Algebra I Practice Exam Review

A collection of vocabulary flashcards covering key concepts from an Algebra I practice exam including function analysis, statistics, financial modeling, and polynomial operations.

Average Rate of Change

A measure of how much a function changes over a specific interval, such as $-1 \le x \le 6$ for functions like $f(x) = (0.5)^{2x}$ or $g(x) = 0.5x^2$.

Negative Correlation

A relationship indicated by a negative slope in a line of best fit, such as $y = -5.9x + 91.9$, where test scores decrease as time spent watching TV increases.

y-intercept (Linear Model)

The value of the dependent variable when the independent variable is zero; for example, a y-intercept of $91.9$ predicts a test score of approximately $92$ if no time is spent watching TV.

Growth Comparison (Linear vs. Exponential)

Exponential functions like $h(x) = 2^x - 2$ will eventually exceed both linear functions like $f(x) = 8x + 2$ and quadratic functions like $g(x) = 2x^2$.

Standard Deviation

A measure used to determine how spread out data points are; for example, Nick's scores with a standard deviation of $17.1$ are more spread out than Juan's scores with a standard deviation of $4.6$.

Piecewise Function

A function defined by multiple sub-functions, each applying to a certain interval of the domain, such as $m(x)$ being $2x$ for $0 \le x \le 6$ and $x - 4$ for 6 < x \le 10.

Completing the Square

A method to solve quadratic equations like $x^2 - 10x - 8 = 0$ that involves transforming the equation into a perfect square binomial form such as $(x-5)^2 = 33$.

Exponential Growth Model

A model used when an amount increases by a fixed percentage over time, such as a bank account increasing by $5\%$ each year.

Linear Growth Model

A model used when an amount increases by a constant value over time, such as a bank account increasing by $\$5$ each year.

Profit

The difference between total income and total expenses; for Rashawn's business, it is calculated by subtracting the cost of tee-shirts ($\$11$ each plus $\$100$ initial cost) from the sales price ($\$26$ each).

Volume of a Cone

The formula used to calculate volume, expressed as $V = \frac{1}{3}\pi r^2h$, where height $h$ can be isolated as $h = \frac{3V}{\pi r^2}$.

Exponential Decay (Tournament Round)

A model where values decrease by a constant factor, such as $t = 64(0.5)^r$, representing the number of teams remaining after each round $r$.

Zeros of a Function

The values of $x$ for which $f(x) = 0$; for the factored form $f(x) = (x+1)(x-6)$, the zeros are $-1$ and $6$.

Polynomial Closure

The property where operations like addition, subtraction, and multiplication of two polynomials always result in another polynomial, while division does not.

Standard Form of a Quadratic Polynomial

The arrangement of terms in descending order by degree, written as $ax^2 + bx + c$; for example, $5x + 2 - 4x^2$ in standard form is $-4x^2 + 5x + 2$.

Leading Coefficient

The numerical factor of the term with the highest degree in a polynomial; in the expression $-4x^2 + 5x + 2$, the leading coefficient is $-4$.

Function Definition (Mapping)

A relationship where each input $x$ from the domain is assigned to exactly one output $y$; a diagram fails this if one input maps to multiple different outputs.