With a year of high school, i found a realistic situation: many children had good grades in mathematics at the junior high level, and they had to drop out once they had completed their studies. It must be built as a cornerstone of mathematics throughout high schoolFunctions, index logarithms, trigonometric functions, all of which are concentrated in this volume, which is multi-conceptual, formulaic and very sensitive to the preconditions for the formation of the formula. A large number of students have lost points, not a lack of thought, but rather a mixture of formulas, the omission of definitional fields, the omission of such criteria, and the loss of a large part of the score。
It's compulsory todayFormula summaryIn order to organize the core formula according to the chapter of the textbook, it is suitable to consolidate the first grade simultaneously, as well as for the mid-term and pre-final examinations, and parents can collect printed copies as a pre-test quick check manual. I'm going to add the error-prone points of each chapter to the lessons learned in the classroom, not just to list formulas, to help children understand memories, not to die。
Chapter i, pooling and common logic terms。
This chapter is the beginning of high school mathematics, and many students find it simple, but there are many pitfalls. A\cap b=x\ina} and }inb}, and a\cupb=x\ina= or \inb}, supplement\complement ua=\x\inu and }notina}, it is important to make a distinction between “and” and “or” where the choice is often digging。
There are also sub-sum conclusions: collections containing n elements, with a total of 2^n, the number of genuines is 2^n-1, which fills in, selects high frequency, and many of the same students forget to subtract the collection itself. The rejection of the title and the title is also a consideration, and the title is to be replaced by the title and the conclusion; the title is to be replaced by the title and the conclusion. Many students have changed their words and forgotten the negative conclusion, which is the most classic point of failure in this chapter。
Chapter ii, binary functions, equations and variants。
This chapter, which is the focus of the second function of the connecting junior high school, is based on the basic variant a+b\ge 2\sqrt{ab} (a>0, b>0), so remember here the three premises: one positive, two positive, three equal! Many students make direct equations, ignore positive-number conditions, or forget whether equivalents can be obtained, with a maximum of direct error。
\left (-\frac{b}{2a}, \\frac{4ac-b^2}{4a}\right), symmetricx=-\frac{b}{2a}, symmetrical\delta=b^2-4ac, root formulax {1,2}=\frac{-b\pm\sqrt{\delta}{2a}. It is a core tool for determining the exact number of secondary equations and the basis for the determination of the secondary decomposition, the secondary function images and the x-axis, which is repeated throughout the post-secondary school, and which must be firmly based。
Chapter iii, concept and nature of functions。
A core chapter is the function and the soul of high school mathematics. First, you have to distinguish between defined domains, values and ranges: defined domains are the range of x values that allows resolution to be meaningful. Values are a collection of all functions。
Single-modular addition function: x 1
Section 4, index function and logarithmic function。
Indexing: a^m\cdot a^n=a^m+n}, (a^m)^n=a^m}mn}; logarithmic calculation\log a(mn)=\log am+\log a,\log a\frac{m}} \log am-\an,\log am^n=n\log am, and also a bottom formula。
Index function y=a^x\(a>0 and a\neq1), constant fixed point (0,1); logarithmic function y=\log ax\(a>0 and a\neq1), constant fixed point (10). The greatest difficulty in this chapter is the definition of a numerical domain, where the true number must be greater than zero, the decomposition of a logarithmic equation, and, ultimately, the re-profiling of the equation, otherwise there will be an easy increase. Index logarithms are inverse to each other, and combining image memories is recommended for learning,a more than 1 and 0
Chapter v, triangular functions。
This is the hard part to fix, and it is the basis for the transformation of the triangle behind it. The radial system 180^circ=\text{rad}, the arc formulal=alpha r, the sector area s=\frac12lr=\frac12\alpha r^2. Triangular function definition \sin\alpha=\frac{y}, \cos\alpha=\frac{x{r}, \tan\alpha=\frac{y}x} (x\neq0), basic relationship to the same angle \sin^alpha+\cos^alpha=1, \tan\alpha=\frac}。
The induction formula is designed to be “unchanged, symbol-reading range”, as well as the difference angle formula, the double angle formula, the auxiliary angle formulaa\sin x + b\cos x=\sqrt{a^2+b^2}\sin (x+\varphi). Auxiliary angle formula is a high frequency test, followed by a cycle, a maximum value, and a single-temperature interval, with many students bearing the wrong double-angle sign, and the triptych of the triangulation goes wrong in the first step。
Learning advice
The memory alarm at the bottom of the list is critical: the formula structure is recorded first, then the conditions for establishment, and the function type formula must be combined with image memory. Many children have to learn one of the biggest error areas, the pre-test ad hoc back attack formula, which will not work unless they understand it。
My classroom suggested that it would take 10 minutes each day to read the list in silence, and for each formula to be written, to say its limitations orally, for example, to write basic variations, and immediately to say “one plus two equal”; to write a logarithmic, immediately to remind the true number above zero. In order to be truly mastery, the formula will be put into the subject, in conjunction with the accompanying training。
And it shall be replaced by an epitome, and it shall be solid, and it shall be followed by two, optional, obligatory functions, columns, conical curves that shall not eat. High school mathematics is not based on smartness and proficiency in basic formulas, which directly determine whether or not the basics of the examinations can be scored, and the basics are not lost, and the scores can naturally go up。
