Precalculus Formulas Flashcards

Questions and Answers

What is the Slope-Intercept Form?

I = Prt

y-y1=m(x-x1)

d = rt

y = mx + b (correct)

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?

m₁ = -1 / m₂ Signup and view all the answers

What is the Speed-Time-Distance formula?

d = rt Signup and view all the answers

What is the formula for Simple Interest?

I = Prt Signup and view all the answers

What is the formula for Compounded Interest?

A = P(1 + r/n)^(nt) Signup and view all the answers

What is the Carbon-14 Decay Rate?

-0.00012 Signup and view all the answers

What is the formula for Interest Compounded Continuously?

A = Pe^(rt) Signup and view all the answers

What is the Half-Life Formula?

1/2 = e^(rt) Signup and view all the answers

What is the Doubling Time Formula?

2 = e^(rt) Signup and view all the answers

What is the Distance Formula?

d = √[(x₂ - x₁)² + (y₂ - y₁)²] Signup and view all the answers

What is the Midpoint Formula?

(x₁ + x₂)/2, (y₁ + y₂)/2 Signup and view all the answers

What is the Circle Formula?

(x - h)² + (y - k)² = r² Signup and view all the answers

What is a Complex Number?

a + bi Signup and view all the answers

What is the Difference Quotient?

(f(x + h) - f(x)) / h Signup and view all the answers

What is the Quadratic Formula?

[-b ± √(b² - 4ac)] / (2a) Signup and view all the answers

What is the Direct Variation formula?

y = kx Signup and view all the answers

What is the Inverse Variation formula?

y = k / x Signup and view all the answers

What does (f + g)(x) represent?

f(x) + g(x) Signup and view all the answers

What does (f - g)(x) represent?

f(x) - g(x) Signup and view all the answers

What does (fg)(x) represent?

f(x) * g(x) Signup and view all the answers

What does (f / g)(x) represent?

f(x) / g(x) Signup and view all the answers

What does (f º g)(x) represent?

f(g(x)) Signup and view all the answers

What does y = -f(x) represent?

Reflected across x-axis Signup and view all the answers

What does y = f(-x) represent?

Reflected across y-axis Signup and view all the answers

What is an Even Function?

f(-x) = f(x) Signup and view all the answers

What is an Odd Function?

f(-x) = -f(x) Signup and view all the answers

What is Log Form?

log₁₀ x = y Signup and view all the answers

What is Exponent Form?

10^y = x Signup and view all the answers

What is the Change of Base Formula?

log₅ M = log₁₀ M / log₁₀ 5 Signup and view all the answers

What is the Determinant of a 2x2 Matrix?

| a d | = ad - bc Signup and view all the answers

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.