Reference answers and analysis of test questions

Fill in the blanks: (2 points for each question, ***30 points)

1.(4 points) (20 12? The inverse of Qinghai)-yes; Calculate a2? a3= a5。

. (4 points) (20 12? Qinghai) decomposition factor:-m2+4m =-m (m-4); The solution set of inequality group is -2 < x ≤ 3.

3.(2 points) (20 12? Qinghai) 20 12 In March, the finance of Qinghai Province issued a subsidy of 265 million yuan to improve the nutritional status of primary and secondary school students in the compulsory education stage in agricultural and pastoral areas of our province. The subsidy fund is expressed as 2.65× 108 yuan by scientific notation.

4.(2 points) (20 12? Qinghai) function y=, and the range of independent variable x is x≥﹣4 and x ≠ 2.

5.(2 points) (20 10? Shiyan) As shown in the figure, straight lines l 1∑l2 and l 1, L2 is cut by straight line l3, ∠ 1 = ∠ 2 = 35, ∠ P = 90, then ∠3= 55.

Test site: the nature of parallel lines; Properties of right triangle. 190 187

Special topic: calculation problems.

Analysis: First, calculate the sum of ∠3 and ∠4 according to the parallelism of two straight lines and the remainder of the inner angle of the same side, and then calculate ∠4 and ∠3 according to the remainder of the two acute angles of a right triangle.

Solution: As shown in the figure, ∫l 1∑L2,

∴∠ 1+∠2+∠3+∠4= 180 ,

∵∠ 1=∠2=35 ,

∴∠3+∠4= 1 10 ,

∠∠P = 90，∠2=35，

∴∠4=90 ﹣35 =55 ,

∴∠3= 1 10 ﹣55 =55 .

Comments: This problem is mainly solved by using the nature of parallel lines and the complementary nature of two acute angles of right triangle.

6.(4 points) (20 12? Qinghai) If m and n are real numbers, | 2m+n |1|+= 0, and the value of (m+n)20 12 is1; The solution of the fractional equation+= is x = 1.

7.(2 points) (20 12? Qinghai) randomly throws a bean, and it happens to fall in the square as shown in the figure (each square is exactly the same except the color), then the probability of this bean falling in the black square is.

Test site: geometric probability. 190 187

Analysis: According to the area method, the ratio of the area of beans falling on the black square to the total area can be found.

Answer: Solution: ∫ * * There are 15 squares, of which 4 are black squares.

The probability that this bean will stop in the black square is,

So the answer is:

Comments: This question examines the solution of geometric probability, and it is the key to solve the problem by using probability = the ratio of corresponding area to total area.

8.(2 points) (2008? Wuhu) As shown in the figure, it is known that point E is a point on circle O, b and c are bisectors of bad arc ad, and ∠ bo c = 46, then ∠ the degree of ∠AED is 69 degrees.

Test site: fillet theorem. 190 187

Analysis: If you want to ∠AED, it is known that B and C are bisectors of bad arc ad, ∠ BOC = 46, you can find ∠ AOD = 138, and then use the relationship between the central angle and the central angle to solve it.

Solution: solution: ∵B and c are bisectors of the lower arc AD, ∠ BOC = 46,

∴∠AOD= 138，

∴∠AED= 138 ÷2=69。

Comments:

9.(2 points) As shown in the figure, points D and E are on lines AB and AC respectively, and BE and CD intersect at point O, AE=AD. In order to make △ Abe △ ACD, it is necessary to add a condition ∠ADC=∠AEB or ∠B=∠C or AB.

10.(2 points) (20 12? Qinghai) As shown in the picture, the height of the building is measured by the benchmark BE. The benchmark BE is 1.5m, and AB=2m, BC= 14cm, so the building height CD is 12m.

Test center:. 190 187

Special topic:.

Analysis:

Answer: solution: ∵EB⊥AC, DC⊥AC,

∴EB∥DC，

∴△ABE∽△ACD，

∴ = ,

∫BE = 1.5，AB=2，BC= 14，

∴AC= 16，

∴ = ,

∴CD= 12.

So the answer is: 12.

Comments: The key to solve this problem is to investigate the application of similar triangles and understand the proportional nature of the corresponding edge of similar triangles.

1 1.(2 points) (20 12? Qinghai) Observe the following set of charts:

They are arranged according to certain rules. According to this rule, there are 3n+ 1 ★ in the * * of the nth graph.

