Questions and Answers
What is the Slope-Intercept Form?
What is the Slope-Point Form?
y - y1 = m(x - x1)
What is the Slope Formula?
(y₂ - y₁) / (x₂ - x₁)
What does L₁ | L₂ represent?
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What is the Speed-Time-Distance formula?
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What is the formula for Simple Interest?
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What is the formula for Compounded Interest?
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What is the Carbon-14 Decay Rate?
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What is the formula for Interest Compounded Continuously?
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What is the Half-Life Formula?
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What is the Doubling Time Formula?
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What is the Distance Formula?
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What is the Midpoint Formula?
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What is the Circle Formula?
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What is a Complex Number?
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What is the Difference Quotient?
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What is the Quadratic Formula?
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What is the Direct Variation formula?
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What is the Inverse Variation formula?
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What does (f + g)(x) represent?
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What does (f - g)(x) represent?
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What does (fg)(x) represent?
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What does (f / g)(x) represent?
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What does (f º g)(x) represent?
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What does y = -f(x) represent?
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What does y = f(-x) represent?
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What is an Even Function?
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What is an Odd Function?
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What is Log Form?
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What is Exponent Form?
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What is the Change of Base Formula?
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What is the Determinant of a 2x2 Matrix?
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Study Notes
Linear Equations
- Slope-Intercept Form: Expressed as y = mx + b, where m is the slope and b is the y-intercept.
- Slope-Point Form: Given by y - y₁ = m(x - x₁), representing a linear equation using a point (x₁, y₁) and slope m.
- Slope Formula: Calculated as (y₂ - y₁) / (x₂ - x₁), determines the steepness of a line between two points.
Line Relationships
- Perpendicular Lines: If two lines L₁ and L₂ are perpendicular, their slopes satisfy m₁ = -1 / m₂.
Motion and Financial Calculations
- Speed-Time-Distance: d = rt, where d is distance, r is rate, and t is time.
- Simple Interest: Calculated as I = Prt, where I is interest, P is principal, r is rate, and t is time.
- Compounded Interest: A = P(1 + r/n)^(nt) reflects interest added at specified intervals.
Exponential Decay
- Carbon-14 Decay Rate: Approximately -0.00012, representing the rate of decay for carbon-14 isotopes.
- Continuously Compounded Interest: Utilized with A = Pe^rt, where e is the base of natural logarithms.
- Half-Life Formula: Expressed as 1/2 = e^rt, denotes the time required for half of a substance to decay.
- Doubling Time Formula: Stated as 2 = e^rt, indicates the time required for a quantity to double.
Geometry and Distance
- Distance Formula: Determined with d = √[(x₂ - x₁)² + (y₂ - y₁)²], representing the distance between two points in a plane.
- Midpoint Formula: Given by (x₁ + x₂/2, y₁ + y₂/2), calculates the midpoint between two points.
- Circle Formula: Represented as (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Algebraic Concepts
- Complex Numbers: Formed as a + bi, combining real and imaginary parts.
- Difference Quotient: Calculated as (f(x + h) - f(x)) / h, essential in finding derivatives.
Quadratic Equations
- Quadratic Formula: Solving for x in ax² + bx + c = 0 provides x = [-b ± √(b² - 4ac)] / (2a).
Variation Relations
- Direct Variation: Expressed as y = kx, indicating a proportional relationship where k is constant.
- Inverse Variation: Written as y = k / x, showing a relationship where y decreases as x increases.
Function Operations
- Function Addition: (f + g)(x) = f(x) + g(x), combining two functions.
- Function Subtraction: (f - g)(x) = f(x) - g(x), determining the difference between two functions.
- Function Multiplication: (fg)(x) = f(x) * g(x), represents the product of two functions.
- Function Division: (f / g)(x) = f(x) / g(x), portraying the division of two functions.
- Function Composition: (f º g)(x) = f(g(x)), combining two functions by substituting.
Function Transformations
- Reflection Across X-axis: y = -f(x) indicates a vertical reflection of the function.
- Reflection Across Y-axis: y = f(-x) indicates a horizontal reflection of the function.
Function Symmetry
- Even Function: Characterized by f(-x) = f(x), symmetrical around the y-axis.
- Odd Function: Identified by f(-x) = -f(x), symmetrical around the origin.
Logarithmic Functions
- Logarithmic Form: log₁₀ x = y denotes the logarithm of x to the base 10.
- Exponent Form: 10^y = x transforms the logarithmic equation to exponential.
- Change of Base Formula: log₅ M = log₁₀ M / log₁₀ 5 allows conversion between logarithmic bases.
Matrix Calculations
- Determinant of 2x2 Matrix: Calculated using | a d | | b c | = ad - bc, providing a scalar value representing matrix properties.
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Test your knowledge of essential precalculus formulas with these flashcards. Covering concepts such as slope-intercept form, slope-point form, and various interest calculations, these cards are a great way to reinforce your understanding. Perfect for students looking to master precalculus concepts quickly and effectively.