Hebei education publishing house, the second day of mathematics, the first volume of the final exam questions.
Multiple choice questions: 3 points for each question, with a total of 48 points. Of the four options given in each question, only one fits the meaning of the question.
1. The following figures are centrosymmetric figures, and those are ().
A.B. C. D。
2. The following approximate view is correct ()
A.=x3 B. =0
C.= D. =
3. If the formula is meaningful, the value range of X is ()
A.x？ 2 B.x？ 3 C.x？ 2 or x? 3 D.x？ 2 and x? three
4. The following figures are irrational ()
B.-1downtown
5. Among the following roots, the simplest quadratic root is ()
A.B. C. D。
6. When solving the fractional equation +=3, it will be deformed into () after removing the denominator.
a.2+(x+2)=3(x﹣ 1)b.2﹣x+2=3(x﹣ 1)c.2﹣(x+2)=3( 1﹣x)d.2﹣(x+2)=3(x﹣ 1)
7. The result of simplifying++is ()
C.﹣2
8. As shown in the figure, △ ACB △ DCE,? BCE=25？ And then what? The degree of ACD is ()
.20 caliber? B.25？ C.30？ D.35？
9. Simplify? The result of is ()
A. 2 years BC (x+ 1)
10. As shown in the figure, B=? D=90？ ，BC=CD，？ 1=40? And then what? 2=( )
.40 caliber? B.50？ C.60？ D.75？
1 1. If, the value of xy is ().
C.﹣6 D.﹣8
12. As shown in the figure, in △ABC,? B=40？ , rotate △ABC counterclockwise around point A to get △ADE, and point D just falls on the straight line BC, then the degree of rotation angle is ().
Point 70? B.80？ C.90？ D. 100？
13. As shown in the figure, AB∨CD, BP and CP are equally divided? ABC and? DCB, AD crosses point p, perpendicular to AB. If AD=8, the distance from point P to BC is ().
A8 b . 6 c . 4d . 2
14. A factory now produces 50 more machines every day than originally planned, and it takes the same time to produce 800 machines as originally planned to produce 600 machines. Assuming that the original plan produces X machines on average every day, according to the meaning of the question, the following equation is correct ().
A.= B. = C. = D. =
15. As shown in the figure, in △ABC, AB=AC=5, BC=8, and D is the moving point on line BC (excluding endpoints B and C). If the length of the line segment AD is a positive integer, then the number of points d is common ().
A.5 B.4 C.3 D.2
16. If m is an integer, then the value of m that makes the score an integer is ().
A.2 B.3 C.4 D.5
Fill-in-the-blank: Please fill in the score directly on the question line, with 3 points for each small question, totaling 12 points.
17.= .
18.|﹣ +2|= .
19. If it is the same quadratic form as the simplest quadratic form, then m=.
20. As shown in the figure, BOC=60? , point A is a point on the extension line of BO, OA= 10cm, moving point P starts from point A and moves along AB at a speed of 2cm/s, and moving point Q starts from point O and moves along OC at a speed of1cm/s. If point P and point Q start at the same time, t(s) indicates the moving time, when t = s.
3. Answer: 10.
2 1.( 10 points) (1) For any two unequal real numbers A and B, define the operation ※ as follows: a※b=, for example, 3※2= =, and find the value of 8 ※ 12.
(2) Simplify first, then evaluate:+? , where a= 1+.
4. Answer: 9 points.
22.(9 points) As shown in the figure, there are three points A, B and C on the grid paper. Please find a point D on the grid and make a quadrilateral with vertices A, B, C and D, and satisfy the following conditions.
(1) makes the quadrangle in Figure A an axisymmetric figure instead of a centrally symmetric figure;
(2) Make the quadrangle in Figure B not an axisymmetric figure, but a centrally symmetric figure;
(3) Make the quadrilateral in Figure C both symmetrical and central.
5. Answer: 9 points.
23.(9 points) As shown in the figure, in △ABC,? C=90？ , AB in the vertical line DE AC in d, vertical foot for e, if? A=30？ ，CD=3。
(1) Q? The degree of BDC.
(2) Find the length of AC.
6. Answer: 8 points.
24.(8 points) As shown in the figure, the pattern is made up of matchsticks of equal length according to certain rules. Pattern ① needs 8 matchsticks, and pattern ② needs 15 matchsticks. ,
(1) According to this rule, pattern ⑦ needs a matchstick; The nth pattern needs a matchstick.
(2) Can 2017 matchsticks be put together into a pattern regularly? If so, what mode is it? If not, please explain why.
