Hunan Education Publishing House, Grade 8, Volume I, Final Mathematics Examination Questions 1. Multiple choice questions (3 points for each small question, *** 12 small questions, out of 36 points. Please fill in the letters indicating the correct answers under the corresponding question numbers in the table below. )
1. Among the following scores, the simplest score is ().
A.B.
C.D.
2. When the score is 0, the value of the letter X should be ().
A.﹣ 1 b 1 c.﹣2 d . 2
3. The following calculation is correct ()
A.2﹣3=﹣8 B.20= 1 C.a2？ a3=a6 D.a2+a3=a5
4. The cube root of (-8) 2 is ()
B.﹣4
5. If the algebraic expression is meaningful, then X must satisfy the condition ().
A.x？ -Bank & GTC.X & gt-Dacres? ﹣
6. It is known that the internal angle of an isosceles triangle is 50? Then the other two internal angles of this isosceles triangle are ()
.50 caliber? ,80? B.65？ ,65?
C.50？ ,80? Still 65? ,65? D. unable to determine
7. The following proposition belongs to the false proposition is ()
A. Real numbers correspond to points on the number axis.
B. If the absolute values of two numbers are equal, then the two numbers must be equal.
C. Equal antipodal angle
D. the center of gravity of a triangle is the intersection of three midlines of the triangle.
8. The length of the following three line segments, can form a triangle is ().
A.3cm， 10cm，5cm B.4cm，8cm，4cm
C.5cm， 13cm， 12cm D.2cm，7cm，4cm
9. The solution set of inequality group is ()
A.x >1Bakers? 3 C. 1
10. The calculation result is estimated as ()
Between A.5 and 6, B.6 and 7, C.7 and 8, and D.8 and 9.
1 1. Given that the augmented root of equation | = 0 about x is 1, then the value of the letter A is ().
B.﹣2 C. 1 D.﹣ 1
12. Prove the proposition by reducing to absurdity? When at least one angle in a triangle is greater than or equal to 60, () in this triangle should be assumed first.
A. Is there an internal angle greater than 60? B. is there an internal angle less than 60?
C. Each internal angle is greater than 60? D. each internal angle is less than 60?
Fill in the blanks (3 points for each small question, ***6 small questions, full score 18)
13. A diamond ruler with a minimum scale of 0.2 nm (1 nm = 10-9m) can measure the distance less than 1% of the hair diameter, which is also the smallest scale in the world at present. The minimum scale is expressed as m in scientific notation.
14. The solution of the fractional equation =-4 is x=.
15. Calculation:? = .
16. As shown in the figure, put the right-angle vertex of the triangular ruler on one side of the ruler, like this? 1=60? ,? 2= 100? And then what? 3= ? .
17. As shown in the figure, you know? BAC=？ DAC, and then add a condition, you can make △ ABC△ ADC.
18. As shown in the figure, it is known that in △ABC, AB=7, BC=6, the midline DE of AC intersects with AC at point E, and AB intersects with point D and connects CD, then the circumference of △BCD is.
Iii. Answer: (8 points for each minor question in 19, 6 points for 20 questions, full mark 14 points)
19.( 1) Calculation: ﹣
(2) Calculation: (2-5)-(-)
20. Solve the following inequalities? -1, and represents the solution set on the number axis.
4. Analytical reasoning: (8 points for each small question, ***2 small questions, full score 16)
2 1. Known: As shown in the figure, AB=AC, CE and BF intersect at point D, BD=CD. Verification: DE=DF.
22. As shown in the figure, in an equilateral △ABC with a side length of 4, AD is the center line of BC, AD=2, and one side of AD is left as equilateral △ADE.
(1) Find the area of △ABC;
(2) What is the positional relationship between 2)AB and DE? Please prove it.