12.(2 points) (20 10? Hengyang) as shown in the figure, in Rt△ABC, ∠ c = 90, AC=4, BC=2, and draw semicircles with the diameters of AC and BC respectively, then the area of the shaded part in the figure is π-4 (the result keeps π).

Test center:. 190 187

Analysis:

Solution: Let the area of each part be S 1, S2, S3, S4 and S5, as shown in the figure.

∫ The sum of the areas of the two semicircles is S 1+S5+S4+S2+S3+S4, the area of △ABC is S3+S4+S5, and the area of the shaded part is S 1+S2+S4.

The area of the shaded part in the figure is the area of two semicircles minus the area of the triangle.

That is, the shadow area = π× 4 ÷ 2+π× 1 ÷ 2 戣 4× 2 ÷ 2 =.

Comments: The key to this problem is that the area of the shadow part in the picture is the area of two semicircles-the area of a triangle.

Second, multiple-choice questions: (3 points for each question, ***24 points)

13.(3 points) (20 12? Foshan) In the following figures, the one that is both symmetrical and central is ().

A.B. C. D。

Examination center: 190 187

Special topic:.

Analysis:

Solution: Solution: A, this figure is a central symmetrical figure, not an axisymmetric figure, so the option is wrong;

B, this graph is a centrosymmetric graph and an axisymmetric graph, so the option is correct;

C, this figure is not a central symmetric figure, but an axisymmetric figure, so the option is wrong;

D, this graph is not a centrosymmetric graph, but an axisymmetric graph, so the option is wrong.

So choose B.

Comments:.

14.(3 points) (20 12? Qinghai) In the following operations, the incorrect one is ().

A.(x3y)2= x6y2 B. 2x3÷x2=2x C. x2？ x4=x6 D. (﹣x2)3=﹣x5

Examination center: 190 187

Special topic:.

Analysis: a, according to the operational nature of product power, it can be judged;

B, according to the law that the monomial is divided by the monomial, a judgment can be made;

C, calculating the nature of multiplication operation with the same base number and making a judgment;

D, according to the operation nature of product power, can make a judgment.

Solution: Solution: A, (x3y)2= x6y2, correct, so this option is wrong;

B, 2 x3÷x2=2x, correct, so this option is wrong;

c、x2？ X4=x6, correct, so this option is wrong;

D, (-x2) 3 =-x6 is wrong, so this option is correct.

So choose D.

Comments: This topic examines the operational nature of the power of the product. The law of dividing the monomial by the monomial and the nature of multiplying with the base power are relatively simple.

15.(3 points) (20 12? Qinghai) Two shooters, A and B, each had a shooting practice of 10, with a score of 95 rings. The variance of their scores is =0.6 and =0.4 respectively, so the following statement is correct ().

A.a is more stable than b, and b is more stable than a.

C. the results of both parties are equally stable. D. it is impossible to determine whose performance is more stable.

Test center: variance. 190 187

Analysis: Variance reflects the fluctuation of a set of data. The smaller the variance, the smaller the data fluctuation and the more stable the score.

Solution: solution: ∫S a2 = 0.6, S2 = 0.4,

Then S2 > S2,

It can be seen that B is more stable.

So choose B.

Comments: This question examines the significance of variance. Variance is a measure of the fluctuation of a set of data. The greater the variance, the greater the deviation between this group of data and the average, that is, the greater the fluctuation, the more unstable the data; Conversely, the smaller the variance, the more concentrated the distribution of this group of data, and the smaller the deviation of each data from the average, that is, the smaller the fluctuation, the more stable the data.

16.(3 points) (20 12? Qinghai) As shown in the figure, the image of linear function y= kx-3 and the image of inverse proportional function y= intersect at point A and point B, where the coordinate of point A is (2, 1), then the values of k and m are ().

A.k= 1，m=2 B. k=2，m= 1 C. k=2，m=2 D. k= 1，m= 1

Test site: the intersection of inverse proportional function and linear function. 190 187

Analysis: Substituting A (2, 1) into inverse proportional resolution function can get M, and substituting the coordinates of A into linear resolution function can get the equation about K, and then get the solution of the equation.

Solution: Solution: Substitute A (2, 1) into the analytical formula of the inverse proportional function to get: m=xy=2,

Substituting the coordinates of a into the analytical formula of linear function gives: 1 = 2k-3,

Solution: k = 2.

So choose C.

Comments: This topic examines the intersection of a linear function and an inverse proportional function, and mainly examines students' computing ability.