7. Answer: 12.
25.( 12 points) Define new operations: observe the following:
1⊙3= 1? 4+3=7 3⊙(﹣ 1)=3? 4﹣ 1= 1 1 5⊙4=5? 4+4=24 4⊙(﹣3)=4? 4﹣3= 13
(1) Please think about it: a ⊙ b =;
(2) if a? B, then a⊙b b⊙a (fill in? =? Or)
(3) If a⊙(﹣2b)=4, then 2a ﹣ b =; Please calculate the value of (a-b) ⊙ (2a+b).
8. Answer: 12.
26.( 12 points) As shown in the figure, in △ABC, AB=AC=2,? B=？ C=40？ , point D moves on line BC (D does not coincide with B and C) and connects AD. ADE=40？ The intersection of DE and AC is at e.
(1) When? BDA= 1 15？ What time? EDC=？ ,? DEC=？ ; When point D moves from point B to point C, BDA changes gradually (fill in the blank? Big? Or? Small? );
(2) When DC is equal to △ Abd △ DCE, please explain the reasons;
(3) Can the shape of △ADE be an isosceles triangle during the movement of point D? If you can, please write directly? BDA degrees. If not, please explain why.
Hebei education publishing house, the second day of mathematics, the first volume of the final exam questions reference answer.
Multiple choice questions: 3 points for each question, with a total of 48 points. Of the four options given in each question, only one fits the meaning of the question.
1. The following figures are centrosymmetric figures, and those are ().
A.B. C. D。
The center of the test center is symmetrical.
According to the analysis, rotate a graph around a certain point 180? If the rotated graph can coincide with the original graph, then this graph is called a centrosymmetric graph.
Solution: A, it is not a centrally symmetric figure, so the option is wrong;
B, it is not a central symmetrical figure, so the option is wrong;
C, is a central symmetric figure, so the option is correct;
D, is not a centrally symmetric figure, so the option is wrong;
So choose: C.
This topic mainly investigates the central symmetric figure, and the key is to find the symmetric center. After rotating 180 degrees, the two parts overlap.
2. The following approximate view is correct ()
A.=x3 B. =0
C.= D. =
About the test center.
According to the basic nature of the score, each item can be simplified separately.
Solution: A, =x4, so this option is wrong;
B, = 1, so this option is wrong;
C, =, so this option is correct;
D, =, so this option is wrong;
So choose C.
The comments on this topic mainly focus on divisor. The knowledge used is the nature of the score. Note that divisor is the common factor of numerator and denominator. When numerator and denominator are the same, the result of divisor should be 1, not 0.
3. If the formula is meaningful, the value range of X is ()
A.x？ 2 B.x？ 3 C.x？ 2 or x? 3 D.x？ 2 and x? three
The meaningful condition of the second root of the inspection center; Conditions for meaningful scores.
According to the nature of quadratic root and the meaning of fraction, if the root number is greater than or equal to 0 and the denominator is not equal to 0, we can solve it.
Solution: it makes sense to press the square root and the fraction makes sense: x﹣2? 0 and x > 3? 0,
Solution: x? 2 and x? 3.
So choose D.
This topic reviews the meaningful conditions of quadratic roots and the significance of fractions. The knowledge points examined are: the score is meaningful and the denominator is not 0; The square root of quadratic form is nonnegative.
4. The following figures are irrational ()
B.-1downtown
The number of test sites is unreasonable.
According to the analysis, the irrational number is an infinite acyclic decimal, and the answer can be obtained.
Solution: 0,-1, is a rational number and an irrational number.
So choose: C.
The commentary on this topic mainly examines the definition of irrational numbers. Note that an infinite number with a root sign is an irrational number, and an infinite cycle of decimals is an irrational number. Like what? , ,0.8080080008? (20 16? Linxia Prefecture) The simplest quadratic root is ()
A.B. C. D。
The simplest quadratic root of the test center.
The analysis directly uses the simplest definition of quadratic root to get the answer.
Solution: A, =, so the option is wrong;
B is the simplest quadratic radical, so the option is correct;
C =3, so the option is wrong;
D =2, so the option is wrong;
Therefore, choose: B.
This review mainly examines the simplest quadratic root, and correctly grasping the definition is the key to solving the problem.
6. When solving the fractional equation +=3, it will be deformed into () after removing the denominator.
a.2+(x+2)=3(x﹣ 1)b.2﹣x+2=3(x﹣ 1)c.2﹣(x+2)=3( 1﹣x)d.2﹣(x+2)=3(x﹣ 1)
Test sites solve fractional equations.
Analyze this problem to examine the ability to determine the simplest common denominator and remove the denominator of a fraction. Observing that the expressions x﹣ 1 and X ﹣ 1﹣x are opposite, we can get 1 ﹣ X = ﹣ (X ﹣ 65438+).
Solution: multiply both sides of the equation by x- 1,
Get: 2 ~ (x+2) = 3 ~ (x ~ 1)。
So choose D.
