Junior two mathematics Shanghai education edition volume two final examination questions.
First, multiple-choice questions (this big question 10 small questions, 3 points for each small question, 30 points for * * *).
1. The quadratic root is meaningful if ()
A.x & gt2 B.x & lt2 C.x？ 2 D.x？ 2
2. The following groups of numbers can be used as the length of three sides of a right triangle is ().
A. 1，2，3 B.3，4，5 C.4，5，6 D.7，8，9
3. The number of target rings of a shooter's five shots is as follows: 6, 7, 9, 8, 9, and the median of these five data is ().
a6 b . 7 c . 8d . 9
4. If the point (3, 1) is in the linear function y = kx-2 (k? 0), then the value of k is ()
A.5 B.4 C.3 D. 1
5. The following formula must be the simplest quadratic root ()
A.B. C. D。
6. As shown in the figure, in the rectangular ABCD, diagonal lines AC and BD intersect at point O,? ACB=30？ And then what? The size of AOB is ()
.30 caliber? B.60？ C.90？ D. 120？
7. As shown in the figure, in the rhombic ABCD, diagonal AC and BD intersect at point O, OE∨DC intersects at point E, and AD= 10cm, then the length of OE is ().
6 cm long, 5 cm wide, 4 cm high and 3 cm deep.
8. As shown in the figure, draw an arc with the origin o as the center and OB as the radius, intersect with the number axis at point A, and the number represented by point A is X, then the cube root of x2- 10 is ().
A.B.﹣ C.2 D.﹣2
9. It is known that the images of linear functions y=2x+a and Y =-x+B both pass through a (-2,0) and intersect the Y axis at b and c respectively, so the area of △ABC is ().
a4 b . 5 c . 6d . 7
10. Translate a small diamond with a side length of 1 to get a beautiful one? Chinese knot? Mode. Are the following four patterns similar after translation? Chinese knot? , in which the (1) th graph contains two diamonds with side length of 1, the (2nd) graph contains eight diamonds with side length of 1, the (3rd) graph contains 18 diamonds with side length of 1, and the (3rd) graph contains1.
32 BC to 36 BC
2. Fill in the blanks (6 small questions in this big question, 4 points for each small question, ***24 points)
1 1.20 14 In the physical fitness test for junior high school graduates in Chongqing, the physical fitness test scores (unit: minutes) of seven students in a school are as follows: 50, 48, 47, 50, 48, 49 and 48. The pattern of this set of data is.
12. As shown in the figure, in ABCD, diagonal AC and BD intersect at point O. Please add a condition to make ABCD a diamond (just write a condition that meets the meaning of the question).
13. In the function, the range of independent variable x is.
14. The image of the linear function y =-3x+6 does not pass through the quadrant.
15. In △ABC,? C=90？ If a+b=7cm and c=5cm, the area of △ABC is.
16. As shown in the figure, in the rhombic ABCD, AB=4,? A= 120？ If points P, Q and K are arbitrary points on line segments BC, CD and BD, the minimum value of PK+QK is.
Third, solve the problem (3 small questions in this big question, 6 points for each small question, *** 18 points)
17.？ ﹣ ? 2 .
18. As shown in the figure, quadrilateral ABCD is a parallelogram, diagonal lines AC and BD intersect at point O, and straight lines EF intersecting with point O intersect at points E and F respectively, which proves that AE = CF 。
19. In order to know the water consumption of residents in a residential area, the monthly water consumption of residents in this residential area 10 was randomly selected, and the results were as follows:
Monthly water consumption (ton)1013141718
Number of families 2 2 3 2 1
(1) Calculate the average monthly water consumption of this family;
(2) If there are 500 households in this community, according to the above calculation results, how many tons of water do residents in this community use every month?
Fourth, solve the problem (3 small questions in this big question, 7 points for each small question, ***2 1 point)
20. It is known that after the rectangular paper ABCD is folded along EF, point D coincides with point B, and point C falls on point C? In position, if? 1=60? ，AE=2。
(1) Q? 2,? 3 degrees.
(2) Find the area s of rectangular ABCD paper.
2 1. As shown in the figure, the straight line Y =-x+ 10 intersects with the X axis and the Y axis at point B and point C respectively, the coordinate of point A is (8,0), and P(x, y) is the first quadrant straight line Y =-x+ 10.
