I. Scores
1, same base powers division, constant base, exponential subtraction. am an=am-n(a 0)
2. Divide by two monomials, just divide by the coefficient and the same base respectively.
3. The formula in the form (A and B are algebraic expressions, B contains letters, and B 0) is called a fraction. =0(A=0，B 0).
4. Both the numerator and denominator of the fraction are multiplied by (or divided by) the same algebraic expression that is not equal to zero, and the value of the fraction remains unchanged. After simplification, the fraction with no common factor between numerator and denominator is called simplest fraction. The result of fractional operation must be the simplest.
5. The simplest common denominator is the product of the highest power of all factors of each denominator.
6. When a fractional equation is transformed into an integral equation, both sides of the equation are multiplied by an algebraic expression of an unknown number, and the denominator is removed, sometimes a solution (or root) that is not suitable for the original equation may be generated, and this root is called an increased root. Therefore, it is necessary to check when solving the fractional equation.
7. The zeroth power of any number not equal to zero is equal to 1. a0= 1(a 0)
8. The power of -n(n is a positive integer) of any number that is not equal to zero is equal to the reciprocal of the power of n of this number. n=( )n= (a
9. Use scientific notation to represent some numbers with small absolute values, that is, in the form of a, where n is a positive integer, 1 ≤ < 10. For example, 0.00002 1=2. 1
Second, the unary quadratic equation 1, the whole equation has only one unknown, and the highest degree of the unknown is 2, which is called the unary quadratic equation. General form: ax2+bx+c=0(a, B and C are known numbers, where A, B and C are called quadratic coefficient, linear coefficient and constant term respectively.
2. Solution of quadratic equation in one variable: (1) Direct Kaiping method (2) Factorial decomposition method (cross multiplication) (3) Formula method x= (b2-4ac (4) Matching method (see P32 for details).
3. Discriminating formula for roots of quadratic equation with one variable (2-4ac) When a is (1) > 0, the equation has two unequal real roots; (2) When = 0, the equation has two unequal real roots; (3) When < 0, the equation has no real root.
4. The relationship between the root and the coefficient of a quadratic equation (Vieta theorem): ax2+bx+c=0(a, B and C are known numbers. When A≥0, let two equations be x 1, and x2 be X 1+X2 =-, x1.
5. The quadratic equation with x 1 and x2 as roots is:
Third, the quadratic function 2, the axis of symmetry of the parabola is the axis, and the vertex is the origin. When the time is up, the opening will be made.
Fourth, the consistency of graphics.
1, two graphs that can completely overlap are congruent graphs. The mutually coincident vertices are called corresponding vertices, the mutually coincident edges are called corresponding edges, and the mutually coincident angles are called corresponding angles.
2. The edges and angles corresponding to congruent graphs are equal.
3. Identification of congruent triangles (1) If three sides of two triangles are equal respectively, then the two triangles are congruent. Note (edge or SSS)(2) If two triangles have two sides and their included angles are equal, the triangles are congruent. Abbreviated as (Angle SAS) (3) Two triangles are congruent if their two angles and their clamping sides are equal respectively, abbreviated as (Angle ASA) (4) If their hypotenuses and a right-angled side are equal respectively, two right-angled triangles are congruent. Abbreviated as (HL)
4. Sentences that can judge whether it is right or wrong are called propositions, often written in the form of "if ……", and the original basis for judging the truth of other propositions is called axioms. Some propositions can be judged to be correct by axioms or other true propositions through logical reasoning, and can be further used as the basis for judging the truth value of other propositions. Such a true proposition is called a theorem. According to topics, definitions, axioms, theorems, etc. , through logical reasoning, judge whether a proposition is correct. This reasoning process is called proof.