Comments on the understanding of fractional equation. For a fractional equation, after determining the simplest common denominator, we should be careful not to omit multiplication, which is the focus of this question. Avoid the form of 2-(x+2) = 3 after removing the denominator.
7. The result of simplifying++is ()
C.﹣2
Addition and subtraction of quadratic roots in test sites.
According to the radical, we can simplify the quadratic radical and get the answer according to the addition and subtraction of the quadratic radical.
Solution: +-= 3+-2 = 2,
Therefore, choose: d.
This topic reviews the addition and subtraction of quadratic roots, simplifying first, then adding and subtracting.
8. As shown in the figure, △ ACB △ DCE,? BCE=25？ And then what? The degree of ACD is ()
.20 caliber? B.25？ C.30？ D.35？
Test the properties of congruent triangles.
According to △ ACB △ DCE, can it be analyzed? DCE=？ ACB, and then get it? DCA=？ BCE, you can get the answer.
Solution: ∫△ACB?△DCE,? BCE=25？ ,
? DCE=？ ACB，
∵? DCE=？ DCA+？ ACE？ ACB=？ BCE+？ ECA,
? DCA+？ ACE=？ BCE+？ ECA,
? DCA=？ BCE=25？ ,
Therefore, choose: B.
This topic reviews the application nature of congruent triangles. Can you find it? ACD=？ BCE is the key to solve this problem. Note that the angles corresponding to congruent triangles are equal.
9. Simplify? The result of is ()
A. 2 years BC (x+ 1)
Multiplication and division of test center scores.
The original formula is deformed by division, and the result can be obtained by reduction.
Solution: The original formula =? (x﹣ 1)=，
So choose one
This topic reviews the multiplication and division of scores, and mastering the algorithm is the key to solve this problem.
10. As shown in the figure, B=? D=90？ ，BC=CD，？ 1=40? And then what? 2=( )
.40 caliber? B.50？ C.60？ D.75？
Determination of congruence of right triangle in test center: the nature of congruent triangles.
Analyze the requirements of this problem? 2. First, we must prove Rt△ABC≌Rt△ADC(HL), and then we can get? 2=? ACB=90？ ﹣? The value is 1.
Solution: ∵? B=？ D=90？
In Rt△ABC and Rt△ADC.
? Rt△ABC≌Rt△ADC(HL)
? 2=? ACB=90？ ﹣? 1=50? .
So choose B.
The judgment of triangle congruence is a hot topic in the senior high school entrance examination. Generally speaking, the main method to judge whether two triangles are coincident is to check whether the triangles are coincident. Firstly, the triangle is determined according to the known conditions or the verified conclusions. Then, according to the judgment method of triangle congruence, see what conditions are missing and then prove what conditions.
1 1. If, the value of xy is ().
C.﹣6 D.﹣8
The nature of non-negative number of test sites: arithmetic square root; The property of non-negative number: even power.
According to the properties of non-negative numbers, the equations are listed, the values of x and y are obtained, and then the values are calculated by substituting them into algebraic expressions.
Solution: ∫,
? ,
Solve,
? xy=﹣2？ 3=﹣6.
So choose C.
This topic reviews the nature of non-negative numbers: when the sum of several non-negative numbers is 0, these non-negative numbers are all 0.
12. As shown in the figure, in △ABC,? B=40？ , rotate △ABC counterclockwise around point A to get △ADE, and point D just falls on the straight line BC, then the degree of rotation angle is ().
Point 70? B.80？ C.90？ D. 100？
Test the nature of center rotation.
According to the nature of rotation, the corresponding edges and angles before and after rotation are equal, and the isosceles triangle is obtained, and then the solution is based on the nature of isosceles triangle.
Solution: according to the nature of rotation, The degree of bad is the degree of rotation, AB=AD,? ADE=？ B=40？ ,
At △ABD,
AB = AD，
? ADB=？ B=40？ ,
? Bad = 100? ,
So choose D.
This paper mainly investigates the nature of rotation, and finds out the rotation angle and the corresponding edges before and after rotation is the key to get the isosceles triangle.
13. As shown in the figure, AB∨CD, BP and CP are equally divided? ABC and? DCB, AD crosses point p, perpendicular to AB. If AD=8, the distance from point P to BC is ().
A8 b . 6 c . 4d . 2
Test the properties of the bisector of the central angle.
Analyze a little p for PE? BC in E, according to the equal distance from the point on the bisector of the angle to both sides of the angle, we can get PA=PE, PD=PE, PE=PA=PD, AD=8, and PE=4.
