Rotational Geometry, Proportionality, and Algebra Review

Vocabulary flashcards covering key geometry, algebraic identities, linear functions, and data analysis concepts from the lecture transcript.

Rotational Angle of 5 Complete Rolls

The total angle rotated by a wheel's pin after 5 complete revolutions, calculated as $5 \times 360^\circ = 1800^\circ$.

Algebraic Identity $(n)(n) - [(n + 1)(n - 1)]$

An identity that simplifies to $1$ for all integer values of $n$, calculated as $n^2 - (n^2 - 1) = 1$.

Distance Travelled by a Rolled Wheel

The total distance calculated as $\text{Distance} = 5 \times \text{Circumference} = 5 \times (\pi \times 60) = 300\pi\,\text{cm} = 942.48\,\text{cm}$ (or $9.42\,\text{meters}$).

Volume of a Divided Pool

The volume expression $25(2.1)/2\,\text{cubic meters}$ derived from dividing a pool into two equal parts with depths $1.5\,\text{meters}$ and $0.6\,\text{meters}$ and base area $25\pi$.

Sidewalk Area Surrounding a Pool

The area calculated by subtracting the inner pool area from the outer area: $\pi(6)^2 - \pi(5)^2 = 11\pi \approx 34.54\,\text{m}^2$.

Power of 2

A number such as $1024$ (expressed as $2^{10}$) that reduces completely to 1 after 10 continuous divisions by 2.

Negative Linear Trend

A scatter plot relationship where an increase in one variable (such as number of absences) corresponds to a decrease in another variable (such as overall academic grade).

Exterior Angle Theorem

A geometric theorem stating that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Linear Pair of Angles

An exterior angle and its adjacent interior angle in a triangle that lie on the same line and sum to $180^\circ$.

Triangle Angle Sum Theorem

The fundamental geometric property stating that the sum of all interior angles inside any triangle equals $180^\circ$ ($p + q + r = 180^\circ$).

Slope in a Rental Cost Function

The variable rate of change represented by the number $200$ in the linear formula $c = 250 + 200d$, indicating the daily rental rate.

Fixed Cost in a Rental Function

The constant term represented by the number $250$ in the formula $c = 250 + 200d$, indicating the initial fixed cost before daily charges.

Line Equation $y = 2x - 4$

The linear equation passing through points $B$ and $C$ in Figure 4, containing ordered pairs $(3, 2)$ and $(5, 6)$.

Line Equation $y = -x + 2$

The linear equation representing all points passing through points $A$ and $B$ in Figure 4, expressed as ordered pairs $(x, -x + 2)$.

Addition Property of Equality

The algebraic property used to transform $5y - 8 = 14 - 3y$ into $5y + 3y - 8 = 14$ by adding $3y$ to both sides of the equation.

Proportional Cost Expression

An expression such as $\text{cost} = \frac{100n}{3}$ used to find the total price for $n$ items priced at 3 for $\text{Php}100$.

Algebraic Expression $2r - 1$

An algebraic expression that represents any odd integer when $r$ is an integer (e.g., $-5$, $-27$, $99$).

Basic Proportionality in Similar Triangles

The geometric condition where two triangles have proportional corresponding sides because an inner base line is parallel to an outer base line.