Verb (abbreviation for verb) circle
1, the related concept of circle: (1), and determine that the elements of a circle are the center and radius. (2) A line segment connecting any two points on a circle is called a chord. The chord passing through the center of the circle is called the diameter. The part between any two points on a circle is called an arc. An arc smaller than half a circle is called a bad arc. An arc larger than half a circle is called an optimal arc. In the same circle or equal circle, arcs that can overlap each other are called equal arcs. The vertex is on the circle, and the angle at which both sides intersect the circle is called the circumferential angle. You can draw a circle through the three vertices of a triangle, and only one can be drawn. The circle passing through the three vertices of a triangle is called the circumscribed circle of the triangle, and the center of the circumscribed circle of the triangle is called the circumscribed circle of the triangle, and the center of the circumscribed circle is the intersection of the vertical lines of each side of the triangle. The radius of the circumscribed circle of a right triangle is equal to half of the hypotenuse. The circle tangent to each side of the triangle is called the inscribed circle of the triangle, the center of the inscribed circle of the triangle is called the inner circle of the triangle, and this triangle is called the circumscribed triangle. The inner circle of the triangle is the intersection of bisectors of three inner angles of the triangle. The radius of the inscribed circle of a right triangle satisfies:
2. Theorem about the nature of a circle (1) is in the same circle or within the same circle. If the central angles of the circle are equal, then the arcs it faces are equal, the chords it faces are equal, and the chord center distances of the chords it faces are equal. It is inferred that in the same circle or equal circle, if one set of quantities of two central angles, two arcs, two chords or the distance between two chords are equal, the other set of quantities of their pairs are equal respectively. (2) Vertical diameter theorem: the diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord. Inference1(i) bisects the diameter (not the diameter) of the chord perpendicular to the chord and bisects the two arcs opposite to the chord. (Ⅱ) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord. (iii) bisect the diameter of the arc subtended by the chord, bisect the chord vertically and bisect the other arc subtended by the chord. Inference 2 The arcs sandwiched between two parallel chords of a circle are equal. (3) Theorem of circumferential angle: the circumferential angle of an arc is equal to half the central angle of the arc. Inference 1 In the same circle or equal circle, the circumferential angles of the same arc or equal arc are equal, and so are the arcs with equal circumferential angles. Inference 2 The circumferential angles of semicircles or diameters are all equal, all equal to 90. The chord subtended by a circumferential angle of 90 is the diameter of the circle. Inference 3 If the median line of one side of a triangle is equal to half of this side, then this triangle is a right triangle. (4) Determination and properties of the tangent: Determination theorem: The straight line passing through the outer end of the radius and perpendicular to this radius is the tangent of the circle. Property theorem: the tangent of a circle is perpendicular to the radius passing through the tangent point; A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point; A straight line perpendicular to the tangent through the tangent point must pass through the center of the circle. (5) Theorem: Three points that are not on the same straight line determine a circle. (6) The length of the line segment between a point on the tangent of a circle and the tangent point is called the tangent length from the point to the circle; Tangent length theorem: two tangents of a circle can be drawn from a point outside the circle, and their tangents are equal in length. The connecting line between this point and the center of the circle bisects the included angle between the two tangents. (7) The quadrangles inscribed in the circle are diagonally complementary, and one outer angle is equal to the inner diagonal; The sum of the opposite sides of the circumscribed quadrangle is equal; (8) Chord angle theorem: the chord angle is equal to the circumferential angle of the arc pair it clamps. (9) Proportional line segments related to a circle: the theorem of intersecting chords: the product of two intersecting chords in a circle is equal to the length of two lines divided by the intersection. If the chord intersects the diameter vertically, then half of the chord is the proportional average of two line segments formed by its separate diameters. Secant theorem: the tangent and secant of a circle are drawn from a point outside the circle, and the length of the tangent is the middle term in the length ratio of the two lines where this point intersects the secant. Draw two secants of a circle from a point outside the circle, and the product of the lengths of the two lines from that point to the intersection of each secant and the circle is equal. (10) Two circles are tangent, and the connecting line intersects the tangent point; Two circles intersect, and the connecting line bisects the common chord vertically.
3. Position relation related to the circle
(1) positional relationship between point and circle: point in circle d (2) positional relationship between straight line and circle: straight line and circle are separated (D >；); r)； The straight line is tangent to the circle (), and this straight line is called the tangent of the circle; A straight line intersects a circle (), which is called the secant of the circle. (3) the positional relationship between circles: outward (D >；); r+r)； External cutting; Intersection (); cut()； Contain
4. Calculation in circle: lateral area of cone =; Sector arc length of cone-side expansion diagram =