2020 Senior Two Mathematics Summer Homework Answers 1
1.(Chongqing College Entrance Examination in 2009) The positional relationship between a straight line and a circle is ()
A. Tangency B. Intersection but the straight line does not pass through the center of the circle
C. A straight line passes through the center of the circle D. Separation
2. Equation x2+y2+2ax-by+c=0 represents a circle with a center of c (2 2,2) and a radius of 2, then the values of a, b and c.
On the other hand, it is ()
A.2、4、4； B- 2、4、4；
C2 、-4、4； D.2、-4、-4
3 (Chongqing College Entrance Examination 20 1 1) The equation of a circle with the center on the axis, the radius of 1 and the passing point of (1, 2) is ().
A.B
CD。
4. The chord length of the line 3x-4y-4=0 cut by the circle (x-3)2+y2=9 is ().
A.B.4
C.D.2
5.M(x0, y0) is a circle x2+y2 = a2 (a >; 0) is different from the center of the circle, so the positional relationship between the straight line x0x+y0y=a2 and the circle is ().
A. Tangency B. Intersection
C. Phase separation D. Tangency or intersection
6. The equation of a circle about a linearly symmetric circle is ().
A.
B.
C.
D.
7. The equation for connecting two circles x2+y2-4x+6y=0 and x2+y2-6x=0 is ().
A.x+y+3=0B.2x-y-5=0
C.3x-y-9=0D.4x-3y+7=0
8. In the straight line passing through this point, the equation of the straight line cutting the longest chord is ()
A.B
CD。
9.(20 1 1 Sichuan College Entrance Examination) The coordinates of the center of the circle are
10. A considerable sum.
The linear equation of the chord is _ _ _ _.
11.(2011Tianjin College Entrance Examination) Given that the center of the circle is the intersection of a straight line and an axis, and the circle is tangent to the straight line, the equation of the circle is.
12(20 10 Shandong College Entrance Examination) It is known that the circle passes through this point, the center of the circle is on the positive semi-axis of the shaft, and the chord length of the straight line cut by the circle is, then the standard equation of the circle is _ _ _ _ _ _ _ _ _.
13. Find the straight line equation of the chord that passes through the point P(6, -4).
14, the equation of circle c is known as x2+y2=4.
(1) The straight line L passes through point P( 1, 2) and intersects with circle C at points A and B. If |AB|=23, find the equation of the straight line L;
(2) A fixed point M(x0, y0) on the circle C, ON→=(0, y0), if the vector OQ→=OM→+ON→, find the trajectory equation of the fixed point Q.
The structure of "people" supports each other, and the cause of "many people" needs everyone's participation.
2020 Senior Two Mathematics Summer Homework Answer 2
1. Within the point, the value range of is ()
A.B
CD。
2. The midpoint trajectory equation of point P(4, -2) continuous with any point on the circle is ().
A.
B.
C.
D.
3. (Shaanxi College Entrance Examination in 2009) The chord length of a straight line passing through the origin with an inclination of is cut by a circle.
A.B.2C.D.2
4. Given the equation x2+y2+4x-2y-4=0, the value of x2+y2 is ().
a . 9b . 14c . 14-d . 14+。
5. (Liaoning College Entrance Examination in 2009) It is known that circle C is tangent to straight lines x-y=0 and x-y-4=0, and the center of circle is on straight line x+y=0, then the equation of circle C is ().
A.
B.
C.
D.
6. Two circles intersect at (1, 3) and (m, 1), and the centers of both circles are on the straight line x-y+c2=0, then the value of m+c is ().
A.- 1B.2C.3D.0
7.(20 1 1 Anhui) If a straight line passes through the center of the circle, the value of a is ().
A. 1B
8. (Guangdong College Entrance Examination in 2009) Let the circumscribed circle x2+(y-3)2= 1 of the circle C be tangent to the straight line y=0, then the locus of the center of the circle C is ().
A. parabola B. hyperbola
C. ellipse D. circle
9. (Tianjin College Entrance Examination in 2009) If the chord length of a circle is, then a = _ _ _ _ _ _
10. (Guangdong College Entrance Examination in 2009) The equation of a circle with point (2,) as the center and tangent to a straight line is.
11.(Shaanxi College Entrance Examination in 2009) A straight line passes through the origin, and the chord length of the inclination angle is.
