Mathematics examination paper and answer in the second volume of the eighth grade

Final examination questions of mathematics knowledge in the second volume of the eighth grade 1. Multiple-choice question: this big question * *12 is a small one, with a score of ***36. Only one of the four options given in each question is correct. Please choose the correct answer. If you answer each small question correctly, you will get 3 points, if you choose wrong, if you don't choose or choose multiple questions, you will get 0 points.

1. If =x holds, then x must be ().

A. positive number B.0 C. negative number D. non-negative number

2. Take the following groups as three sides of a triangle, which can form a right triangle is ().

A.4，5，6 B. 1， 1 c . 6，8， 1 1 D.5， 12，23

3. Rectangles have properties that diamonds don't have ().

A. diagonal bisection. B. Diagonal lines are equal.

C. Diagonal lines are vertical. D. Each diagonal line bisects a set of diagonal lines.

4. It is known that |a+ 1|+ =0, then the straight line y = ax-b does not pass ().

A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant

5. The following four equations: ①; ②(﹣ )2= 16; ③( )2=4; (4). The correct one is ()

A.①② B.③④ C.②④ D.①③

6. Connect the midpoint of each side of the rectangle ABCD in turn, and the quadrilateral obtained must be ().

A. parallelogram with unequal adjacent sides

C. square D. diamond

7. If the image of function y=kx+2 passes through the point (1, 3), then when y=0, x= ().

A.﹣2

8. If the length of an equilateral triangle is 2, the area of the triangle is ().

A. 3rd century BC

9. The time (hours) for a classmate to finish his homework every day for five days is 2, 3, 2, 1, 2 respectively. The following statements about this set of data are incorrect.

( )

A. the average is 2 B, the mode is 2 C, the median is 2 D, and the variance is 2.

10. Among the following functions, the value range of the independent variable is not selected correctly ().

In A.y=x+2, x takes any real number B.y=, and x takes the real number of x- 1

In C.y=, x is in the real number D.y= of x-2, and x is in any real number.

1 1. As shown in the figure, the straight line y=kx+b passes through point A (2 1), so the following conclusion is correct ().

A. when y2, x 1, b. when y 1, x2 c. when y2, x 1, d. when y 1, x2.

12. The perimeter of parallelogram ABCD is 32, 5AB=3BC, so the value range of diagonal AC is ().

A.6

Fill in the blanks: this big question is ***6 small questions, and the score is ***24. Just need the final result, and fill in 4 points correctly for each small question.

13. The result of calculating (+) (﹣) is.

14. As shown in the figure, the circumference of diamond-shaped ABCD is 32, diagonal AC and BD intersect at point O, and e is the midpoint of BC, so OE=.

15. If both sides of a triangle are 6 and 8, to make it a right triangle, the length of the third side is.

16. Move the straight line y =-x- 1 2 units to the right along the X axis, and the resolution function of the straight line is.

17. In order to know the monthly water consumption of residents in a residential area, the water consumption of 10 households in this residential area was randomly selected. The results are shown in the following table:

Monthly water consumption/ton1013141718

Number of families 2 2 3 2 1

Then the average monthly water consumption of this 10 household is tons.

18. As shown in the figure, in the plane rectangular coordinate system, the right-angle AOCD is folded along the straight line AE (point E is on the side DC), and the folded end point D just falls on the point F on the side OC. If the coordinate of point D is (10,8), the coordinate of point E is.

Third, the answer: this big question ***6 small questions, out of 60 points. Please write down the necessary deduction process when answering.

19. Calculation:

( 1)

(2) .

20. As shown in the figure, given AC=4, BC=3, BD= 12, AD= 13, ACB=90, try to find the area of the shadow part.

2 1. In order to select one athlete from A and one athlete from B to participate in the city shooting competition, each athlete made 10 rounds in the trial, in which the number of shooting rings of A was 10, 8, 7, 9, 8, 10 and 10 respectively.

(1) Calculate the variance of A's shooting score;

(2) According to statistics, the average score of B-rays is 9, and the variance is 1.4. Who do you think is more suitable for the competition? Why?