Practice and application of verb (abbreviation of verb) (8 points for each small question, ***2 small questions, full score 16)
23. It is known that the total length of Beihai-Nanning railway is 2 10 km. After the bullet train was put into use, its average speed was three times that of the ordinary train, thus shortening the travel time from Beihai to Nanning by 1.75 hours. What is the average speed of the ordinary train? (column equation solution)
24. Teacher Zhang Hua took 200 yuan cash to Starlight Stationery to buy prizes for students' final exams. He took a fancy to a notebook and a pen. The unit price of notebook is 5 yuan, and the unit price of pen is 2 yuan. Teacher Zhang is going to buy 50 copies of these two prizes. How many notebooks can he buy at most? (column inequality solution)
Six, reading and inquiry (65438 +00 points for each small question, ***2 small questions, out of 20 points)
25. Before solving the problem, please read the following materials:
Reading material: There is a kind of numbers with radical signs in mathematics, which can be transformed into a layer of radical signs through the complete square formula and the properties of quadratic roots.
For example:
= = = =| 1+ |= 1+
Solve the problem:
① Fill in the appropriate numbers in brackets:
= = = =| |=
According to the above ideas, try to simplify.
26. Known: in △ABC,? BAC=90？ ,? ABC=45？ Point D is a moving point on line BC (point D does not coincide with B and C). Take AD as the edge and make a square ADEF on the right to connect FC. Inquiry: No matter where point D moves, what is the quantitative relationship between the lengths of line segments FC, DC and BC? Please prove it.
Hunan Education Publishing House, Grade Eight, Volume One, Reference Answers to Mathematics 1 Final Examination Paper. Multiple choice questions (3 points for each small question, *** 12 small questions, out of 36 points. Please fill in the letters indicating the correct answers under the corresponding questions in the table below. )
1. Among the following scores, the simplest score is ().
A.B.
C.D.
The simplest part of the examination center.
The standard for analyzing the simplest fraction is numerator, and the denominator does not contain common factors, so it cannot be simplified. The method of judgment is to decompose the numerator and denominator into factors and observe whether there are contradictory factors. These factors can be reduced by changing the symbols to the same factors.
Solution: The numerator and denominator of A and A cannot be decomposed or reduced, which is the simplest fraction;
B,, is not the simplest score;
C,, is not the simplest score;
D,, is not the simplest fraction;
So choose one
2. When the score is 0, the value of the letter X should be ().
A.﹣ 1 b 1 c.﹣2 d . 2
The condition that the score of the inspection center is zero.
If the value of the fraction is zero, the numerator is zero and the denominator is not zero, the answer is obtained.
Solution: Proceed from the meaning of the problem and get it.
X+2=0 and x ~ 1? 0,
The solution is x =-2,
So choose: C.
3. The following calculation is correct ()
A.2﹣3=﹣8 B.20= 1 C.a2？ a3=a6 D.a2+a3=a5
Multiplication with the same base; Merge similar projects; Zero exponential power; Negative integer exponential power.
According to the power, zero power and negative integer exponential power of the same base number, we can get the answer.
Solution: A, 2-3 = =, so A is wrong;
B, 20= 1, so b is correct;
c、a2？ A3=a2+3=a5, so C is wrong;
D, the multiplication exponents of different base powers cannot be added, so D is wrong;
Therefore, choose: B.
4. The cube root of (-8) 2 is ()
B.﹣4
Cubic root of test center.
The analysis can be solved by finding (-8) 2 first, and then using the definition of cube root.
Solution: ∵ (∵ 8) 2 = 64, and the cube root of 64 is 4.
? The cube root of (-8) 2 is 4.
So choose: a.
5. If the algebraic expression is meaningful, then X must satisfy the condition ().
A.x？ -Bank & GTC.X & gt-Dacres? ﹣
A meaningful condition for testing the quadratic root of the center.
The square root of the quadratic root is nonnegative.
Solution: According to the meaning of the question: 2x+ 1? 0,
Get x? ﹣ .
Therefore, choose: d.
6. It is known that the internal angle of an isosceles triangle is 50? Then the other two internal angles of this isosceles triangle are ()
.50 caliber? ,80? B.65？ ,65?
C.50？ ,80? Still 65? ,65? D. unable to determine
Properties of isosceles triangle.
