Why did you do so badly in the exam? From the surface of the paper, there is no problem in the blank paper, and he can start every problem, but the beginning is wrong, which shows that he is still in an incomprehensible state of knowledge and his ability has not yet formed.
In order to completely change this situation, it seems necessary to scan the textbook knowledge again, understand concepts, laws, learn basic methods, master basic ideas, clarify ambiguity, clarify right and wrong, and eliminate doubts.
The following are specific errors:
1. The discussion about the inclusion relation of sets is exposed, ignoring the existence of empty sets.
1. The number of sets p that match the {a, b} contained in the {a, b, c} is.
2. If the set A = {x | x2-3x+2 = 0}, B={x|mx-2=0}, and B is a subset of A, then the set consists of the real number m. 。
2. I can't control the complicated set problem.
3. the known set a = {x | x2-ax+a2- 19 = 0}, b = {m | m2-5m+4.
3. I don't understand the sufficient and necessary conditions clearly.
4. "x-1= 0" is the condition that "(x- 1)(x-3)=0".
5. set a = {x | x >；; 2, or x < 1}, B = {x | x & lt0}, then "x∈ A" is the condition of "x∈ B".
4. Lack of understanding of the nature of inequality.
6. If a>b, d>c, the following inequality holds ()
a a+c & gt； b+ d B ad & gt； 200 BC to 200 BC. b-D D c/a & gt； bill of lading
7. When a> is 1, the range of algebraic expression (a-1)+1(a-1) is.
8. Comparison size: (a2- 1)2 and A4-3a2+a. 。
5. Have not mastered the basic methods to solve inequality.
9. The solution set of inequality x2+5x-6≤0 is.
10. The solution set of inequality x/( 1-x)≤ 1 is.
1 1. Solve inequality:
⑴|x2-3x|≥4。
⑵x2-(a+ 1)x+a & lt； 0 .
6. The relationship among inequality, function and equation is not clear.
12. inequality x2+ax+b
13. When k is what value, the inequality (k-1) x2+(k-1) x+4 >; The solution set of 0 is r.
7. Weak application of inequality.
14. There is a rule in the market: the higher the price of a commodity, the fewer people buy it, and the lower the price, the more people buy it. If a magazine can issue 654.38+million copies at the price of 2 yuan, the circulation of each book will be reduced by 5,000 copies every time the price of 0.2 yuan is raised. If the total income is not less than 224 thousand yuan, then we must seek the pricing range of the magazine.
Mathematics examination questions at the end of last semester in senior one.
Note: 1. The total score of the test paper is 150, and the test time is 120 minutes;
2. Calculators are not allowed;
(Volume I)
1. Multiple choice questions (only one option in each question is correct, with 5 points for each question and 50 points for * * *).
1. The geometry shown in the three views on the left is ().
A. hexagonal prism B. hexagonal prism C. hexagonal pyramid D. hexagon
2. The following propositions:
(1) Two straight lines parallel to the same plane are parallel;
(2) Two straight lines perpendicular to the same plane are parallel;
(3) Two planes parallel to the same straight line are parallel;
(4) Two planes perpendicular to the same straight line are parallel;
The correct one is ()
A.( 1) (2) and (4) B. (2) and (4) B. (2) (3) and (4) D. (3) and (4)
3. Let A be on the X-axis, and its distance to P (0 0,3) is twice that to Q (0, 1,-1), then the coordinate of point A is ().
A.( 1, 0,0) and (-1, 0,0 0) B. (2 2,0,0) and (-2,0,0).
C. (,0,0) and (–,0,0) D. (–,0,0) and (,0,0).
4. Let the height on the hypotenuse AB of Rt△ABC be CD, and AC=BC=2. Fold the height CD into two straight faces.
Angle A-CD-B (as shown in the figure), then the cosine of dihedral angle C-AB-D is equal to ().
A.B. C. D。
(Figure 4)
(Figure 5)
5. As shown in the figure, it is a prism with a volume of 1, and the volumes of the four pyramids are ().
A.B. C. D。
6. According to the data in the table, it can be determined that the interval where a root of the equation ex-x-2=0 is located is ().
x
- 1
1
2
three
Ex-husband; Ex-wife; Ex-boyfriend; Ex-girlfriend
0.37
1
2.72
7.39
20.09
x+2
1
2
three
four
five
A.(- 1，0) B. (0， 1) C. ( 1，2) D. (2，3)
7. Points E, F, G and H are respectively in the space quadrilateral ABCD.
The midpoint of AB, BC, CD and AD, if AC=BD, and
Both AC and BD are 900, so the quadrilateral EFGH is ()
(a) rhombus (b) trapezoid
(Figure 7)
(c) Square (d) Spatial quadrilateral
8. It is known that the even function defined on the set of real numbers is increasing function in the interval (0,+), so the size relation of sum is ().
A.y 1 & lt； y3 & lty2 b . y 1 & lt； y2 & lty3 C. y3 & lty 1 & lt； y2 D. y3 & lty2 & lty 1
9. The positional relationship between the straight line y = x and the circle (x-2)2+y2=3 is ().
(a) The straight line passes through the center of the circle (b) The straight line intersects the circle, but it does not pass through the center of the circle.