12, the equation of a straight line with a chord length of 8 passing through point p (-3, -32) and being cut by circle x2+y2=25 is _ _ _ _ _ _ _.
13. It is known that the center C is on the straight line L 1: x-y- 1 = 0, which is tangent to the straight line L2: 4x+3y+ 14 = 0, and the tangent line L3: 3x+4y+10 =
2020 Senior Two Mathematics Summer Homework Answers Daquan 3
one
1, it is known that point P is the moving point on the parabola y2=4x, so the sum of the distance from point P to point A (-1, 1) and the distance from point P to the straight line x=- 1 is the smallest. If b (3,2), the minimum value is
2, parabola y2 = 2px (p >; 0), the line with inclination intersects the parabola at two points, and if the length of line segment AB is 8, then p=
3. If the number of regular triangles whose two vertices are on the parabola and the other vertex is the focus of the parabola is n, then n = _ _ _ _ _ _ _ _
4. Take two points on the parabola y=x2+ax-5(a≠0) with X 1 =-4 and x2 = 2, and draw a secant through these two points. If a line parallel to the secant is tangent to both the parabola and the circle, the vertex coordinate of the parabola is _ _ _ _ _ _ _ _.
two
1. (full mark for this question 12) There are 6 students standing in a row, and the requirements are:
(1) How many different ways can there be for a row without standing at the head or the tail?
(2)A doesn't stand at the head and B doesn't stand at the tail. How many different arrangements are there?
(3) When A, B and C are not adjacent, how many different arrangements are there?
(12) Party A and Party B take the oral English test. It is known that among the 1 ~ 10 questions, Party A can correctly answer the 6 questions 1 ~ 6, and Party B can correctly answer the 8 questions/3 ~ 10.
(1) Find the probability distribution and mathematical expectation of the number of questions correctly answered by A;
(2) Find the probability that at least one of Party A and Party B will pass the exam.
three
1. The positional relationship between a straight line and a circle is ()
A. Tangency B. Intersection but the straight line does not pass through the center of the circle
C. A straight line passes through the center of the circle D. Separation
2. Equation x2+y2+2ax-by+c=0 represents a circle with a center of c (2 2,2) and a radius of 2, so the values of a, b and c are () in turn.
A.2、4、4； B- 2、4、4；
C2 、-4、4； D.2、-4、-4
3 The equation of the circle whose center is on the axis, radius is 1, and passing point (1, 2) is ().
4. The chord length of the line 3x-4y-4=0 cut by the circle (x-3)2+y2=9 is ().
5.M(x0, y0) is a circle x2+y2 = a2 (a >; 0) is different from the center of the circle, so the positional relationship between the straight line x0x+y0y=a2 and the circle is ().
A. Tangency B. Intersection
C. Phase separation D. Tangency or intersection
2020 Senior Two Mathematics Summer Homework Answers Daquan 4
(a) multiple-choice questions (5 points for each question, * *10, ***50 points)
1, the ordinate of a point on the parabola is 4, so the distance between the point and the focus of the parabola is ()
A2B3C4D5
2. For any point q on the parabola y2=2x, all points P(a, 0) satisfy |PQ|≥|a|, then the range of a is ().
A(0， 1)B(0， 1)CD(-∞，0)
3. The focal coordinate of parabola y2=4ax is ().
A(0，a)B(0，-a)C(a，0)D(-a，0)
4. Let a (x 1, y 1) and b (x2, y2) be parabolas y2 = 2px(p & gt；; 0), and OA⊥OB is satisfied, then y 1y2 is equal to.
()
a–4p 2 B4 p2c–2p2d 2p 2
5. It is known that point P is on parabola y2=4x, so when the sum of the distance from point P to point Q(2,-1) and the distance from point P to the focus of parabola reaches the minimum, the coordinate of point P is ().
A.(，- 1)B .(， 1)C.( 1，2)D.( 1，-2)
6. The focus of a given parabola is, the intersection of the directrix and the axis is, the point is above, and the area is ().
(A)(B)(C)(D)
7. The straight line y=x-3 intersects the parabola at points A and B, and passes through points A and B..
The directrix of the parabola is vertical, and the vertical feet are P and Q respectively, so the area of the trapezoidal APQB is ().
