High School Mathematical Functions and Derivatives Core Knowledge Framework (Final Review)

The biggest difference between high school mathematics and junior high school is abstraction, and functions are a concentrated embodiment of abstraction. Many students are familiar with the formula. As soon as they ask the question, they are blinded. What is lacking is the “framework” – I don’t know which knowledge point and tool to use for this question.

1. There are routines for judging the nature of functions

Monotonicity: Definition (let x1 < x2, compare f (x1) and f (x2)) or derivative method (see symbol); Parity: first look at the symmetry of the domain, then use the relationship between f (-x) and f (x); Periodicity: remember the common periodic functions (sin, cos period 2π, tan period π).

Second, the derivative is not the back formula

The derivation formula is a tool, not an end. What you really need to know is when to use the derivative (to judge monotonicity, extremum, maximum, tangent) and how to use it (to derive the f ‘→(x) = 0→ list analysis). The derivative questions in the college entrance examination paper have a score of 20 +, which is worth focusing on.

III. Common Point Losses

• Definition field omission: the first thing in the function question is always to find the definition field first;
• Compound function to derive leakage and multiply the inner derivative;
• Extremes are confused with maxima: extremes are not necessarily maxima;
• The tangent question forgets to check if the tangent point is on the curve.

IV. Sprint strategy at the end of the period

Use a week to finish this framework, then do the function derivative part of the real question at the end of the last three years, mark the wrong question, and return to the framework to find the corresponding weak knowledge points. Frame + real questions combined, the fastest score.

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