[PEP Edition] Junior High Math Grade 7 Vol. 1: The Logical Leap from "Numbers" to "Expressions"

In elementary school, we learned to use letters to represent numbers, and we know that letters or expressions containing letters can represent numbers and quantitative relationships. Leaping from concrete numerical calculations to using letters to represent patterns is a great milestone in mathematical thinking.

Why is this leap necessary?

On the Qinghai-Tibet Railway, a train travels at a speed of $v \text{ km/h}$ through the permafrost section. If we calculate the distance for specific times:

The distance for $2\text{h}$ is $2v \text{ km}$
The distance for $3\text{h}$ is $3v \text{ km}$
When we use $t$ to represent time, the distance is $vt$.

This is the power of mathematics:The introduction of the letter $t$ lets us leap from calculating "the distance at a specific time" to describing "the general relationship between any time and any distance." When letters represent numbers, they can participate in operations just like numbers, and expressions can concisely represent quantitative relationships.

From "static numbers" to "dynamic expressions," this shift is the cognitive foundation for later learning about polynomial operations and function modeling. It lets us solve not just a single problem, but a whole class of problems.

QUESTION 1

In the Qinghai-Tibet Railway example, if the train's speed is $100\text{ km/h}$, what is the distance traveled in $t\text{h}$?

$100 + t$

$100/t$

$100t$

$t/100$

QUESTION 2

Regarding "using letters to represent numbers," which of the following statements is incorrect?

Letters can participate in operations just like numbers

Letters can only represent positive numbers

Letters can concisely represent quantitative relationships

Letters can represent operational laws (e.g., $a+b=b+a$)

QUESTION 3

A product costs $4.8$ yuan per bag. If $m$ bags are sold in one month, how should the total revenue be expressed?

$4.8 + m$ yuan

$4.8m$ yuan

$m/4.8$ yuan

$4.8^m$ yuan

QUESTION 4

What is the coefficient of the monomial $-a^2h$?

$0$

$1$

$-1$

$a$

QUESTION 5

What is the degree of the monomial $\f\frac{2}{3}\pi r^3$?

$3$

$4$

$2$

$1$

QUESTION 6

What is the result of $100t - 252t$?

$152t$

$-152t$

$-352t$

$-152$

QUESTION 7

For a two-digit number where the ones digit is $a$ and the tens digit is $b$, how can this number be expressed?

$ab$

$a + b$

$10b + a$

$10a + b$

QUESTION 8

Which of the following pairs of monomials are like terms?

$x^2y$ and $xy^2$

$3ab$ and $-ba$

$a^2$ and $b^2$

$2x$ and $2$

QUESTION 9

Remove the parentheses: $-5(1 - \f\frac{1}{5}x) = $

$-5 - x$

$-5 + x$

$5 - x$

$-5 + \f\frac{1}{5}x$

QUESTION 10

According to the classification of rational numbers, which group does $0$ belong to?

Positive numbers

Negative numbers

Integers

Fractions