(A)48。 56(C)64(D)72。
8.(20 1 1 national college entrance examination Guangdong paper Kewen 8) Let circle c be tangent to the circle and tangent to the straight line. Then the trajectory of the center of c is ().
A. parabola b hyperbola c ellipse d circle
9. It is known that the eccentricity of hyperbola is 2. If the distance from the focus of the parabola to the hyperbolic asymptote is 2, the equation of the parabola is
(A)(B)(C)(D)
10, (20 1 1) Let m (,) be the upper point of parabola C, F be the focus of parabola C, and a circle with the center of F and the radius intersect with the directrix of parabola C, then the range of values is
(A)(0，2)(B)[0，2](C)(2，+∞)(D)[2，+∞)
(2) Fill in the blanks: (5 points for each question, ***4 small questions, ***20 points)
1 1, it is known that point p is the moving point on the parabola y2=4x, so the minimum sum of the distance from point p to point a (-1, 1) and the distance from point p to line x =- 1. If b (3,2), the minimum value is
12, parabola y2 = 2px (p >; 0), the line with inclination intersects the parabola at two points, and if the length of line segment AB is 8, then p=
13. If the number of regular triangles with two vertices on a parabola and the other vertex being the focus of this parabola is n, then n = _ _ _ _ _ _ _ _.
14, on the parabola y=x2+ax-5(a≠0), take two points with x 1 =-4 and x2 = 2, and draw a secant through these two points. If the line parallel to the secant is tangent to both the parabola and the circle, the vertex coordinate of the parabola is _ _ _ _ _ _.
(3) Problem solving: (15, 16, 17 is 12, 18 is 14 * * 50).
15, the focus of parabola is known, and the slope is a straight line.
A straight line intersects a parabola at two points (), and.
(1) Equation for finding parabola;
(2) is the coordinate origin, a point on the parabola, if, the value of.
16, (201/year college entrance examination Fujian liberal arts 18) (full mark for this small question is 12)
As shown in the figure, the straight line L: Y = X+B and the parabola C: X2 = 4Y are tangent to point A.
(1) the value of the real number b;
(1 1) Find the equation of a circle with point A as the center and tangent to the parabola c directrix.
17. There is a parabolic arch bridge on the river. When the water surface is 5 meters away from the top of the arch bridge, the water surface is 8 meters wide, and a boat is 4 meters wide and 2 meters high. After loading, the part of the ship exposed to the water is 0.75 meters high. When the water level rises to several meters from the parabolic arch, the ship can't sail at first.
18, (Jiangxi 20 10) Known parabola: passing through two focuses of an ellipse.
(1) Find the eccentricity of the ellipse;
(2) Set the summation equation with two intersection points not on the axis, if the center of gravity is on the parabola.
Topic 3 1: straight lines and conic curves
Proposer: Wang Yexing Reviewer: Zhu Tian 20 12-7.
First, review the textbook.
1. rebate textbook: the reading textbook can be selected from1-1P31-p72 or 2- 1p3 1-p76, with the straight line.
2, master the following questions:
① The positional relationship between a straight line and a conic curve is,,. There are intersections when they intersect, intersections when they are tangent, and intersections when they leave.
② To judge the positional relationship between a straight line and a conic, it is usually to substitute the equation of a straight line into the equation of a conic, and eliminate Y (or X) to get a unary equation about the variable X (or Y), that is, to eliminate Y to get ax2+bx+c=0 (this equation is called elimination equation).
A0, if there are > 0, straight lines and conic curves. & lt0, straight line and conic curve
When a=0, a linear equation is obtained, in which there is only one intersection point between the straight line and the conic. At this time, if it is a hyperbola, the straight line is parallel to the hyperbola. If it is a parabola, the straight line L is parallel to the parabola.
③ The line segment connecting two points of the conic becomes the chord of the conic.
Let the equation of a straight line and the equation of a conic curve have two different intersections, and eliminate Y to get ax2+bx+c=0, which are its two unequal real roots.
The relationship between (1) root and coefficient is as follows
(2) Let the slope of a straight line be the distance between two points |AB|==
If x is eliminated, the distance between a and b is |AB|=
④ In a given conic, there are usually two methods to solve the linear equation where the chord AB of the midpoint (m, n) is located: (1) the relationship between roots and coefficients: substitute the linear equation into the equation of the conic, get a quadratic equation with one variable after elimination, and establish the equation to solve it by using the relationship between roots and coefficients and the coordinate formula of the midpoint. (2) Point difference method: If there are two different intersections a and b between a straight line and a conic curve, firstly, the equation of substituting the intersection coordinates into the curve is established, and then the relationship between the midpoint coordinates and the slope is established through the difference.