(1) Find the functional relationship between the area s of △OPA and x, and write the range of the independent variable x;
(2) When the area of △OPA is 10, find the coordinates of point P. 。
22. As shown in the figure, in △ABC, point D and point E are the midpoint of BC and AC sides respectively, and point A is the extension line of ABC intersection point d E at point F, connecting AD and CF. 。
(1) Verification: Quadrilateral ADCF is a parallelogram;
(2) When △ABC meets what conditions, the quadrilateral ADCF is a diamond? Why?
V. Answer questions (3 small questions in this big question, 9 points for each small question, 27 points for * * *)
23. As shown in the figure, take a point E outside the square ABCD to connect AE, BE and de, and the crossing point A is the perpendicular of AE, if AE=AP.
(1) verification: △ Abe △ ADP;
(2) verification: BE? De.
24. City A has two sets of 10 and city B has six sets of stocks, so it is decided to support village C10 and village D. It is known that the freight charges for transporting a machine from city A to village C and village D are 400 yuan and 800 yuan respectively, and the freight charges for transporting a machine from city B to village C and village D are 300 yuan and 500 yuan respectively.
(1) Let machine X be transported from city B to village C, and find the function relation of total freight W about X;
(2) How many transportation schemes does * * * have if the total freight is required to be less than 9000 yuan?
(3) Find out the transportation scheme with the lowest total freight, and what is the lowest freight?
Fill in the following table for the analysis of known conditions:
Inventory machines support villages c and d.
Six (6-x) units in B city.
A city has12 (10-x) and [8-(6-x)] sets.
25. In the plane rectangular coordinate system, points A(a, 0) and C(0, b) are known, and A and B satisfy (a+ 1)2+ =0.
(1) Write directly: a=, b =；;
(2) As shown in the figure, point B is a point on the positive semi-axis of X axis, and point B is BE? AC is at point e, cross the y axis at point d, and then connect with OE. What if OE shares it equally? AEB, what is the size relationship between OB and OC at this time? Prove your conclusion.
(3) Under the condition of (2), find the analytical formula of the straight line BE.
The second grade mathematics Shanghai Education Edition Volume II Final Examination Paper Reference Answer
First, multiple-choice questions (this big question 10 small questions, 3 points for each small question, 30 points for * * *).
1. The quadratic root is meaningful if ()
A.x & gt2 B.x & lt2 C.x？ 2 D.x？ 2
The analysis can be calculated according to the formula that the number of roots is greater than or equal to 0, and the solution can be obtained.
Solution: from the meaning of the question, x-2? 0,
Get x? 2.
So choose C.
Comment on the knowledge points examined in this question: the number of roots of quadratic form is non-negative.
2. The following groups of numbers can be used as the length of three sides of a right triangle is ().
A. 1，2，3 B.3，4，5 C.4，5，6 D.7，8，9
To analyze the inverse theorem of Pythagorean theorem, we only need to verify that the sum of squares of two small sides is equal to the square of the longest side.
Solution: a, because 12+22? 32, so it is not the Pythagorean number; Therefore, the option is wrong;
B, because 32+42=52 is the number of stocks. Therefore, the option is correct;
C, because 42+52? 62, so it is not the Pythagorean number; Therefore, the option is wrong;
D, because 72+82? 92, so it's not Pythagoras number. Therefore, the option is wrong;
Therefore, choose: B.
Comment on the application of the inverse theorem of Pythagorean theorem. To judge whether a triangle is a right triangle, we only need to use the inverse theorem of Pythagorean theorem to judge the length of three sides of the triangle.
3. The number of target rings of a shooter's five shots is as follows: 6, 7, 9, 8, 9, and the median of these five data is ().
a6 b . 7 c . 8d . 9
The analysis is based on the concept of median.
Solution: This set of data is arranged as follows: 6, 7, 8, 9, 9,
The median is: 8.
So choose: C.
Comment on this question to examine the knowledge of median: arrange a set of data in the order from small to large (or from large to small). If the number of data is odd, the middle number is the median of this set of data; If the number of this set of data is even, the average of the middle two data is the median of this set of data.
4. If the point (3, 1) is in the linear function y = kx-2 (k? 0), then the value of k is ()
A.5 B.4 C.3 D. 1
The solution can be obtained by substituting the coordinates of points into the resolution function.
Solution: ∵ point (3, 1) is in the linear function y = kx ﹣ 2 (in k? 0),
? 3k﹣2= 1，
The solution is k= 1
Therefore, choose: d.
