1. Notes on five knowledge points that must be tested in senior one mathematics.
The root of the equation and the zero point of the function 1, the concept of the zero point of the function: for the function, the real number that makes it true is called the zero point 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. That is, the equation has real roots, the image of the function intersects with the coordinate axis, and the function has zero points.
3, the role of zero solution:
(1) (algebraic method) to find the real root of the equation;
(2) (Geometric method) For the equation that cannot be solved by the root formula, we can relate it with the image of the function and use the properties of the function to find the zero point.
4. Zero point of 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 double zeros or second-order zeros.
2. Notes on the five knowledge points that must be tested in Mathematics 2 of Senior One.
Dihedral angle (1) half-plane: A straight line in the plane divides this plane into two parts, and each part is called a half-plane.
(2) dihedral angle: The figure composed of two half planes starting from a straight line is called dihedral angle. The range of dihedral angle is [0, 180].
(3) The edge of dihedral angle: This straight line is called the edge of dihedral angle.
(4) Dihedral facet: These two half planes are called dihedral facets.
(5) Plane angle of dihedral angle: Take any point on the edge of dihedral angle as the endpoint, and make two rays perpendicular to the edge in two planes respectively. The angle formed by these two rays is called the plane angle of dihedral angle.
(6) Straight dihedral angle: A dihedral angle whose plane angle is a right angle is called a straight dihedral angle.
3. Notes on five knowledge points in the Three Compulsory Exams of Mathematics in Senior One.
The value of determinant algorithm 1 and triangular determinant is equal to the product of diagonal elements. When calculating, it usually takes many operations to convert determinant into upper triangle or lower triangle.
2. Swap two rows (columns) in the determinant, and the determinant changes sign.
3. The common factor of a row (column) in the determinant can be placed outside the determinant.
4. Multiply one row of the determinant by a and add it to another row. Determinants are invariant and are often used to eliminate certain elements.
5. If the two rows (columns) in the determinant are exactly the same, the determinant is 0; It can be inferred that if two rows (columns) are proportional, the determinant is 0.
6. Expansion of determinant: the value of determinant is equal to the sum of the products of each element of a row (column) and its algebraic cofactor; However, if the elements of another row (column) are added to the algebraic cofactor product of that row (column), the sum is 0.
7. When solving the related problems of algebraic cofactor, the determinant can be replaced by value.
8. Cramer's rule: use the coefficient determinant of linear equations to solve equations.
9. Homogeneous linear equations: When all the constant terms on the right side of a linear equation group are 0, the equation group is called homogeneous linear equations, otherwise it is nonhomogeneous linear equations. Homogeneous linear equations must have zero solutions, but not necessarily non-zero solutions. When D=0, there is a nonzero solution; When d! When =0, the equation has no zero solution.
4. Notes on Five Required Knowledge of Mathematics in Senior One Four
Sum formula of proportional series (1) Geometric series: a(n+ 1)/an=q(n∈n).
(2) General formula: an = a1× q (n-1); Generalization: an = am× q (n-m);
(3) summation formula: sn = n× a1(q =1) sn = a1(1-q n)/(1-q) = (a1)
(4) nature:
(1) if m, n, p, q∈n, m+n=p+q, then am×an = AP×AQ；;
(2) In geometric series, every k term is added in turn and still becomes a geometric series.
③ If m, n, q∈n and m+n=2q, then am× an = AQ 2.
(5) "G is the equal ratio mean of A and B" and "G 2 = AB (G ≠ 0)".
(6) In geometric series, the first term a 1 and the common ratio q are not zero.
Note: In the above formula, an stands for the nth term of geometric series.
Derivation of summation formula of equal ratio series: sn=a 1+a2+a3+...+an (common ratio q) q _ sn = a1_ q+a2 _ q+a3 _ q+... sn=a 1-a 1_q^nsn=(a 1-a 1_q^n)/( 1-q)sn=(a 1-an_q)/( 1-q)sn=a 1( 1-q^n)/( 1-q)sn=k_( 1-q^n)~y=k_( 1-a^x)。
5. Five knowledge notes of compulsory mathematics in senior one.
Concept of function: Let A and B be non-empty number sets. If any number X in set A has a certain number f(x) corresponding to it according to a certain correspondence F, then F: A-B is a function from set A to set B, denoted as: y=f(x), x ∈.
(1), where x is called the independent variable and the value range a of x is called the domain of the function;
(2) The value of y corresponding to the value of x is called the function value, and the set of function values {f(x)|x∈A} is called the range of the function.
Three elements of a function: domain, range and corresponding rules.
Representation of function:
(1) Analytic Method: Define the domain of a function.
(2) Graphic imagination: determine whether the functional images are connected. Function images can be continuous curves, straight lines, broken lines, discrete points and so on.
(3) List method: the selected independent variables should be representative and reflect the characteristics of the domain.
6. Notes on five knowledge points that must be tested in senior one mathematics.
Structural characteristics of polyhedron (1) Two faces of a prism are parallel to each other, and the other faces are parallelograms, and the common edges of every two adjacent quadrangles are parallel.
Regular prism: a prism whose side is perpendicular to the bottom is called a regular prism, and a regular prism whose bottom is a regular polygon is called a regular prism. On the contrary, a regular prism has a regular bottom surface and rectangular side surfaces, and the side edges of the bottom surface are perpendicular to the bottom surface.
(2) The base of the pyramid is an arbitrary polygon, and the sides are triangles with common vertices.
Regular pyramid: A pyramid whose bottom is a regular polygon and whose vertices are projected on the bottom is called a regular pyramid. In particular, an equilateral regular triangular pyramid is called a regular tetrahedron. On the contrary, the base of a regular pyramid is a regular polygon, and the projection of its vertex on the base is the center of the regular polygon.
(3) A frustum can be obtained from a plane truncated pyramid parallel to the bottom surface, and its upper and lower bottom surfaces are similar polygons.