⑤ college entrance examination requirements
In the college entrance examination, the comprehensive questions linked by straight lines and conic curves mostly appear in the form of high scores and finale questions, which mainly involve the determination of position relationship, chord length, maximum value, symmetry, trajectory and so on. The combination of numbers and shapes, classified discussion, functional equation, equivalent transformation and other mathematical thinking methods are highlighted, which requires candidates to have high ability of analyzing and solving problems and calculating, which is conducive to candidates' choice.
Whether a straight line and a conic have a common point or several common points is actually to study whether the equations formed by their equations have real number solutions or the number of real number solutions. At this time, we should pay attention to the idea of classified discussion and combination of numbers and shapes.
When a straight line intersects a conic curve, the chord length is involved. Vieta theorem is often used to set the chord length, and the chord length is not calculated (that is, the chord length formula is applied). When it comes to the midpoint of chord length, the "point difference method" is often used instead of finding it. The slope of the straight line where the chord is located is related to the coordinates of the midpoint of the chord. We should fully explore the implicit conditions of the topic and find the flexible transformation of the relationship between quantity and quantity.
Second, self-test exercise: self-test (mutual evaluation, other evaluation) score: _ _ _ _ _ _ _ _ _ Parent's signature: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(a) multiple-choice questions (5 points for each question, * *10, ***50 points)
1, it is known that the length of a chord whose midpoint is (1, 1) is ().
(A)(B)(C)(D)
2. If the two asymptotes are x+2y=0 and x-2y=0 respectively, the hyperbolic equation with chord length obtained by cutting the straight line x-y-3=0 is ().
(A)(B)(C)(D)
3, hyperbola, the intersection point P( 1, 1) is a straight line m, so that the straight line m and hyperbola only have a common * * * point, then the straight line M * * satisfying the above conditions has ().
(a) One article (b) Two articles (c) Three articles (d) Four articles
4、( 10? Liaoning) Let the focus y2=8x of the parabola be F, the directrix be L, P be the point on the parabola, PA⊥l, and A be the vertical foot. If the slope of the straight line AF is -3, then |PF|= ().
A.43B.8C.83D. 16
5. The straight line L passing through point M (-2,0) intersects with ellipse x2+2y2=2 at P 1, P2, and the midpoint of straight line P 1P2 is P. Let the slope of straight line L be k 1(k 1≠0) and the slope of straight line OP.
A.- 12B。 -2C. 12D.2
6. It is known that the equation of parabola C is x2= 12y, and the straight line passing through point A (0,-1) and point B (t, 3) has nothing in common with parabola C, so the value range of real number T is ().
A.(-∞，- 1)∩( 1，+∞)B.-∞，-22∪22，+∞
C.(-∞，-22)∩(22，+∞)D.(-∞，-2)∩(2，+∞)
7. The known points F 1 and F2 are hyperbolas X2A2-Y2B2 =1(a >; 0, b>0), a straight line passing through F 1 and perpendicular to the x axis intersects the hyperbola at points A and B. If △ABF2 is a regular triangle, the eccentricity of the hyperbola is ().
A.2B.2C.3D.3
8.( 12 Shandong) It is known that the eccentricity of ellipse C is that the asymptote of hyperbola x2-y2= 1 has four intersections with the ellipse, and the area of the quadrilateral with these four intersections as the vertex is 16, then the equation of ellipse C is
9. If the straight line y=kx+2 intersects the right branch of the hyperbola x2-y2=6 at two different points, then the range of k is ().
A.- 153， 153B.0， 153C。 - 153，0D。 - 153,- 1
10, known ellipse c: (a >; B>0) has an eccentricity of 0, passes through the right focus F, and has a slope of k (k >; 0) and c intersect at point a and point b, if. So k=
(A) 1(B)(C)(D)2
(2) Fill in the blanks (5 points for each question, ***4 small questions, ***20 points)
1 1, given an ellipse, there are two different points on the ellipse that are symmetrical about a straight line, then the value range of is.
12, and the chord length of the parabola is, then.
