Senior one compulsory mathematics 1 summary of knowledge points in each chapter. The first chapter is the concept of set and function. Concepts related to set 1 The meaning of set 2. Three characteristics of elements in a set: (1) the certainty of elements, such as: the highest mountain in the world; (2) the mutual dissimilarity of elements, such as the happy letters {H, a, p, Y}; (3) the disorder of elements, such as {a, b, c} and {a, c, b}, represent the same. 3. Representation of assembly: {…} For example, {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean and Arctic Ocean }( 1) use Latin letters to represent assemblies. U Note: Common number sets and their notation: non-negative integer sets (i.e. natural number set) are recorded as: n positive integer sets N* or N+ integer sets z rational number sets q real number sets R 1) Enumeration: {a, b, c...} 2) Description: describes the public * * attribute of the elements in the set, which is written in braces to represent the set. {x？ 0? 2R | x-3 & gt； 2}，{ x | x-3 & gt； 2}3) Language Description: Example: {A triangle that is not a right triangle }4) venn diagram: 4. Classification of sets: (1) A set with finite elements in a finite set; (2) An infinite set contains infinite elements; (3) There is no set of elements in the empty set: {x | x

(1) on [a, b], the range is or;

(2) If yes, then; Take all positive numbers if and only if;

(3) For exponential function, there is always; Second, the logarithm function (1) logarithm 1. The concept of logarithm: generally, if, then this number is called the logarithm of the base, and it is recorded as: (-base,-real number,-logarithmic formula) Description: 1 Pay attention to the limit of the base, and; 2 ; Pay attention to the writing format of logarithm. Two important logarithms: 1 common logarithms: logarithms based on 10; Natural logarithm: Logarithm based on the logarithm of irrational numbers. The reciprocal power of u exponential formula and logarithmic formula is true number = n = b.

Logarithm of the base exponent (2) Operational properties of logarithms If, and, then:1+; 2 -; 3. Note: the formula for changing the bottom (,and; And; ). The following conclusions are derived from the formula of changing the bottom (1); (2).(2) Logarithmic function 1, the concept of logarithmic function: function, and it is called logarithmic function, here is the independent variable, and the domain of the function is (0, +∞). Note: the definition of logarithmic function 1 is similar to that of exponential function, both of which are formal definitions. Pay attention to discrimination. For example, none of them are logarithmic functions, but only logarithmic functions. 2. The limit of logarithmic function on the base. 2. The properties of logarithmic function: a >；; 1 0 & lt； A< 1 domain X > 0 domain X > 0 value domain r value domain r increases on r and decreases function images all pass through fixed point (1, 0) function images all pass through fixed point (1, 0) (3) power function 1, power function definition. The properties of power function are summarized. (1) All power functions are defined at (0, +∞), and images pass through points (1, 1). (2) At this time, the image of the power function passes through the origin and is an increasing function in the interval. Especially at that time, the image of power function is convex; At that time, the image of power function was convex; (3) The image of power function is a decreasing function in the interval. In the first quadrant, when moving from the right side to the origin, the image is infinitely close to the positive semi-axis of the shaft on the right side of the shaft, and when moving to it, the image is infinitely close to the positive semi-axis of the shaft above the shaft. For example: 1. The image of 0, a0, function y=ax and y=loga(-x) can only be () 2. Calculation: ①; ②= ; = ; ③ = 3. The decreasing interval of the function y=log(2x2-3x+ 1) is 4. If the maximum value of the function in the interval is three times the minimum value, then a= 5. Solving the domain of known (1) (2) solving the domain of function value. Chapter III Application of Functions. The roots of equations and the zeros of functions. 2. The meaning of the zero point of the function: the zero point of the function is the real root of the equation, that is, the abscissa of the intersection of the image of the function and the axis. That is, the image of the real root function equation intersects with the axis. 3. Solution of function zero: 1 (algebraic method) to find the real root of the equation; 2 (Geometric method) For the equation that can't be solved by the root formula, we can relate it with the image of the function and find the zero point by using the properties of the function. 4. Zero point of quadratic function. (1) △ > 0, the equation has two unequal real roots, the image of the quadratic function has two intersections with the axis, and the quadratic function has two zeros. (2) △ = 0.

And the map can't be sent out. LZ can leave an email and I'll send it.