This question examines the coordinate characteristics of points on the function image, and accurate calculation is the key to solving the problem.
5. The following formula must be the simplest quadratic root ()
A.B. C. D。
According to the simplest concept analysis of quadratic root, (1) root sign does not contain denominator; (2) If the number of roots does not include the factor that can be opened to the maximum, you can get the answer.
Solution: A. The number of roots that can be completely opened contains factors that are not the simplest quadratic roots, so this option is wrong;
B. The root sign of the square root contains the denominator, which is not the simplest quadratic root, so this option is wrong;
C. The root sign does not contain the denominator, and the root sign does not contain the best factor or factor. It is the simplest quadratic root, so this option is correct;
D. The root sign contains factors that can be completely opened, not the simplest quadratic root, so this option is wrong;
So choose C.
This question examines the definition of the simplest quadratic radical. According to the definition of the simplest quadratic root, the simplest quadratic root must meet two conditions:
(1) Root sign does not contain denominator;
(2) The number of square roots does not contain factors or factors that can be opened to the maximum.
6. As shown in the figure, in the rectangular ABCD, diagonal lines AC and BD intersect at point O,? ACB=30？ And then what? The size of AOB is ()
.30 caliber? B.60？ C.90？ D. 120？
According to the analysis, if the diagonal lines of the rectangle are divided into two and equal to each other, OB=OC can be obtained, and then ob = oc can be obtained from equilateral angles. OBC=？ ACB, and then according to the summation formula, one external angle of the triangle is equal to two non-adjacent internal angles, and the solution can be obtained.
Solution: the diagonal AC and BD of rectangular ABCD intersect at point o,
? OB=OC，
OBC=？ ACB=30？ ,
AOB=？ OBC+？ ACB=30？ +30? =60? .
Therefore, choose: B.
Comments This topic examines the properties of rectangle, equilateral and equilateral angle, and the property that an outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it. Remembering all the properties is the key to solving the problem.
7. As shown in the figure, in the rhombic ABCD, diagonal AC and BD intersect at point O, OE∨DC intersects at point E, and AD= 10cm, then the length of OE is ().
6 cm long, 5 cm wide, 4 cm high and 3 cm deep.
It is known that OE is the center line of △ABC, so the length of OE can be obtained.
Solution: ∫OE∨DC, AO=CO,
? OE is the center line of △ABC,
The quadrilateral ABCD is a diamond,
? AB=AD= 10cm，
? OE=5cm。
So choose B.
This topic examines the properties of diamonds and the mean value theorem of triangles, which belongs to the basic topic. The key is to get that OE is the median of △ABC, which is generally difficult.
8. As shown in the figure, draw an arc with the origin o as the center and OB as the radius, intersect with the number axis at point A, and the number represented by point A is X, then the cube root of x2- 10 is ().
A.B.﹣ C.2 D.﹣2
X2 is calculated according to Pythagorean theorem, and then solved by the definition of cube root.
Solution: As can be seen from the figure, x2= 12+ 12=2,
Then x2- 10 = 2- 10 =-8,
The cube root of-8 is-2,
Therefore, choose: d.
This topic reviews the real number and the number axis, mainly the practice of irrational numbers on the number axis, which needs to be mastered skillfully.
9. It is known that the images of linear functions y=2x+a and Y =-x+B both pass through a (-2,0) and intersect the Y axis at b and c respectively, so the area of △ABC is ().
a4 b . 5 c . 6d . 7
Analysis substitutes the coordinates of A into the linear functions y=2x+a and Y =-x+B, and obtains the values of A and B, that is, the coordinates of B and C, and then calculates the area of △ABC according to the area formula of triangle.
Solution: Substitute the coordinates of A into the linear functions y=2x+a and y =-x+b respectively.
You can get a=4 and b =-2.
Then the coordinates of b and c are: b (0 0,4), c (0 0,2),
So the area of △ABC is: BC? OA？ 2=6? 2? 2=6.
So choose C.
Comment on the knowledge points examined in this question are the nature of linear function, the distance between points and so on. It should be noted that the distance of line segments cannot be negative.
10. Translate a small diamond with a side length of 1 to get a beautiful one? Chinese knot? Mode. Are the following four patterns similar after translation? Chinese knot? , in which the (1) th graph contains two diamonds with side length of 1, the (2nd) graph contains eight diamonds with side length of 1, the (3rd) graph contains 18 diamonds with side length of 1, and the (3rd) graph contains1.