22. Given the image passing points (3, 5) and (-4, -9) of a linear function, find the analytical expression of this linear function.

23. As shown in the figure, it is known that the diagonal AC of ABCD intersects BD at point O, and the intersection point O is EFAC, which intersects edges AD and BC at points E and F respectively. It is proved that the quadrilateral AFCE is a diamond.

24. As shown in figure 1, in the square ABCD, points E and F are points on the sides of AD and CD respectively, and DE=CF, AF and BE intersect at point G. 。

(1) Q: What is the relationship between the position and quantity of AF line and BE line? (Write the conclusion directly, without proof)

Answer:.

(2) If point E and point F are moved to the extension line on the AD side and the extension line on the DC side respectively, and other conditions remain unchanged (as shown in Figure 2), BF and EF are connected, and M, N, P and Q are the midpoint of AE, EF, BF and AB respectively. Please judge whether the quadrilateral of MNPQ is a rectangle, a diamond or a square. And write the proof process.

The eighth grade first volume mathematics final examination paper reference answer 1. Multiple-choice question: this big question * *12 small question, with a score of ***36. Only one of the four options given in each question is correct. Please choose the correct answer. If you answer each small question correctly, you will get 3 points, if you choose wrong, if you don't choose or choose multiple questions, you will get 0 points.

1. If =x holds, then x must be ().

A. positive number B.0 C. negative number D. non-negative number

Properties and simplification of quadratic roots in inspection center.

Analysis can be answered according to the properties of quadratic roots.

Solution: ∫= x, x0, so choose: d.

2. Take the following groups as three sides of a triangle, which can form a right triangle is ().

A.4，5，6 B. 1， 1 c . 6，8， 1 1 D.5， 12，23

The Inverse Theorem of Pythagorean Theorem in Test Sites.

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, 42+5262, so it is not a right triangle, so the option is wrong;

B, 12+ 12=( )2, so it is a right triangle, so the option is correct;

C, 62+82 1 12, so it is not a right triangle, so the option is wrong;

D, 52+ 122232, so it is not a right triangle, so the option is wrong.

So choose B.

3. Rectangles have properties that diamonds don't have ().

A. diagonal bisection. B. Diagonal lines are equal.

C. Diagonal lines are vertical. D. Each diagonal line bisects a set of diagonal lines.

Test the properties of the central rectangle; The quality of diamonds.

According to the properties of rectangle and diamond, we can get different diagonal properties and get the answer.

Solution: The diagonals of rectangles are equal and bisected, and the diagonals of diamonds are vertical and bisected.

So the rectangle and the diamond have the same diagonal,

So choose B.

4. It is known that |a+ 1|+ =0, then the straight line y = ax-b does not pass ().

A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant

The relationship between linear function image and test center coefficient; The nature of non-negative number: absolute value; Properties of non-negative numbers: arithmetic square root.

According to the nonnegativity of the absolute value and the arithmetic square root, the values of A and B are found, which are substituted into the analytical formula of the straight line, and then the quadrant through which the straight line passes is found by using the relationship between the function image and the coefficient, so that the problem can be solved.

Solution: ∫| a+ 1 |+= 0,

, that is,

The straight line y = ax-b =-x-2,

∵﹣ 10,﹣20,

The straight line y = ax-b passes through the second, third and fourth quadrants.

So choose a.

5. The following four equations: ①; ②(﹣ )2= 16; ③( )2=4; (4). The correct one is ()

A.①② B.③④ C.②④ D.①③

Properties and simplification of quadratic root of inspection center; The meaningful conditions of quadratic roots.

This topic analyzes and examines the meaning of quadratic root: ① =a(a0), ② =a(a0), and judge them one by one.

Solution: ① = =4, correct;

② = (-1) 2 =14 = 416, which is incorrect;

③ =4 accords with the meaning of quadratic root and is correct;

④ = = 4-4, which is incorrect.

① ③ Correct.

Therefore, choose: d.

6. Connect the midpoint of each side of the rectangle ABCD in turn, and the quadrilateral obtained must be ().

A. parallelogram with unequal adjacent sides

C. square D. diamond

The center of the test center is a quadrangle.

