ISEE Upper Level Quantitative Reasoning Flashcards: Word Problems To Expressions

What this deck covers

This deck focuses on Word Problems To Expressions, 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 algebraic expression represents "one half of a number $x$"?

Answer: $\frac{1}{2}x$. Multiplies x by one-half to represent half the value.

Flashcard 2: What algebraic expression represents "five more than a number $x$"?

Answer: $x + 5$. Adds 5 to the variable x to express an increase by five units.

Flashcard 3: What algebraic expression represents "$x$ is at least $10$"?

Answer: $x \ge 10$. Uses greater than or equal to show x is 10 or more.

Flashcard 4: What algebraic expression represents "the product of $x$ and $y$"?

Answer: $xy$. Multiplies x and y to express their product.

Flashcard 5: What algebraic expression represents "seven less than a number $x$"?

Answer: $x - 7$. Subtracts 7 from x to indicate a reduction by seven.

Flashcard 6: What algebraic expression represents "twice the sum of $x$ and $5$"?

Answer: $2(x + 5)$. First adds x and 5, then multiplies by 2 to double the sum.

Flashcard 7: What algebraic expression represents "the average of $x$ and $y$"?

Answer: $\frac{x + y}{2}$. Divides the sum of x and y by 2 to find their mean.

Flashcard 8: What algebraic expression represents "$x$ divided by $y$"?

Answer: $\frac{x}{y}$. Divides x by y to represent the ratio.

Flashcard 9: What algebraic expression represents "three times a number $x$"?

Answer: $3x$. Multiplies x by 3 to denote tripling the value.

Flashcard 10: What algebraic expression represents "$12$ less than $x$"?

Answer: $x - 12$. Subtracts 12 from x to show a decrease by 12.

Flashcard 11: What algebraic expression represents "a number $x$ increased by $15\%$"?

Answer: $x + 0.15x$. Adds 15% of x to x itself to show the increase.

Flashcard 12: What algebraic expression represents "$7$ divided by $x$"?

Answer: $\frac{7}{x}$. Divides 7 by x to express the division.

Flashcard 13: What algebraic expression represents "the sum of $x$ and $12$"?

Answer: $x + 12$. Combines x and 12 through addition to form their total.

Flashcard 14: What algebraic expression represents "the quotient of $x$ and $7$"?

Answer: $\frac{x}{7}$. Divides x by 7 to form the quotient with x as numerator.

Flashcard 15: What algebraic expression represents "the sum of twice $x$ and $5$"?

Answer: $2x + 5$. Doubles x and then adds 5 to form the sum.

Flashcard 16: What algebraic expression represents "$3$ less than the square of $x$"?

Answer: $x^2 - 3$. Subtracts 3 from the square of x to decrease it by 3.

Flashcard 17: What algebraic expression represents "the difference between $x$ and $12$"?

Answer: $x - 12$. Represents the subtraction of 12 from x as the difference.

Flashcard 18: What algebraic expression represents "$15\%$ of a number $x$"?

Answer: $0.15x$. Multiplies x by 0.15 to calculate 15% of the value.

Flashcard 19: What algebraic expression represents "$x$ is $4$ less than $y$"?

Answer: $x = y - 4$. Sets x equal to y minus 4 to show it is 4 less.

Flashcard 20: What algebraic expression represents "$x$ is no more than $10$"?

Answer: $x \le 10$. Uses less than or equal to indicate x does not exceed 10.

Flashcard 21: What algebraic expression represents "$x$ is between $3$ and $8$, inclusive"?

Answer: $3 \le x \le 8$. Bounds x between 3 and 8 inclusive with inequalities.

Flashcard 22: What algebraic expression represents "$x$ decreased by $20\%$"?

Answer: $0.8x$. Multiplies x by 0.8 to subtract 20% from x.

Flashcard 23: What algebraic expression represents "$5$ more than twice $x$"?

Answer: $2x + 5$. Increases twice x by adding 5.

Flashcard 24: What algebraic expression represents "the sum of the squares of $x$ and $3$"?

Answer: $x^2 + 3^2$. Adds the square of x to the square of 3.

Flashcard 25: What algebraic expression represents "the square of the sum of $x$ and $3$"?

Answer: $(x + 3)^2$. Squares the sum of x and 3 as a whole.