32 BC to 36 BC
The analysis and careful observation of the graphs show that the first graph has 2? 12=2 small diamonds; The second number is 2? 22=8 small diamonds; The third number is 2? 32= 18 small diamond; The general formula is obtained from this law, and then the answer can be obtained by substituting n=6.
Solution: The number (1) has 2? 12=2 small diamonds;
The second figure has 2? 22=8 small diamonds;
The third number is 2? 32= 18 small diamond;
?
The (n) th figure has 2n2 small diamonds;
The sixth number is 2? 62=72 small diamonds;
So choose D.
The comment on this topic mainly examines the change of graphics. It is the key to solve the problem to observe the change of graphics carefully and find the changing law of graphics.
2. Fill in the blanks (6 small questions in this big question, 4 points for each small question, ***24 points)
1 1.20 14 In the physical fitness test for junior high school graduates in Chongqing, the physical fitness test scores (unit: minutes) of seven students in a school are as follows: 50, 48, 47, 50, 48, 49 and 48. The mode of this set of data is 48.
This problem is solved by the definition of pattern. Just find the number that appears most frequently in the data.
Solution: Data 48 appears three times, and the largest is the majority.
So the answer is: 48.
The review examined the definition of the model. The data that appears most frequently in a set of data is called a pattern. It reflects the majority level of a set of data, and the pattern of a set of data may not be unique.
12. As shown in the figure, in ABCD, diagonal AC and BD intersect at point O. Please add a condition AB=AD to make ABCD a diamond (just write a condition that meets the meaning of the question).
According to the analysis, the parallelogram with equal adjacent sides is a rhombus, and the addition condition AB=AD can be obtained.
Solution: add AB=AD,
∵ quadrilateral ABCD is a parallelogram, AB=AD,
? ABCD became a diamond.
So the answer is: AB=AD.
In this paper, the determination of rhombus is mainly investigated. The key is to master that a group of parallelograms with equal adjacent sides are rhombus.
13. In the function, the value range of the independent variable x is x? -2 and x? 1 .
Analysis According to the nature of the quadratic root and the meaning of the fraction, if the root number is greater than or equal to 0 and the denominator is not equal to 0, it can be solved.
Solution: According to the meaning of the problem,
Solution: x? -2 and x? 1.
So the answer is: x? -2 and x? 1.
Comment on the knowledge points examined in this question: the score is meaningful and the denominator is not 0; The square root of quadratic form is nonnegative.
14. The image of linear function y =-3x+6 does not pass through three quadrants.
This analysis can draw a conclusion directly from the relationship between the image and the coefficients of the linear function.
Solution: ∫ In the linear function y =-3x+6, k =-3.
? The image of this function passes through one, two and four quadrants.
So it doesn't go through three quadrants,
So the answer is: three.
Comment on this topic to examine the relationship between the image of a function and the coefficient, and be familiar with the primary function y=kx+b(k? 0), when k
15. In △ABC,? C=90？ If a+b=7cm and c=5cm, the area of △ABC is 6cm2.
Analysis requires the area of Rt△abC, which is only the product of two right angles. According to Pythagorean Theorem, a2+b2=c2=25. According to Pythagorean Theorem, the value of AB can be calculated, and then the area of triangle can be calculated.
Solution: ∫a+b = 7,
? (a+b)2=49，
? 2ab=49﹣(a2+b2)=49﹣25=24，
? ab=6，
So the answer is: 6cm2.
This topic examines how to use the deformation of the complete square formula and Pythagorean theorem to find the area of a triangle.
16. As shown in the figure, in the rhombic ABCD, AB=4,? A= 120？ If points P, Q and K are any points on line segments BC, CD and BD, the minimum value of PK+QK is 2.
The problem of determining the shortest path according to axial symmetry is analyzed, so that the symmetrical point P of point P is about BD? , pick up p? The intersection of q and BD is point k, and then according to the shortest vertical line segment in all the connecting lines from a point outside the straight line to the straight line, P? q？ The minimum value of PK+QK in CD, and then solve.
Solution: As shown in the figure, AB = 4,? A= 120？ ,
? Point p? The distance to the CD is 4? =2 ,
? The minimum value of PK+QK is 2.
So the answer is: 2.