According to the midline theorem of triangle, EF=GH= AC, FG=EH= BD can be obtained, and then AC=BD can be obtained according to the equality of diagonal lines of rectangle, so that all four sides of quadrilateral EFGH are equal, so the quadrilateral with all four sides is a rhombic solution.

Solution: as shown in the figure, connect AC, BD,

∫E, F, G and H are the midpoint of the AB, BC, CD and AD sides of the rectangular ABCD respectively.

EF=GH= AC, FG=EH= BD (the center line of the triangle is equal to half of the third side),

∫ Diagonal ABCD of rectangle = BD,

EF=GH=FG=EH，

The quadrilateral EFGH is a diamond.

Therefore, choose: d.

7. If the image of function y=kx+2 passes through the point (1, 3), then when y=0, x= ().

A.﹣2

Coordinate characteristics of points on linear function image of test center.

The analysis directly substitutes the point (1, 3) into the function y=kx+2 to find the value of k, and then substitutes it for the solution.

Solution: ∵ Image passing point of linear function y=kx+2 (1, 3),

3=k+2 and the solution is k= 1.

Substituting y=0 into y=x+2, the solution is: x=﹣2.

So choose one

8. If the length of an equilateral triangle is 2, the area of the triangle is ().

A. 3rd century BC

Properties of equilateral triangle in test center.

As shown in the analysis diagram, if CDAB is used, then CD is the height of equilateral △ABC on the bottom AB. According to the combination of three lines of isosceles triangle, we can get AD= 1. Therefore, in right-angle △ △ADC, we can use Pythagorean theorem to find the length of CD and substitute it into the area calculation formula to solve it.

Solution: make CDAB,

∫△ABC is an equilateral triangle, AB=BC=AC=2,

AD= 1，

In a right-angle delta δδADC,

CD= = =，

s△ABC = 2 =；

So choose C.

9. The time (hours) for a classmate to finish his homework every day for five days is 2, 3, 2, 1, 2 respectively. The following statements about this set of data are incorrect.

( )

A. the average is 2 B, the mode is 2 C, the median is 2 D, and the variance is 2.

Test site variance; Arithmetic average; Median; majority

According to the calculation formula of mode, median, average and variance, the answer is obtained.

Solution: the average is: (2+3+2+1+2) 5 = 2;

Data 2 appears three times, the most times, then the mode is 2;

The data are arranged from small to large: 1, 2, 2, 2, 3, and the median is 2;

The variance is [(2-2) 2+(3-2) 2+(2-2) 2+(1-2) 2+(2-2) 2] =,

Then the error in the statement is d;

So choose D.

10. Among the following functions, the value range of the independent variable is not selected correctly ().

In A.y=x+2, x takes any real number B.y=, and x takes the real number of x- 1

In C.y=, x is in the real number D.y= of x-2, and x is in any real number.

Test the independent variable range of the central function.

This analysis can be obtained by calculating the number of roots greater than or equal to 0 and the denominator not equal to 0.

Solution: In A and y=x+2, X is an arbitrary real number, which is correct, so this option is wrong;

B, from x+ 10, x- 1, so this option is correct;

C, from x+20, x-2, so this option is wrong;

d、x20，

x2+ 1 1，

Y= in, x is any real number, which is correct, so this option is wrong.

So choose B.

1 1. As shown in the figure, the straight line y=kx+b passes through point A (2 1), so the following conclusion is correct ().

A. when y2, x 1, b. when y 1, x2 c. when y2, x 1, d. when y 1, x2.

Properties of linear functions of test points.

Analysis can directly get the answer according to the function image.

Solution: ∫ The straight line y=kx+b passes through point A (2, 1),

When y 1, x2,

Therefore, choose: B.

12. The perimeter of parallelogram ABCD is 32, 5AB=3BC, so the value range of diagonal AC is ().

A.6

The nature of the parallelogram in the examination center; The trilateral relationship of a triangle.

According to the parallelogram perimeter formula, the lengths of AB and BC are obtained, and then the value range of diagonal AC is obtained according to the trilateral relationship of triangle.