17.(3 points) (20 12? Qinghai) As shown in the figure, in Rt△ABC, CD is the midline on the hypotenuse AB, and given that CD=5 and AC=6, the value of tanB is ().

Here.

Test site: the definition of acute trigonometric function; The midline on the hypotenuse of a right triangle; Pythagorean Theorem 190 187

Analysis: According to the fact that the midline on the hypotenuse of a right triangle is equal to half of the hypotenuse, calculate the length of AB, then calculate the length of BC by Pythagorean theorem, and then solve it according to the fact that the tangent of the acute angle is equal to the opposite side.

Solution: Solution: ∵CD is the midline on the hypotenuse AB, and CD=5.

∴AB=2CD= 10，

According to Pythagorean theorem, BC= = =8,

tanB= = =。

So choose C.

Comments:?

18.(3 points) (20 12? Qinghai) After translating the parabola y=3x2 to the right by 1 unit length, the resolution function obtained is ().

A.y=3x2﹣ 1 b y=3(x﹣ 1)2 c y = 3 x2+ 1d y = 3(x+ 1)2

Test center: quadratic function image and geometric transformation. 190 187

Topic: Existentialism.

Analysis: Answer according to the principle of "left plus right minus".

Solution: According to the principle of "adding left and subtracting right", after the parabola y=3x2 moves to the right 1 unit length, the analytic function is y = 3 (x- 1) 2.

So choose B.

Comments: This question examines the image and geometric transformation of quadratic function, and understanding the image translation law of function is the key to solve this question.

19.(3 points) (20 12? Qinghai) The competition in the communication market is becoming more and more fierce. The local telephone tariff of a communication company was reduced by one yuan per minute according to the original standard, and then reduced by 20% again. Now the charging standard is B yuan per minute, so the original charging standard is ().

A.(A+B) Yuan B. (A-B) Yuan C. (A+5B) Yuan D. (A-5B) Yuan

Test center: column algebra. 190 187

Analysis: first show the price after 20% reduction, and then add one yuan to get it.

Answer: solution: b ÷ (1-20%)+a = a+b.

So choose a.

Comments: This topic examines column algebra, and correctly understanding the relationship in the topic is the key.

20.(3 points) (20 12? Qinghai) The process reflected in the picture is: Xiaogang went to the vegetable field from home to water it, then went to the highland barley field to weed it, and then went home. If the distance between vegetable field and highland barley field is one kilometer, it takes Xiaogang b minutes to weed in highland barley field than to water in vegetable field, then the values of a and b are () respectively.

A. 1.8

Test center: image of function. 190 187

Topic: Chart types.

Analysis: First, make clear the meaning of abscissa and total coordinates, and then analyze the whole function image according to each special point.

Solution: Solution: This function can be roughly divided into the following stages:

① 0- 12 minutes, Xiaogang walked from home to the vegetable field;

② 12-27 minutes, Xiaogang watered the vegetable field;

③ In 27-33 minutes, Xiaogang walked from vegetable field to highland barley field;

④ For 33-56 minutes, Xiaogang weeded in the highland barley field;

⑤ 56-74 minutes, Xiaogang returned home from highland barley;

Based on the above analysis, it is concluded from the process of ③ that a =1.5-1= 0.5km;

From the process of ② and ④, we know that B = (56-33)-(27- 12) = 8 minutes.

So choose D.

Comments: This paper mainly examines the reading ability of function images and the application of combining functions with practical problems. We should be able to get the type and required conditions of the function according to the nature of the function image and the data analysis on the image, and draw the correct conclusion in combination with the practical significance.

Three. (This big title is ***3 small questions, 2 1 5 points, 22 questions 6 points, 23 questions 8 points, *** 19 points)

2 1.(5 points) (20 12? Qinghai) calculation: |-5 |-2coS60++.

Test center: the operation of real numbers; Zero exponential power; Negative integer exponential power; Trigonometric function value of special angle. 190 187

Analysis: This question involves zero exponential power, negative integer exponential power and trigonometric function value of special angle. When calculating, it is necessary to calculate each test center separately, and then get the calculation result according to the arithmetic of real numbers.

Solution: The original formula = 5 ~ 2×+22+ 1.

=5﹣ 1+4+ 1

=9.

Comments: This question examines the comprehensive calculation ability of real numbers, which is a common calculation problem in the senior high school entrance examination questions all over the country. The key to solve this kind of problem is to master the operation of negative integer exponential power, zero exponential power and absolute value.