13. It is known that the vertex coordinates of parabola C are the origin and the focus is on the X axis. The straight line y=x intersects with parabola C at point A and point B. If it is the midpoint, the equation of parabola C is.
14, among the following propositions about conic curves.
① Let A and B be two fixed points, and k be a non-zero constant, then the trajectory of the moving point P is a hyperbola;
② A fixed point A on the overdetermined circle C is the moving chord AB of the circle, and O is the coordinate origin. If so, the trajectory of the moving point P is an ellipse;
③ The two roots of the equation can be regarded as eccentricity of ellipse and hyperbola respectively;
Hyperboles have the same focus.
The serial number of the true proposition is (write the serial number of all true propositions)
(3) Solving problems (15, 16, 17, 12, 18, * * 50).
15. In the plane rectangular coordinate system xOy, the straight line L passing through the point (0,2) and having a slope of k and the ellipse x22+y2= 1 have two different intersections p and q. 。
(1) Find the value range of k;
(2) If the intersections of an ellipse with the positive semi-axis of the X axis and the positive semi-axis of the Y axis are A and B respectively, is there a constant k that makes the vectors OP→+OQ→ and AB → * *? If it exists, find the value of k; If it does not exist, please explain why.
16. Take two fixed points A1(-2,0) and A2 (2,0) on the rectangular coordinate system xOy, and then take two fixed points N1(0, m), N2 (0 0,n) and mn=3.
(1) Find the equation of the locus m where the straight line A 1N 1 intersects with A2N2;
(2) known point A( 1, t) (t >; 0) is a fixed point on the trajectory m, and e and f are two moving points on the trajectory m. If the slope kAE of the straight line AE and the slope kAF of the straight line AF satisfy kAE+kAF=0, try to find whether the slope of the straight line EF is constant. If it is a fixed value, find this fixed value, if not, explain the reason.
17.(09 Shandong) Set an ellipse e: (a, b >；; 0) after m and n, o is the origin of coordinates,
(i) Find the equation of ellipse E;
(II) Is there a circle whose center is at the origin, so that any tangent of the circle and ellipse E always has two intersections A and B? If it exists, write the equation of the circle and find the range of |AB|. If it does not exist, explain why.
18.( 1 1 Shandong) In the plane rectangular coordinate system, the ellipse is known. As shown in the figure, a straight line with a slope not exceeding the origin intersects the ellipse at two points, the midpoint of the line segment is, the ray intersects the ellipse at one point, and the straight line intersects the point.
(i) Minimum value;
(2) What if? ,
(i) Verification: A straight line passes through a fixed point; (2) Question: Can it be about axial symmetry? If yes, find out the circumscribed circle equation at this time; If not, please explain why.
2020 Senior Two Mathematics Summer Homework Answers Daquan 5
First, multiple choice questions
1. The calculation result is equal to ()
Asian Development Bank.
2. ""Yes ""()
A. sufficient and unnecessary conditions. B. necessary and insufficient conditions.
C. necessary and sufficient conditions. D. Conditions that are neither sufficient nor necessary
3. In △ABC, c = 120, tanA+tanB=23, then tanA? The value of tanB is ()
A. 14B
4. If (0, π) is known, then = ()
A. 1B。 Ad 1
5. Known equal to ()
Asian Development Bank.
6.[20 12? Chongqing volume] sin 47-sin17cos30cos17 = ()
A.B.- 12C. 12D。
7. Let it be the two roots of the equation, then the value is ().
A. BC 1D.3
8.()
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Second, fill in the blanks
9. The value of this function is;
10.=;
1 1. Let's estimate the value when k = 1, 2, 3. The guessing range of k∈N_ is (the result is represented by k).
12. It is known that the vertex of the angle is at the coordinate origin, the starting edge coincides with the positive semi-axis of the X axis, the abscissa of the intersection of the ending edge of the angle and the unit circle is, and the ordinate of the intersection of the ending edge of the angle and the unit circle is, then =.
Third, answer questions.
13. A classmate found in research study that the values of the following five formulas are all equal to the same constant:
( 1)sin 2 13+cos 2 17-sin 13 cos 17；
(2)sin 2 15+cos 2 15-sin 15 cos 15；
(3)sin 2 18+cos 2 12-sin 18 cos 12；
(4)sin 2(- 18)+cos 248-sin(- 18)cos 48；
(5)sin 2(-25)+cos 255-sin(-25)cos 55。
(1) Try to find this constant by choosing one of the above five formulas;
(2) According to the calculation result of (1), extend this classmate's discovery to trigonometric identities and prove your conclusion.