Solution: ∫ The circumference of parallelogram ABCD is 32, 5AB=3BC,

2(AB+BC)=2( BC+BC)=32，

BC= 10，

AB=6，

BC﹣AB

So choose D.

Fill in the blanks: this big question is ***6 small questions, and the score is ***24. Just need the final result, and fill in 4 points correctly for each small question.

13. The result of calculating (+) (﹣) is ﹣ 1.

Mixed operation of quadratic root of test center.

According to the square difference formula: (A+B) (A-B) = A2-B2) What is the result of formula (+) (-)?

Solution: (+) (﹣)

=2﹣3

=﹣ 1

The result of (+) (|) is |1.

So the answer is:-1

14. As shown in the figure, the circumference of diamond-shaped ABCD is 32, diagonal AC and BD intersect at point O, and e is the midpoint of BC, so OE= 4.

Test the nature of diamonds in the center.

Firstly, BC=8 and ACBD are obtained according to the properties of rhombus, and then they are solved according to the properties of the midline on the hypotenuse of right triangle.

Solution: ∫ quadrilateral ABCD is a diamond,

BC =8 years, ACBD,

E is the midpoint of BC,

OE= BC=4。

So the answer is 4.

15. If both sides of a triangle are 6 and 8, to make it a right triangle, the length of the third side is 10 or 2.

The Inverse Theorem of Pythagorean Theorem in Test Sites.

The analysis is divided into different situations: when the larger number 8 is a right-angled side, the third side length is10 according to Pythagorean theorem; When the larger number 8 is the hypotenuse, according to Pythagorean theorem, the length of the third side =2.

Solution: ① When 6 and 8 are right angles,

The third side length =10;

② When 8 is the hypotenuse and 6 is the right angle,

The length of the third side =2.

So the answer is: 10 or 2.

16. Move the straight line Y =-x- 1 2 units to the right along the X axis, and the resolution function of the straight line is Y =-x+ 1.

First-order function image and geometric transformation.

The analysis can be directly solved according to the translation law of adding left and subtracting right.

Solution: move the straight line y=﹣x﹣ 1 2 units to the right along the x axis, and the resolution function of the straight line is y=﹣(x﹣2)﹣ 1, that is, Y = ﹣ x+65438+.

So the answer is y =-x+ 1.

Monthly water consumption/ton1013141718

Number of families 2 2 3 2 1

Then the average monthly water consumption of this 10 household is 14 tons.

Weighted average of test points.

The weighted average of monthly water consumption of 10 households can be analyzed and calculated to get the answer to the question.

Solution: According to the meaning of the problem:

= 14 (ton),

A: The average monthly water consumption of this 10 household is 14 tons.

So the answer is: 14.

Test center folding transformation (folding problem); Coordinates and graphic properties.

According to the nature of folding, we get AF=AD, so in the right angle △AOF, we use Pythagorean theorem to find OF=6, and then if EC=x, EF = DE = 8-X, CF = 10-6 = 4, we can get the coordinates of point E that EC can get according to Pythagorean theorem.

Solution: ∵ Quadrilateral A0CD is a rectangle, and the coordinate of D is (10,8).

AD=BC= 10，DC=AB=8，

∫ The rectangle is folded along AE, so that D falls at point F on BC.

AD=AF= 10，DE=EF，

In Rt△AOF, OF= =6,

FC= 10﹣6=4，

Let EC=x, then de = ef = 8-x,

In Rt△CEF, we get EF2=EC2+FC2, that is, (8-x) 2 = x2+42, and x=3.

That is, the length of EC is 3.

The coordinates of point E are (10,3),

So the answer is: (10,3).

Third, the answer: this big question ***6 small questions, out of 60 points. Please write down the necessary deduction process when answering.

19. Calculation:

( 1)

(2) .

Mixed operation of quadratic root of test center.

Analysis (1) first simplifies the quadratic root, calculates the power, then calculates the multiplication and division, removes the brackets with the square difference formula, and finally calculates the addition and subtraction.

(2) Remove the brackets by the law of multiplicative distribution, and then merge similar quadratic roots.

