One-line summary:The section in which second-year middle school students fail the most is:linear functionno see. The reason is simple. function"Formula y = ax + b"Because you learn first, you will not be able to explain the relationship between graphs and expressions in your own words. School exams ask about the meaning of functions, but students enter the test room with only the equations memorized.
How are linear functions asked on school exams?
As a result of analyzing 8 years' worth of past questions from Bucheon Wonmi Middle School, Simwon Middle School, and Dowon Middle School, the following three types of questions are most frequently asked in the linear functions unit.
- Graph → Find Expression— The problem of finding the equation of a linear function by looking at two points. Check the basics.
- Expression → Draw graph— The problem of translating expressions such as y = -2x + 4 to a graph. Meaning of slope and y-intercept.
- real life applications— The problem of translating sentences such as “position of a car traveling at speed v per second” into a functional expression. Variant types come out every year.
Areas where weaknesses are most often revealed
Students who have memorized "y = ax + b, where a is the slope and b is the y-intercept" at the academy can solve type 1. However, it is blocked in types 2 and 3. The reason isI can't explain in my own words what exactly "slope" is.Because.
Hanmungi’s 4-step linear function prescription
Step 1: 1 week of plotting points on the coordinate plane
Draw by hand how the dots come together to form a straight line. The task of tabulating (x, y) pairs and plotting them is repeated for the first week.
Step 2: Explain what slope means 1 week
Take time to present until you can explain in your own words, “How much does y increase when x increases by 1?”
Step 3: 2 weeks of past exam patterns for each school
Solve the frequently asked transformation questions in the 8 years of past papers from the student's school (Wonmi Middle School/Simwon Middle School/Dowon Middle School).
Step 4: Solution presentation + 2 weeks of practical simulation
The student explains the solution process in his or her own words in front of the blackboard. Mock test + time distribution check.
Frequently Asked Questions
Q. My child has a low test score on linear functions, but he has already finished the unit. Is it possible again?
yes. During the end-of-semester or vacation clinic, only the units are separated and redone. Since it is directly connected to the basis of the next grade's quadratic function, you must pick it up again.
Q. How are linear and quadratic functions connected?
The graph of a quadratic function (parabola) is naturally introduced as a “curve whose slope gradually changes” with an understanding of the graph of a linear function (a straight line). If the linear function is ambiguous, we face a second crisis in the quadratic function.
Q. What is the proportion of school tests and own textbooks?
Approximately 60% of the linear function unit clinic is operated as a variation of past exam questions from the student's school, and the remaining 40% is operated as a concept unit from the student's own textbook.
Related pages: Middle School (Grades 1-3) Program·self-produced textbooks