High school mathematics compulsory chapter 2 knowledge points 1
Roots of equations and zeros of functions
1, the concept of function zero: for a function, the real number that makes it true is called the zero of the function.
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. Namely:
The equation has a real root function, the image has an intersection with the axis, and the function has a zero point.
3, the role of zero solution:
Find the zero point of a function:
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:
Quadratic function.
1)△& gt； 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, the equation has two equal real roots (multiple roots), the image of the quadratic function intersects with the axis, and the quadratic function has a double zero or a second-order zero.
3)△& lt； 0, the equation has no real root, the image of the quadratic function has no intersection with the axis, and the quadratic function has no zero.
High school mathematics compulsory chapter 2 knowledge points 2
Surface area volume formula of space geometry;
1, cylinder: surface area: 2πRr+2πRh volume: πR2h(R is the radius of the upper and lower bottom circles of the cylinder, and h is the height of the cylinder).
2. Cone: surface area: πR2+πR[(h2+R2)] Volume: πR2h/3(r is the radius of the low circle of the cone, and H is its height.
3. Length of side A, S=6a2, V=a3.
4. Cuboid a- length, b- width, c- height S=2(ab+ac+bc)V=abc.
5. prism S-h- height V=Sh
6. pyramid S-h- height V=Sh/3
7.S 1 and S2- upper and lower h- height v = h [s1+S2+(s1S2)1/2]/3.
8.S 1- upper bottom area, S2- lower bottom area, S0- medium h- high, V=h(S 1+S2+4S0)/6.
9, cylinder r- base radius, h- height, C- base perimeter S- base area, S- side, S- surface area C=2πrS base =πr2, S- side =Ch, S- table =Ch+2S base, V = S- base h=πr2h.
10, hollow cylinder r- outer circle radius, R- inner circle radius h- height v = π h (r 2-r 2)
1 1, r- bottom radius h- height v = π r 2h/3.
12, r- upper bottom radius, r- lower bottom radius, h- height V=πh(R2+Rr+r2)/3 13, ball R- radius d- diameter v = 4/3 π r 3 = π d 3/6.
14, ball gap h- ball gap height, r- ball radius, a- ball gap bottom radius V=πh(3a2+h2)/6=πh2(3r-h)/3.
15, table r 1 and r2- radius h- height V=πh[3(r 12+r22)+h2]/6.
16, ring r- ring radius d- ring diameter R- ring section radius D- ring section diameter V = 2π 2RR2 = π 2d2/4.
17, barrel d- barrel belly diameter D- barrel bottom diameter h- barrel height V=πh(2D2+d2)/ 12, (the bus is round with the center of the barrel) v = π h (2d2+DD+3d2/4)/1.
High school mathematics compulsory chapter 2 knowledge point 3
(1) inclination angle of straight line
Definition: The angle between the positive direction of the X axis and the upward direction of the straight line is called the inclination angle of the straight line. In particular, when a straight line is parallel or coincident with the X axis, we specify that its inclination angle is 0 degrees. Therefore, the range of inclination angle is 0 ≤α.
(2) the slope of the straight line
① Definition: A straight line whose inclination is not 90, and the tangent of its inclination is called the slope of this straight line. The slope of a straight line is usually represented by k, that is. Slope reflects the inclination of straight line and axis.
② Slope formula of straight line passing through two points:
Pay attention to the following four points:
(1) At that time, the right side of the formula was meaningless, the slope of the straight line did not exist, and the inclination angle was 90;
(2)k has nothing to do with the order of P 1 and P2;
(3) The slope can be obtained directly from the coordinates of two points on a straight line without inclination angle;
(4) To find the inclination angle of a straight line, we can find the slope from the coordinates of two points on the straight line.
(3) Linear equation
① Point-oblique type: the slope of the straight line is k, passing through the point.
Note: When the slope of the straight line is 0, k=0, and the equation of the straight line is y=y 1. When the slope of the straight line is 90, the slope of the straight line does not exist, and its equation can not be expressed by point inclination. But because the abscissa of each point on L is equal to x 1, its equation is x=x 1.
② Oblique section: the slope of the straight line is k, and the intercept of the straight line on the Y axis is b..
③ Two-point formula: () Two points on a straight line,
④ Intercept formula: where the straight line intersects with the axis at the point and intersects with the axis at the point, that is, the intercepts with the axis and the axis are respectively.
⑤ General formula: (A, B are not all 0)
⑤ General formula: (A, B are not all 0)
Note: ○ 1 scope of application.
○2 Special equations such as: straight line parallel to X axis: (b is constant); A straight line parallel to the Y axis: (A is a constant);
(4) Linear system equation: that is, a straight line with some * * * property.
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