Solution: (1) Original formula = 322+(7+4) (4-7)

= +48﹣49

= .

(2) The original formula = 3+- 1 = 2.

20. As shown in the figure, given AC=4, BC=3, BD= 12, AD= 13, ACB=90, try to find the area of the shadow part.

Pythagorean theorem of test sites; Inverse theorem of Pythagorean theorem.

Firstly, the Pythagorean theorem is used to find AB, and then the inverse theorem of Pythagorean theorem is used to determine that △ABD is a right triangle. Then calculate the areas of the two triangles respectively, and subtract them to get the area of the shadow part.

Solution: connect AB,

∫ACB = 90,

AB= =5，

∫AD = 13，BD= 12，

AB2+BD2=AD2，

△ABD is a right triangle,

Shadow area = Abd -ACBC = 30-6 = 24.

A: The shaded part is 24.

(1) Calculate the variance of A's shooting score;

(2) According to statistics, the average score of B-rays is 9, and the variance is 1.4. Who do you think is more suitable for the competition? Why?

Test site differences.

Analysis (1) First, find the average value of A's shooting score, and then use variance formula to find the variance of A's shooting score.

(2) According to the meaning of mean and variance, the result is obtained.

Solution: (1) ∫ = (10+8+7+9+8+10+9) = 9,

= [( 10﹣9)2+( 10﹣8)2++(9﹣9)2]= 1,;

(2) It is more appropriate to choose an athlete to participate in the competition; The reason for this is the following：

Because the average scores of A and B are the same, the variance of A's scores is small, which shows that A and B have the same shooting level, but A's competition state is more stable, so it is more appropriate to choose A athlete to participate in the competition.

22. Given the image passing points (3, 5) and (-4, -9) of a linear function, find the analytical expression of this linear function.

Using undetermined coefficient method to find the first resolution function.

Substituting two points into the resolution function, we can get a set of binary linear equations, which can be solved to get the values of k and b, and the resolution function can also be obtained.

Solution: Let the linear function be y=kx+b(k0),

Because its image goes through (3, 5), (-4, -9),

therefore

Solution:

So this linear function is y = 2x- 1.

Determination of diamond test center; Properties of parallelogram.

By analyzing that the diagonal AC of ABCD intersects BD at point O, EFAC, it is easy to get the vertical AC of EF, and then we can get △ AOE △ COF, and then AE=CF, and then we can get a conclusion.

This solution proves that the∵ quadrilateral ABCD is a parallelogram.

AO=CO，AD∨BC

∵ EFAC again,

EF vertically divides AC,

AE=EC

∫ AD ∨ BC,

DAC=ACB，AE∑CF，

At △AOE and △COF,

△AOE?△COF(ASA)、

AE=CF，

And ∵AE∨CF,

The quadrilateral AFCE is a diamond.

24. As shown in figure 1, in the square ABCD, points E and F are points on the sides of AD and CD respectively, and DE=CF, AF and BE intersect at point G. 。

(1) Q: What is the relationship between the position and quantity of AF line and BE line? (Write the conclusion directly, without proof)

A: The positional relationship between the line segments AF and BE is perpendicular to each other, and the quantitative relationship is equal.

Test site quadrilateral comprehensive questions.

Analysis (1) Conclusion: AFBE, AF=BE. As long as △ Abe △ DAF is proved, the problem can be solved.

(2) Conclusion: Quadrilateral MNPQ is a square. Firstly, it is proved that △ Abe △ DAF, and AF=BE, AFBE are deduced, and then it is proved that quadrilateral MNPQ is a square.

Solution: (1) As shown in figure 1, ∵ quadrilateral ABCD is a square.

AB=AD=CD，BAC=ADC=90，

DE = CF，

AE=DF，

In △ Abe and △DAF,

△ Abe△ ?△DAF

AF=BE，AEB=AFD，

∫AFD+FAD = 90，

AEB+ fashion =90,

EGA=90，

BEAF。

So the answer is that the positional relationship between AF and BE is perpendicular to each other, and the quantitative relationship is equal.