
Quo es le expression correcte pro le sum de 15x²y - 20x²z?
Quo es le summe de le terminos √5 + √23 + √45?
Quo es le summe de le terminos √5 + √23 + √45?
Quo es le differantia pro le terminos a2 - a1 in le sequenza?
Quo es le differantia pro le terminos a2 - a1 in le sequenza?
Flashcards
General Term of an Arithmetic Sequence
General Term of an Arithmetic Sequence
Formula for the nth term in an arithmetic sequence. an = a1 + (n-1)d
Common Ratio of a Geometric Sequence
Common Ratio of a Geometric Sequence
The ratio between consecutive terms in a geometric sequence.
Extract Factors (Radicals)
Extract Factors (Radicals)
Express a radical as a product of a rational number and a radical with a simplified radicand (the number inside the radical).
Rationalizing Factors (Radicals)
Rationalizing Factors (Radicals)
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Sum of Arithmetic Sequence (Formula)
Sum of Arithmetic Sequence (Formula)
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Binomial Expansion - Sum
Binomial Expansion - Sum
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Polynomial Subtraction
Polynomial Subtraction
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Study Notes
Real Numbers
- Extract factors: √12 = 2√3
- Extract factors: √206 = 2√51.5
- Insert factors: 5√2 = √50
- Combine radicals: 5√5 + √25 + √45 = 5√5 + 5 + 3√5 = 8√5 + 5 (approximately)
- Simplify radicals: equivalent radical expressions
- Root of a root: (9²)³ = 9⁶
Sequences
- Arithmetic sequence: general term = aₙ = a₁ + (n - 1)d, where aₙ =nth term, a₁ = first term, n = term number, and d = common difference
- Arithmetic sequence: find a specific term like aₙ = aₖ + (n - k)d
- Arithmetic sequence: interpolation: d = (m₁ - m₀) / (n₁ - n₀)
- Arithmetic sequence: sum of terms: Sₙ = ½(a₁ + aₙ)
- Geometric sequence: common ratio = r = aₙ / aₙ₋₁
- Geometric sequence: general term = aₙ = a₁ * rⁿ⁻¹
- Find difference: difference = a₂ - a₁
Polynomials
- Numeric value: P(2). Example: x³ + 4x² + x - 2 = 2³ + 4(2²) + 2 -2 =8 + 16 + 2 - 2 = 24
- Addition: x³ + 3x³ + 2x - 1 + 10x⁵ - 3x² + 6x + 8 = 10x⁵ + x³ +(-3x²) + (2x+6x) - 1+8 = 10x⁵ + x³ - 3x² + 8x + 7
- Subtraction: x⁵ + 3x⁴ + 9x³ + 4x² - (x⁵ + 5x⁴ + 9x³ + 3x²) = Simplify
- Multiplication: (x² + 2x +1)(x) = x³ +2x² + x
- Division: divide polynomials
- Common factors: 15x²y - 20x²z = 5x²(3y - 4z)
- Powers of polynomials: ...
- Binomial sum: (a² + 2ab + b²)
- Binomial difference: (a² - 2ab + b²)
- Sum by difference: a² - b²
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Description
Este quiz explora conceptos fundamentais de algebra, incluyendo numeros reales, sequencias aritmeticas e geometrica, e polinomios. Practica extraction e simplification de radicales e calcula valor numeric de polinomios. Perfecte pro estudantes del 10° annus.
