Geometry & Algebra Review – Lecture Flashcards

A set of flashcards covering formulas and concepts in simple interest, compound interest, circle geometry, distance, exponential change, circular sectors/arcs, trigonometric ratios, and basic triangle geometry.

What is the formula for calculating simple interest?

A = P r t

In the simple-interest formula, what does the symbol P stand for?

The initial (principal) amount invested or borrowed

In the simple-interest formula, what does the symbol r represent?

The annual interest rate (expressed as a decimal)

In the simple-interest formula, what does the symbol t represent?

The time the money is invested or borrowed, usually in years

What is the general compound-interest formula?

A = P (1 + r ⁄ n)^{n t}

In the compound-interest formula, what does n denote?

The number of compounding periods per year

What is the formula for the area of a circle?

A = π r²

What is the circumference of a circle expressed with its diameter?

C = π d

What is the circumference of a circle expressed with its radius?

C = 2 π r

What is the distance formula between two points (x₁ , y₁) and (x₂ , y₂)?

d = √[(x₂ – x₁)² + (y₂ – y₁)²]

Write the exponential growth/decay model used in algebra.

y = a (1 ± r)^x

In the exponential model y = a (1 ± r)^x, what does a represent?

The initial value (starting amount)

In the exponential model y = a (1 ± r)^x, what does r represent?

The rate of growth (+) or decay (–), written as a decimal

How do you calculate the length of an arc with a given central angle?

Arc length = (Central angle / 360°) × π d

How do you calculate the area of a sector of a circle?

Area of sector = (Central angle / 360°) × π r²

How do you find a central angle in radians from an arc length?

Central angle (radians) = Arc length ÷ Radius

What mnemonic summarizes the three basic trig ratios?

SOH-CAH-TOA

According to SOH-CAH-TOA, what is sin θ in a right triangle?

sin θ = Opposite ⁄ Hypotenuse

According to SOH-CAH-TOA, what is cos θ in a right triangle?

cos θ = Adjacent ⁄ Hypotenuse

According to SOH-CAH-TOA, what is tan θ in a right triangle?

tan θ = Opposite ⁄ Adjacent

What is the standard formula for the area of a triangle?

A = ½ b h

How do you solve for the height of a triangle given its area and base?

h = (2 × A) ⁄ b

What is the formula for the area of an equilateral triangle with side length s?

A = (√3 ⁄ 4) s²

What is the standard equation of a circle with center (h, k) and radius r?

(x – h)² + (y – k)² = r²

What is the equation for