22.(6 points) (20 12? Qinghai) Simplify first and then evaluate: (1﹣) ﹣+3x ﹣ 4+3x ﹣ 4, where x =.

23.(8 points) (20 12? Qinghai) is known: as shown in the figure, D is a point on the AB side of △ABC, and CN∨AB and DN intersect with AC at point M, and Ma = MC. ① Verification: CD = an② If ∠AMD=2∠MCD, it is proved that the quadrilateral ADCN is a rectangle.

Test center: rectangular judgment; Congruent triangles's judgment and nature; Determination and properties of parallelogram. 190 187

Special topic: proof questions.

Analysis: ① According to the fact that two straight lines are parallel and the internal angle is equal, find out ∠DAC=∠NCA, then prove the congruence of △ sum and △CMN with "corner", and get AD=CN according to the equivalence of the corresponding sides of congruent triangles, then judge that the quadrilateral ADCN is a parallelogram, and then prove it according to the equivalence of the opposite sides of the parallelogram;

② Deduce ∠MCD=∠MDC according to the fact that one outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it, then get MD=MC according to the equilateral sides of equal angles, then prove AC=DN, and then prove that a parallelogram with equal diagonal lines is a rectangle.

Answer: proof: ①∫CN∨AB,

∴∠DAC=∠NCA，

At △ and △CMN,

∵ ,

∴△AND≌△CMN(ASA)，

∴AD=CN，

And ∵AD∨CN,

∴ Quadrilateral ADCN is a parallelogram,

∴cd=an；

②∫∠AMD = 2∠MCD∠AMD =∠MCD+∠MCD，

∴∠MCD=∠MDC，

∴MD=MC，

According to ①, the quadrilateral ADCN is a parallelogram,

∴MD=MN=MA=MC，

∴AC=DN，

The quadrilateral ADCN is a rectangle.

Comments: This topic examines the judgment of rectangle, the judgment and nature of parallelogram, and the judgment and nature of congruent triangles. Starting from the first question, it is the key to solve the problem to master the relationship between parallelogram and rectangle and find out that quadrilateral ADCN is a parallelogram.

Iv. (This big question is ***3 small questions, 24 questions are 8 points, 25 questions are 7 points, 26 questions 10 points, ***25 points)

24.(8 points) (20 12? Qinghai) Xiadu Flower Base sells two kinds of flowers, one is calla lily in 3.5 yuan and the other is carnation in 5 yuan. If the number of calla lilies purchased by the same customer exceeds 1000, then all calla lilies can enjoy preferential treatment in 0.5 yuan. Now a flower shop has purchased 800 ~ 1, 200 calla lilies and several carnations from Xiadu Flower Base, and this purchase cost 7000 * *.

(Note: 800 ~ 1200 plants means that the number of purchased plants is more than or equal to 800 plants and less than or equal to 1200 plants; Profit = sales revenue (the amount required for purchase).

Test center: the application of linear function. 190 187

Special topic: geometric problems.

Analysis: Suppose you buy X plants of calla lily, because when the number of calla lily is more than 1000 plants, the price of each rose will decrease 0.5 yuan, so you need to discuss it in two situations, namely, 800≤x≤ 1000 and 1000 < x ≤ 1200. According to the equivalence relation, "the cost of buying calla lily+the cost of buying carnation"

Solution: Solution: Suppose we purchase calla lily X and carnation Y, and the profit is W yuan.

① when 800≤x≤ 1000

3.5x+5y=7000，y = = 1400-0.7x。

w=(4.5﹣3.5)x+(7﹣5)y

=x+2y=x+2( 1400﹣0.7x)=2800﹣0.4x

When x is 800, the maximum value of w is 2480;

② When 1000 < x ≤ 1200.

3x+5y=7000，y = = 1400-0.6x。

w=(4.5﹣3)x+(7﹣5)y

= 1.5x+2y= 1.5x+2( 1400﹣0.6x)=2800+0.3x

When x is 1200, the maximum value of w is 3160;

(3) To sum up, the latter method is adopted to purchase water chestnut lotus at1200× 3 = 3,600 yuan; Buy carnations (7000 ~ 3600) ÷ 5 = 680 plants.

Answer: When purchasing 1200 calla lily and 680 carnations, the highest profit is 3 160 yuan.

Remarks: This topic examines the application of functions. This problem is a comprehensive application problem combining equation with practice. Students should learn to use functions to solve practical problems. Note: 800≤ calla lily ≤1000; 1000