14. Known functions
(1) Find the minimum positive period of the function f(x);
(2) the value of 2)if.
15. It is known that in △ABC, sinA(sinB+cosB)-sinC=0, sinB+cos2C=0, and the sizes of angles A, B and C are found.
16. Known,,,
( 1); (2) the value.
Let α be an acute angle, and if cos = 45, the value of sin is _ _ _ _ _.
answer
1 ~ 8 babadcac； 9.； 10.； 1 1.； 12.；
13.(2) The trigonometric identity is sin2α+cos2 (30-α)-sinα cos (30-a) = 34.
The proof is as follows: sin2α+cos 2 (30-α)-sinα cos (30-α)
= sin 2α+(cos 30 cosα+sin 30 sinα)2-sinα(cos 30 cosα+sin 30 sinα)
= sin 2α+34 cos 2α+sinαcosα+ 14 sin 2α-sinαcosα- 12 sin 2α= 34 sin 2α+34 cos 2α= 34。
14.( 1); (2); 15.
16.( 1); (2);
2020 Senior Two Mathematics Summer Homework Answers Daquan 6
1? 1 rate of change and derivative
1. 1. 1 rate of change
1 . D2 . D3 . C4 .-3δt-65 .δx+26.3？ 3 1
7.( 1)0? 1(2)0? 2 1(3)2? 18. 1 1m/s， 10？ 1m/s 9.25+3δt 10. 128 a+64 a2 t 1 1 . f(δx)-f(0)δx = 1+δx(δx & gt； 0),
- 1-δx(δx & lt； 0)
1? 1? 2 the concept of derivative
1 . D2 . C3 . C4- 15 . x0，δx； x06.67.a= 18.a=2
9.-4
10.( 1)2t-6(2) The initial velocity is v0=-6, and the initial position is x0= 1(3) After the movement starts, it changes to the left by 8m (4) X = 1, and V = 6.
1 1. The rising speed of water surface is 0? 16m/ min. Hint: δ V = δ H75+ 15δ H+(δ H) 23,
Then δ v δ t = δ h δ t× 75+15 δ h+(δ h) 23 means lim δ t → 0 δ v δ t = lim δ t → 0 δ h δ t× 75+05 δ h+(δ h) 23 = lim δ t → 0 δ h δ t× 25,
That is, v ′ (t) = 25h ′ (t), then h ′ (t) =125x4 = 0? 16 (m/min)
1? 1? Geometric meaning of the third derivative (1)
1.C2 B3. B4. f(x) slope of tangent at x0, y-f(x0)=f'(x0)(x-x0).
5.36. 135 7. What is the slope of the secant? 3 1, and the slope of the tangent is 38. k =- 1，x+y+2 = 0。
9.2x-y+4 = 010.k =14, and the tangent coordinates are 12 and 12.
1 1. There are two intersections, and the coordinates are (1, 1), (-2, -8).
1? 1? Geometric Significance of the Third Derivative (2)
1.C2 a3 . B4 . y = x+ 15。 16.37 . y = 4x- 18. 1039. 19
10.A = 3，B =- 1 1，C = 9。 Tip: First find out the relationship among A, B and C, that is, c=3+2a.
B=-3a-2, and then find the slope of point (2,-1) to get k=a-2= 1, that is, a=3.
1 1.( 1)y =- 13x-229(2) 125 12
1? Calculation of the derivative of 2
1? 2? 1 derivatives of several commonly used functions
1.C2 d 3.4 c 4. 12，05.45 6。 S=πr2
7.( 1)y = x- 14(2)y =-x- 148 . x0 =-3366
9.y= 12x+ 12，y= 16x+32。 Note: Note that point P (3,2) is not on the curve 10. Proof abbreviation, area unchanged 2.
1 1. Tip: As can be seen from the figure, point P is on the image below the X axis, so y=-2x, then y'=- 1x, let y'=- 12, and x=4, so P(4,-)
1? 2? 2. Derivation formula and algorithm of basic elementary function (1)
1.a2 . a3 . c 4 . 35 . 2 lg2+2 lge 6. 100！
7. (1)1cos2x (2) 2 (1-x) 2 (3) 2excosx8.x0 = 0 or x0 = 2 2.
