ISEE Upper Level Quantitative Reasoning Flashcards: Variables In Context

What this deck covers

This deck focuses on Variables In Context, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Quantitative Reasoning.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What does the variable $n$ represent if $T = 2.99n + 5.50$ is a bill with $n$ items plus a $5.50$ delivery fee?

Answer: $n$ is the number of items ordered. The bill adds delivery to 2.99 times $n$, indicating $n$ as the quantity of items.

Flashcard 2: Identify the meaning of $x$ if $P = 2x + 2(x + 7)$ is the perimeter of a rectangle.

Answer: $x$ is the length of the shorter side of the rectangle. The perimeter sums twice $x$ and twice $x+7$, indicating $x$ as the smaller side length.

Flashcard 3: What does the expression $x + 4$ represent if a rectangle has side lengths $x$ and $x + 4$?

Answer: $x + 4$ is the length of the longer side (4 units more than $x$). The expression adds 4 to the shorter side $x$ to define the adjacent longer side in the rectangle.

Flashcard 4: What does the variable $x$ represent if $C = 2.50x$ is the total cost in dollars for $x$ movie tickets?

Answer: $x$ is the number of movie tickets purchased. The equation multiplies $x$ by the price per ticket to compute total cost, indicating it as the quantity purchased.

Flashcard 5: What does the variable $n$ represent if $S = 3n + 20$ is total savings $S$ after $n$ weeks saving $3$ dollars per week?

Answer: $n$ is the number of weeks of saving. The savings model adds weekly amounts over $n$ periods to an initial sum, signifying $n$ as the time frame.

Flashcard 6: What does the variable $p$ represent if $I = prt$ is simple interest earned $I$ in dollars?

Answer: $p$ is the principal (initial amount of money). The interest formula multiplies $p$ by rate and time, denoting it as the initial investment amount.

Flashcard 7: What does the variable $t$ represent if $I = prt$ gives simple interest $I$ at rate $r$?

Answer: $t$ is the time the money is invested or borrowed (in years). The formula uses $t$ to scale interest accumulation, measured in years for the investment period.

Flashcard 8: What does the variable $x$ represent if $A = x(x + 4)$ is the area of a rectangle with sides $x$ and $x + 4$?

Answer: $x$ is the length of the shorter side of the rectangle. The area formula uses $x$ as one side and multiplies by $x+4$, defining it as the smaller dimension.

Flashcard 9: What does the variable $t$ represent if $d = 60t$ gives distance $d$ in miles traveled at $60$ mph?

Answer: $t$ is the time traveled in hours. The equation multiplies $t$ by speed to find distance, signifying it as the duration of travel.

Flashcard 10: What does the variable $w$ represent if $C = 15w$ is pay $C$ in dollars for working $w$ hours at $15$ per hour?

Answer: $w$ is the number of hours worked. The pay equation multiplies $w$ by hourly rate, denoting it as the duration of labor.

Flashcard 11: Identify the meaning of $12$ in $y = 5x + 12$ if $y$ is total cost and $x$ is number of items.

Answer: $12$ is the fixed fee (cost when $x = 0$). As the $y$-intercept, 12 represents the constant cost incurred even when no items are purchased.

Flashcard 12: What does the variable $b$ represent if $y = mx + b$ models total cost $y$ with units $x$ purchased?

Answer: $b$ is the fixed starting amount (the value when $x = 0$). The $y$-intercept $b$ in the equation indicates the initial value of $y$ when no units are purchased.

Flashcard 13: What does the variable $g$ represent if $m = 0.001g$ converts mass $m$ in kilograms from grams $g$?

Answer: $g$ is the mass in grams. The conversion multiplies $g$ by 0.001 to obtain kilograms, indicating it as the gram measurement.

Flashcard 14: What does the variable $h$ represent if $V = lwh$ is the volume of a rectangular prism?

Answer: $h$ is the height of the rectangular prism. In the volume formula, $h$ is one dimension multiplied with length and width to determine total space.

Flashcard 15: What does the variable $x$ represent if $y = 0.08x$ is the sales tax $y$ on a purchase amount $x$?

Answer: $x$ is the pre-tax purchase price in dollars. The tax equation multiplies $x$ by 0.08, signifying it as the base amount before tax.

Flashcard 16: What does the variable $c$ represent if F = rac{9}{5}c + 32 converts Celsius $c$ to Fahrenheit $F$?

Answer: $c$ is the temperature in degrees Celsius. The formula scales $c$ by $\frac{9}{5}$ and adds 32 to convert to Fahrenheit, marking it as Celsius input.

Flashcard 17: What does the variable $r$ represent if $I = prt$ gives simple interest $I$ over time $t$?

Answer: $r$ is the annual interest rate (as a decimal). In the interest equation, $r$ scales the principal over time to calculate earnings, expressed as a decimal.

Flashcard 18: What does the variable $m$ represent if $y = mx + b$ models cost $y$ with a fixed fee $b$ and per-unit rate $m$?

Answer: $m$ is the per-unit rate (change in $y$ per $1$ unit of $x$). In the linear model, $m$ represents the constant rate of change in $y$ for each unit increase in $x$.

Flashcard 19: Identify the meaning of $x$ if $y = 5x + 12$ models total dollars $y$ after buying $x$ items plus a $12$ fee.

Answer: $x$ is the number of items purchased. The equation adds a fixed fee to 5 times $x$ for total cost, showing $x$ as the variable quantity bought.