(c) A straight line is tangent to a circle (d) A straight line and a circle have nothing in common.
10. If the sum of the maximum and minimum values of the function is, the value of is ().
A. The 4th day of the 2nd year BC
(Volume II)
Fill in the blanks (5 points for each small question, 20 points for * * *)
1 1. Make a cone model with arc length equal to 12 decimeter and radius of 10 decimeter. The volume of this cone is equal to cubic decimeter.
12. The slope of the straight line L is -2, and the sum of its intercepts on the X axis and Y axis is 12, so the general equation of the straight line L is.
13. In the past 12 years, the functional relationship between the total output of a product and time t (year) is shown in the figure, and the following four statements are made:
(1) The total output increased faster and faster in the first three years;
(2) The growth rate of total output in the first three years is getting slower and slower;
(3) Stop producing the product in the third to eighth years;
(4) From the eighth year to 12, the total output increased at a constant speed.
The correct statement is. (DrawingNo. 13)
14. Fold a drawing once, so that points (0,2) and (-2,0) coincide, and points (2004,2005) coincide with points (m, n), then the value of m-n is
3. Answer questions (this big question is ***6 small questions, ***80 points. The solution should be written in words, proving the process or calculation steps)
15. (This little question is 12)
Given the set A=, b = {x | 2.
(1) find A∪B, (CRA) ∩ b; (2) if A∩C≠φ, find the value range of a. ..
16. (This little question is 12)
△ABC, the equation of the straight line with the side height of BC is y=0, if the coordinate of point B is (1, 2).
Find the coordinates of point (1)A; (2) the coordinates of point C.
17 (this small question 14 points)
As shown in the figure, the points in the cuboid, and are the midpoint.
(1) Verification: straight line ‖ plane;
(2) verification: plane plane;
(3) Verification: straight line plane.
18
(This small question 14 points)
Party A and Party B have investigated the scale (total output) of eel farming in rural areas of a county for six consecutive years, provided two aspects of information, and got two pictures, namely:
According to a survey, the average output of each fish pond increased from 654.38+0,000 in 654.38+0 years to 20,000 in 6 years.
Survey B showed that the total number of fish ponds in the county decreased from 30 in 1 year to 10 in the sixth year.
Please explain according to the information provided:
(1) Number of fish ponds and total eel production in the county in the second year.
(2) By the sixth year, has the eel farming scale (i.e. total output) in this county expanded or decreased compared with 1 year? Explain why.
(3) Which year has the largest scale (i.e. total output)? Explain why.
19. (This little question is 14)
Let real numbers meet the conditions at the same time: and
(1) Find the analytic formula and domain of the function;
(2) judging the parity of the function;
(3) If the equation happens to have two different real roots, the value range of the solution.
20. (This little question is 14)
The radius of a circle is 3, the center of the circle is on a straight line, and below the axis, the chord length of the circular section axis is. (1) Find the circle equation;
(2) Is there a straight line with a slope of 1 that makes the circle with the diameter of the chord cut by the circle pass through the origin? If it exists, the equation is solved; If it does not exist, explain why.
Senior one took the final exam last semester.
Answers to math test questions in senior one.
Student number, class name, student number score
First, multiple-choice answer sheet
Title number
1
2
three
four
five
six
seven
eight
nine
10
answer
2. Fill in the blanks (4 small questions in this big question, 5 points for each small question, 20 points for * * *)
1 1.____________________ 12.____________________
13.____________________ 14.____________________
3. Answer questions (this big question is ***6 small questions, ***80 points. The solution should be written in words, proving the process or calculation steps)
15. (The full mark of this question is 12)
16. (The full mark of this question is 12)
17. (The full mark of this question is 14)
18. (The full mark of this question is 14)
19. (The full mark of this question is 14)
20. (The full mark of this question is 12)
Shenzhen senior high school last semester final exam in 2005-06 school year.
The reference answer of the first grade mathematics examination questions.
First, multiple-choice questions (5 points for each small question, 50 points * * *) CBA BC CCCCB
Fill in the blanks (5 points for each small question, 20 points for * * *)
1 1.96 。 12.2x+y-8=0 . 13.(2) (3) (4) 。 14.- 1 。
Three. Problem solving (* * * 80 points)
15. (This little question is 12)
Given the set A=, b = {x | 2.
(2) find A∪B, (CRA) ∩ b; (2) if A∩C≠φ, find the value range of a. ..
Solution: (1) a ∪ b = {x |1≤ x <10}-(3 points)
(CRA)∩B = { x | x & lt； 1 or x ≥ 7} ∩ {x | 2
= { x | 7≤x & lt； 10}-(9 points)
(2) when a >; 1 satisfies a ∩ c ≠ φ-(12).
16. (This little question is 12)
△ABC, where the linear equation of BC side height is y=0, and if the coordinate of point B is (1, 2), find the coordinate of point A (1); (2) the coordinates of point C.
Solution: (1) Get the coordinates of point A (-1, 0). -(4 points)
(2) The bisector of angle A is y=0, so the equation for finding the straight line AC from point A and point D is -(8 points) relative to the symmetrical point D( 1, -2) of y=0.