Solution: Do you still do PE after P? In 200 BC,
∫AB∨CD，PA？ AB，
? PD？ CD，
∵BP and CP split equally? ABC and? DCB，
? PA=PE，PD=PE，
? PE=PA=PD，
∫PA+PD = AD = 8，
? PA=PD=4，
? PE=4。
So choose C.
Comment on this topic to examine the nature that the distance from a point on the bisector of an angle to both sides of the angle is equal. Memorizing attributes and making them auxiliary lines is the key to solving problems.
14. A factory now produces 50 more machines every day than originally planned, and it takes the same time to produce 800 machines as originally planned to produce 600 machines. Assuming that the original plan produces X machines on average every day, according to the meaning of the question, the following equation is correct ().
A.= B. = C. = D. =
The test center abstracts the fractional equation from the actual problem.
According to the meaning of the question, it can be seen that x+50 machines are produced every day, but the time required to produce 800 machines now is equal to the time required to produce 600 machines originally planned, so the equation can be listed.
Solution: Suppose the original plan was to produce an average of X machines a day.
According to the meaning of the question: =
So choose: a.
Comments on this topic mainly examines the application of fractional equation, using this topic? Now, on average, 50 more machines are produced every day than originally planned? This implicit condition, and then the equation equation is the key to solving the problem.
15. As shown in the figure, in △ABC, AB=AC=5, BC=8, and D is the moving point on line BC (excluding endpoints B and C). If the length of the line segment AD is a positive integer, then the number of points d is common ().
A.5 B.4 C.3 D.2
Pythagorean theorem of test sites; Properties of isosceles triangle.
Analyze as AE starting with a? When BC, D and E coincide, AD is the shortest. First, we can get BE=EC by using the properties of isosceles triangle, then we can get the length of BE, then we can calculate the length of AE by using Pythagorean theorem, then we can get the range of AD, and then we can get the answer.
Solution: A as AE? BC,
AB = AC，
? EC=BE= BC=4，
? AE= =3，
D is the moving point on the BC line (excluding endpoints B and C).
? 3? AD & lt5,
? AD=3 or 4,
The length of the line segment AD is a positive integer,
? There can be three advertisements with lengths of 4, 3 and 4 respectively.
? There are three points d,
So choose: C.
This topic mainly examines the nature and pythagorean theorem of isosceles triangle. The key is to correctly use Pythagorean theorem to calculate the minimum value of AD, and then find out the range of AD.
16. If m is an integer, then the value of m that makes the score an integer is ().
A.2 B.3 C.4 D.5
Definition of test center score; Addition and subtraction of fractions.
Just analyze the fraction and discuss it, that is, m+ 1 is the divisor of 2.
Solution: ∫= 1+,
If the original score is an integer, then m+ 1 =-2,-1, 1 or 2.
M =-3 from m+1=-2;
M =-2 from m+1=-1;
M=0 from m+1=1;
M= 1 from m+ 1=2.
? M =-3，-2，0， 1。 So I chose C.
The comment on this topic mainly examines the knowledge points of the score, carefully examines the topic and discusses the deformation of the score.
Fill-in-the-blank: Please fill in the score directly on the question line, with 3 points for each small question, totaling 12 points.
17.= 3 .
Cubic root of test center.
Analysis 33=27, according to the definition of cube root, we can get the result.
Solution: ∫33 = 27,
? ;
So the answer is: 3.
The commentary on this topic examines the definition of cube root; Mastering the reciprocal operation of founder and cube is the key to solve the problem.
18.|﹣ +2|= 2﹣.
Properties of real numbers in test sites.
Analysis can answer this question by removing the absolute value.
Solution: |+2| = 2 |,
So the answer is: 2.
This question examines the nature of real numbers, and the key to solving the problem is to clarify the method of removing absolute values.
19.m= 1 If it is the same quadratic form as the simplest quadratic form.
The test sites are similar to the secondary roots.
Firstly, the analysis is simplified to the simplest quadratic root 2, and then m+ 1=2 is obtained according to the similar quadratic root, and then the equation can be solved.
Solution: ∫= 2,
? m+ 1=2，
? m= 1。
So the answer is 1.
This topic reviews the similar quadratic roots: after several quadratic roots are transformed into the simplest quadratic roots, if the number of roots is the same, then these quadratic roots are called similar quadratic roots.
20. As shown in the figure, BOC=60? , point A is a point on the extension line of BO, OA= 10cm, moving point P starts from point A and moves along AB at a speed of 2cm/s, and moving point Q starts from point O and moves along OC at a speed of1cm/s. If point P and point Q start at the same time, t(s) indicates the moving time, when t= or
Determination of isosceles triangle in examination center.
According to the analysis, △POQ is an isosceles triangle, which is discussed in two points: point P is on AO or point P is on BO.
Solution: When PO=QO, △POQ is an isosceles triangle;
As shown in figure 1: