【People's Education Press】Junior High School English, Grade 7, Semester 1: The Logical Leap from 'Numbers' to 'Expressions'

In elementary school, we learned how to represent numbers using letters, understanding that letters or expressions containing letters can represent numbers and quantitative relationships. Moving from concrete numerical calculations to representing patterns with letters marks a great leap in mathematical thinking.

Why is this leap necessary?

On the Qinghai-Tibet Railway, the train's speed on permafrost sections is $v \text{ km/h}$. If we calculate the distance for specific durations:

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

This is precisely the power of mathematics:Introducing the letter $t$ allows us to move from calculating the distance for a specific time to describing the general rule between any time and distance. Using letters to represent numbers means letters can participate in operations just like numbers, enabling us to express quantitative relationships clearly through expressions.

This shift from 'static numbers' to 'dynamic expressions' forms the cognitive foundation for learning polynomial operations and function modeling. It enables us not only to solve one problem but also to solve entire classes 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

Which of the following statements about 'representing numbers with letters' 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 operation laws (e.g., $a+b=b+a$)

QUESTION 3

A product costs $4.8$ per bag. If $m$ bags are sold in a month, how should 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

A two-digit number has digit $a$ in the units place and digit $b$ in the tens place. How can this number be represented?

$ab$

$a + b$

$10b + a$

$10a + b$

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

$-5 - x$

$-5 + x$

$5 - x$

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

QUESTION 10

According to rational number classification, to which group does $0$ belong?

Positive numbers

Negative numbers

Integers

Fractions