This topic examines the nature of the diamond, the problem of determining the shortest path by using axial symmetry, and the key to solving the problem is to remember the axial symmetry of the diamond and the method of determining the shortest path by using axial symmetry.
Third, solve the problem (3 small questions in this big question, 6 points for each small question, *** 18 points)
17.？ ﹣ ? 2 .
Analyze division and multiplication first, and then simplify the merger.
Solution: Original formula = 2-6
=﹣4 .
Comment on the mixed operation of quadratic root, and pay attention to simplification before evaluation.
18. As shown in the figure, quadrilateral ABCD is a parallelogram, diagonal lines AC and BD intersect at point O, and straight lines EF intersecting with point O intersect at points E and F respectively, which proves that AE = CF 。
By analyzing that the quadrilateral ABCD is a parallelogram, we can get AD∨BC, OA=OC, and then use ASA to judge △ AOE △ COF, and we can prove OE=OF.
The solution proves that the quadrilateral ABCD is a parallelogram,
? AD∨BC，OA=OC，
OAE=？ OCF，
At △AOE and △COF,
,
? △AOE?△COF(ASA)、
? OE=OF。
In this paper, the properties of parallelogram and the judgment and properties of congruent triangles are investigated. The key to solve the problem is to remember the various properties of parallelogram and congruent triangles's judgment method.
19. In order to know the water consumption of residents in a residential area, the monthly water consumption of residents in this residential area 10 was randomly selected, and the results were as follows:
Monthly water consumption (ton)1013141718
Number of families 2 2 3 2 1
(1) Calculate the average monthly water consumption of this family;
(2) If there are 500 households in this community, according to the above calculation results, how many tons of water do residents in this community use every month?
Analysis (1) According to the calculation formula of weighted average, the answer can be obtained;
(2) Use the monthly electricity consumption of each household multiplied by the total number of households to get the answer.
Solution: (1) The average monthly water consumption of this family is (10? 2+ 13? 2+ 14? 3+ 17? 2+ 18)? 10= 14 (ton);
(2) According to the meaning of the question:
14? 500=7000 (tons),
Residents in this community use 7000 tons of water every month.
Comments This topic examines the population estimation with samples, and the knowledge points used are the calculation formula of weighted average and the population estimation with samples.
Fourth, solve the problem (3 small questions in this big question, 7 points for each small question, ***2 1 point)
20. It is known that after the rectangular paper ABCD is folded along EF, point D coincides with point B, and point C falls on point C? In position, if? 1=60? ，AE=2。
(1) Q? 2,? 3 degrees.
(2) Find the area s of rectangular ABCD paper.
Analysis (1) According to AD∨BC,? 1 and? 2 is the inner angle, so you can get it? 2. According to the definition of graph folding, we can get? 4=? 2, and then you can get? 3 degrees;
(2) Given AE=2, in Rt△ABE, the lengths of AB and BE can be found according to trigonometric function, and if BE=DE, the length of AD can be found and the area of rectangle can be found.
Solution: (1)∵AD∨BC,
2=? 1=60? ;
Again? 4=? 2=60? ,
3= 180? ﹣60? ﹣60? =60? .
(2) What does (1) know in the right angle △ABE? 3=60? ,
5=90? ﹣60? =30? ;
? BE=2AE=4，
? AB = 2；
? AD=AE+DE=AE+BE=2+4=6，
? Is the area s of rectangular paper ABCD ABAD=2? 6= 12 .
In this paper, the properties of rectangle, folding and right triangle are investigated. Paying attention to the combination of number and shape and the application of modeling thought is the key to solve the problem.
2 1. As shown in the figure, the straight line Y =-x+ 10 intersects with the X axis and the Y axis at point B and point C respectively, the coordinate of point A is (8,0), and P(x, y) is the first quadrant straight line Y =-x+ 10.
(1) Find the functional relationship between the area s of △OPA and x, and write the range of the independent variable x;
(2) When the area of △OPA is 10, find the coordinates of point P. 。
Analysis (1) According to the triangle area formula S△OPA= OAy, and then convert Y into X, we can get the functional relationship between the area S of △OPA and X;
(2) Substitute s= 10 into S =-4x+40 to get the value of X, and substitute the value of X into Y =-x+10 to get the coordinates of P. 。
Solution (1) ∫ A (8,0),
? OA=8，
S= OA|yP|=？ 8? (﹣x+ 10)=﹣4x+40,(0