9.( 1)π4，π2(2)y=x- 1 1
10.k=2 or k=- 14. Tip: If the tangent point is P(x0, x30-3x20+2x0), the slope is k=3x20-6x0+2, and the tangent equation is y-(x30-3x20+2x0) = (.
1 1. Tip: Let the tangent point of C 1 be P(x 1, x2 1+2x 1), then the tangent equation is: y = (2x1+2. Let the tangent point of C2 be Q(x2-x22+a), then the tangent equation is: y =-2x2x+x22+a. And since L is the common tangent of the intersection of P and Q, x 1+ 1=-x2.
-x2 1=x22+a, when x2 is eliminated, the equation 2x2 1+2x 1+0+a = 0. Because C 1 and C2 have only one common tangent, there is δ = 0, and the solution is A =- 10.
2. Derivation formula and derivation algorithm of basic elementary function (2)
1.D2 a 3 . c 4.50 x(2+5x)9-(2+5x) 10x 25 . 336 . 97 . a = 1
8.y=2x-4, or y=2x+69.π6
10.y'=x2+6x+62x(x+2)(x+3)。 Prompt: y = lnx (x+2) x+3 =12 [lnx+ln (x+2)-ln (x+3)]
1 1.a=2，b=-5，c=2，d=- 12
1? The Application of Third Derivative in Function Learning
1? 3? Monotonicity and derivative of 1
1.A2.B3.C4.33，+∞5。 Monotonically decreasing by 6. ①②③.
7. The function monotonically increases at (1, +∞) and (-∞,-1), and monotonically decreases at (-1, 0) and (0, 1).
8. In the interval (6, +∞), (-∞, -2) monotonically increases, and in the interval (-2, 6) monotonically decreases. A ≤-3。
10 . a & lt； 0, increasing range:-13a,-13a, decreasing range:-∞,-13a,+∞.
11.f' (x) = x2+2ax-3a2, when a
1? 3? Extreme value and derivative of function 2
/kloc-0 1.B2.B3.A4.55.06.4e27 Infinite value
8. The maximum value is f- 13=a+527, and the minimum value is f( 1)=a- 1.
9. (1) f (x) =13x3+12x2 -2x (2) increasing range: (-∞, -2), (1,+∞), decreasing range: (-2, ∞).
10.a=0，b=-3，c=2
1 1. According to the meaning of the question, there is 1+a+b+c=-2.
3+2a+b=0, and a=c is obtained.
B=-2c-3, so f' (x) = 3x2+2cx-(2c+3) = (3x+2c+3) (x-1). Let f ′ (x) = 0, x= 1 or x =-2c+.
① If -2c+33
②If-2c+33 & gt； 1, which is C.
1? 3? (Small) Values and Derivatives of Three Functions
1.B2 . C3 . a4 . x & gt； Sinx5.06.[-4，-3]7。 The minimum value is -2 and the value is 1.
8.A =-29。 (1) A = 2, B =- 12, C = 0 (2) the value is f(3)= 18, and the minimum value is f(2)=-82.
10. The value is ln2- 14, and the minimum value is 0.
1 1.( 1)h(t)=-T3+t- 1(2)m & gt； 1. hint: let g(t) = h (t)-(-2t+m) =-T3+3t-1-m, then when t ∈ (0,2), the function g (t)
1? 4 examples of optimization problems in life (1)
/kloc-0 1.b2.c3.d4.32m,16m5.40km/h6.1760 yuan 7. 1 15 yuan.
8. When q=84, the profit is 9.2.
10. (1) y = kx-12+2000 (x-9) (14 ≤ x ≤ 18) (2) When the commodity price drops to each piece/kloc-0.
1 1. The water supply station is built between A and D, 20km away from a factory, which can save the cost of laying water pipes.
1? 4 examples of optimization problems in life (2)
1.B3.D4 square with side length s 5.36. 10,/kloc-0 196007.2ab
8.4 cm
9. When the length of a circle is x = 100▼+4cm, the sum of the areas is the smallest.
Tip: Let one section of a circle be X, the other section be 100-x, and the sum of the areas of a square and a circle be S, then S=πx2π2+ 100-x42(0
10.h=S43，b=2S427 1 1.33a
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