The equation of the straight line with the height of BC side is,
The equation of line BC is y-2=-2(x- 1).
According to the equations of AC and BC, the coordinate of point C is (5, -6)-12.
17 (this small question 14 points)
As shown in the figure, the points in the cuboid, and are the midpoint. (1) Verification: straight line ‖ plane; (2) verification: plane plane; (3) Verification: straight line plane. Solution: (1) Let AC and BD intersect at POint O, even po,
P and o are the midpoint of BD, so PO//,
So the straight line ‖ plane -(4 points)
(2) In a cuboid,
If the bottom ABCD is square, then AC BD
And ABCD, and then AC,
So for AC plane, plane plane-(9 points).
(3)PC2=2, PB 12=3, and B 1C2=5, so △PB 1C is a right triangle. PC，
Similarly, PA, so straight line plane. -( 14 points)
18. (This little question is 14)
Party A and Party B have investigated the scale (total output) of eel farming in rural areas of a county for six consecutive years, provided two aspects of information, and got two pictures, namely:
According to a survey, the average output of each fish pond increased from 654.38+0,000 in 654.38+0 years to 20,000 in 6 years.
Survey B showed that the total number of fish ponds in the county decreased from 30 in 1 year to 10 in the sixth year.
Please explain according to the information provided:
(1) Number of fish ponds and total eel production in the county in the second year.
(2) By the sixth year, has the eel farming scale (i.e. total output) in this county expanded or decreased compared with 1 year? Explain why.
(3) Which year has the largest scale (i.e. total output)? Explain why.
Solution: According to the meaning of the question, the image in Figure A passes through (1, 1) and (6,2).
In this way, the analytical formula obtained is Y A = 0.2x+0.8-(2 points).
The image in Figure B passes through two points (1, 30) and (6, 10).
So the analytical formula is y b =-4x+34. ——(4 points).
(1) When x=2, Y A =0.2×2+0.8 = 1.2, y B = -4×2+34=26,
Y A Y B = 1.2×26=3 1.2。
So in the second year, there were 26 fish ponds, and the total number of eels produced in the county was 31.2000. -(6 points)
(2) The fish yield in1year is 1×30=30 (ten thousand), and the fish yield in the sixth year is 2× 10=20 (ten thousand). It can be seen that the eel breeding plan in the sixth year of this county is smaller than that in 1 year.
(3) Let the total output of scale in M year be n,
Then n = YAYB = (0.2m+0.8) (-4m+34) =-0.8m2+3.6m+27.2.
=-0.8(m2-4.5m-34)=-0.8(m-2.25)2+3 1.25-(65438。
Therefore, when m=2, the maximum value of n =3 1.2.
That is to say, in the second year, the eel breeding industry was the largest, with the highest output of 31.20 thousand. ——( 1.4 points).
19. (This little question is 14)
Let real numbers meet the conditions at the same time: and
(1) Find the analytic formula and domain of the function;
(2) judging the parity of the function;
(3) If the equation happens to have two different real roots, the value range of the solution.
Solution: (1)-(1).
-(2 points).
.
The domain of a function is the set d =. ——(4 points).
(2) If yes, =-(6 points)
Similarly, when, there is.
Anyway, there is a odd function in the domain. ——(8 points).
(3) simultaneous equations can be obtained,
——(9 points).
(i) When, that is, when the equation has only one solution, which is inconsistent with the meaning of the question; -(10)
(ii) When the equation is an unary quadratic equation,
In order to make the equation have two different real roots, then
Solution, but because the image of the function is in the second and fourth quadrants. -(13 points)
Therefore, the slope of the straight line can be summarized or-(14 points).
20. (This small question 14 points) The radius of the circle is 3, the center of the circle is on a straight line, and below the axis, the chord length of the axis cut by the circle is. (1) Find the circle equation;
(2) Is there a straight line with a slope of 1 that makes the circle with the diameter of the chord cut by the circle pass through the origin? If it exists, the equation is solved; If it does not exist, explain why.
B
A
O
Y
X
L
C
C
Solution: (1) as shown in Figure Yizhi C( 1, -2)
The equation of circle C is (X- 1) 2+(Y+2) 2 = 9-(4 points).
(2) Let the equation L y=x+b, and the circle with the diameter of AB passes through the origin, then
OA OB, let A(x 1, y 1) and B(x2, y2), then
X 1x2+Y 1Y2 = 0①-(6 points)
allow
-(8 points)
In order to make the equation have two different real roots, then
△ = > 0 means < b<- (9 points)
——( 10).
Substitute y 1=x 1+b and y2=x2+b into x 1x2+ y 1y2=0 to get 2x1x2+(x1+x2) b+
That is b2+3b-4=0, b=-4, b= 1 (discarded)-.
So there is a straight line L that satisfies the condition, and the equation is or-(14 minute).
Source: China Philosophers Network
Author: anonymous
Online reading of senior high school information.
This paper is the final math test paper of senior one last semester.
The first part: the final examination paper of mathematics in the last semester of senior one.
Next: Senior one's last semester math final exam questions (Volume B)