The analysis of this problem can be solved according to the theorem of the sum of internal angles of triangles. The angle may be the top angle or the bottom angle, which should be discussed separately.
Solution: at 50? When it is the bottom angle, the top angle is 180? ﹣502=80? ,
At the age of 50? When it is the top angle, what is the bottom angle? 2=65? .
So the other two internal angles of this isosceles triangle are 50 degrees respectively? ,80? Still 65? ,65? .
So choose: C.
7. The following proposition belongs to the false proposition is ()
A. Real numbers correspond to points on the number axis.
B. If the absolute values of two numbers are equal, then the two numbers must be equal.
C. Equal antipodal angle
D. the center of gravity of a triangle is the intersection of three midlines of the triangle.
Propositions and theorems of test sites.
According to the relationship between real number and axis, the nature of absolute value, the equality of vertex angles and the definition of triangle center of gravity, the solution can be obtained by analyzing and judging each option.
Solution: a, real numbers correspond to points on the number axis one by one, which is a true proposition, so this option is wrong;
B, if the absolute values of two numbers are equal, then the two numbers must be equal, which is a false proposition, because if the absolute values of two numbers are equal, then the two numbers must be equal or opposite, so this option is correct;
C, the vertex angles are equal, which is a true proposition, so this option is wrong;
D, the center of gravity of the triangle is the intersection of the three midlines of the triangle, which is a true proposition, so this option is wrong.
So choose B.
8. The length of the following three line segments, can form a triangle is ().
A.3cm， 10cm，5cm B.4cm，8cm，4cm
C.5cm， 13cm， 12cm D.2cm，7cm，4cm
Test the trilateral relationship of the central triangle.
Analysis basis? The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side? Analyze each option one by one.
Solution: According to the trilateral relationship of the triangle, we can get
a、5+3 & lt； 10, which cannot form a triangle, does not meet the meaning of the question;
B, 4+4=8, can't form a triangle, which doesn't meet the meaning of the question;
C, 12+5 > 13, which can form a triangle and meet the meaning of the question;
d、2+4 & lt； 8, can not form a triangle, does not meet the meaning of the question.
So choose: C.
9. The solution set of inequality group is ()
A.x >1Bakers? 3 C. 1
Try to solve a set of linear inequalities.
Find the solution set of each inequality first, and then find the solution set of the inequality group.
Solution:
∵ Solving inequality ①: x > ﹣ 1,
Solve inequality ②: x? 3,
? The solution set of the inequality group is-1
So choose D.
10. The calculation result is estimated as ()
Between A.5 and 6, B.6 and 7, C.7 and 8, and D.8 and 9.
The test center estimates the size of irrational numbers.
The original formula = is obtained by multiplication and division of quadratic root, and then < <
Solution: The original formula = =,
because
So 6
So choose B.
1 1. Given that the augmented root of equation | = 0 about x is 1, then the value of the letter A is ().
B.﹣2 C. 1 D.﹣ 1
Increase the root of the test score equation.
Analyze the denominator to get the whole equation, and substitute x= 1 into the whole equation to get the answer.
Solution: -= 0,
Remove the denominator: 3x-(x+a) = 0 ①,
The root of the equation about x∶0 is 1.
? Substituting x= 1 into ① gives 3-( 1+a) = 0.
Solution: a=2,
So choose a.
12. Prove the proposition by reducing to absurdity? When at least one angle in a triangle is greater than or equal to 60, () in this triangle should be assumed first.
A. Is there an internal angle greater than 60? B. is there an internal angle less than 60?
C. Each internal angle is greater than 60? D. each internal angle is less than 60?
Reduce to absurdity.
When analyzing the steps of reducing to absurdity, the first step is to assume that the conclusion is not true, but on the contrary, we can judge accordingly.
Solution: Prove the proposition by reducing to absurdity? When at least one angle in the triangle is greater than or equal to 60 degrees,
First of all, suppose that every internal angle in this triangle is less than 60? ,
Therefore, choose: d.