Mid-term examination questions of mathematics in the second volume of the seventh grade of Jiangsu Education Edition.

The second semester mid-term mock exam

Mathematics Test

Dear students, hello! Midway through the new semester, congratulations on mastering a lot of new mathematics knowledge and methods and becoming smarter. You must be able to apply mathematics to solve practical problems. Now let's go into the examination room together, give full play to your intelligence, believe in yourself, and success must belong to you!

First, the key choice (this *** 10 question, 3 points for each question, 30 points)

The title is 1 23455 6789 10.

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1. The following equation is correct.

a . x2+x3 = 2x5b .(-2x)2x 3 = 4x5c .(x-y)2 = x2-y2 d . x3y 2÷x2y 3 = x y

3. Suppose, then the size relationship between A and B is

A.a = b.b.a > b.c.a < b.d None of the above three are correct.

3. If (x+5) (2x-n) = 2x2+MX- 15, then

A.m=-7，n=3 B.m=7，n=-3 C.m=-7，n=-3 D.m=7，n=3

3. The calculation result of (28a3- 14a2+7a) ÷ (-7a) is as follows.

A.-4a 2+2a b . 4a 2-2a+ 1 c . 4a 2+2a- 1d .-4a 2+2a- 1

5. A rope with a length of 1 meter is cut off in half for the first time, the remaining half for the second time, and so on. The length of the remaining rope after the sixth time is

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The common factor of polynomial 36a2bc-48ab2c+24abc2 is

a . 12 a2 B2 C2 b . 6 ABC c . 12 ABC d . 36 a2 B2 C2

The following factorization factors are wrong.

a . 15 a2+5a = 5a(3a+ 1)b .――x2―y2 = ―( x+y)(x―y)

c . ax+x+ay+y =(a+ 1)(x+y)d . a2―BC-a b+ AC =(a―b)(a+c)

⒏ There are the following lengths in each group of line segments, which cannot form a triangle.

A. 1.5，2.5，3.5 B .，

C.2a，3a，5a(a>0) D.m+ 1，m+2，m+3(m>0)

⒐ As shown in the figure, if ∠DBC=∠D, BD is divided by ∠ABC, ∠ ABC = 50, then ∠ DBC = ∠ D is

100

C. 130

⒑ As we all know, the lengths of three sides of a triangle with a perimeter less than 15 are prime numbers, and the length of one side is 3. Such a triangle is

A.4 B.5 C.6 D.7

Second, calmly fill in a fill (this item *** 10, 2 points for each question, 20 points)

(1) In the calculation result of (x+ 1) (2x2+AX+ 1), the coefficient of x2 is -2, so the value of a is.

5. Simplification: (a-1) (-a-1) = _ _ _ _ _ _ _ _ _.

⑶ Polynomial x2+px-4 can be decomposed into the product of two linear factors, and the value of integer p is.

Two students decompose a quadratic trinomial factor, and one student decomposes it into a quadratic trinomial factor because he misread the coefficient of the first term.

2(x- 1)(x-9)； Another student decomposed the constant term into 2 (x-2) (x-4) because of a mistake. Please write the correct result of factorization of the original polynomial.

5. It is known that x2+y2+4x-6y+ 13 = 0, where both x and y are rational numbers, then yx = _ _ _ _ _ _ _ _ _ _ _ _

Mom takes out 100 new RMB 100 from the bank, and Xiao Ming measures that their thickness is about 0.9cm, so the thickness of each RMB 100 is about m (expressed by scientific notation).

⒘ Polynomial 4x2+9 can be factorized by the complete square formula after adding a monomial, so the added monomial can be _ _ _ _ _ _ _ _ _ _ _ (only fill in the one you think is correct, without considering all possible situations).

⒙ If, then =

If two parallel straight lines are cut by a third straight line, then: ① A pair of bisectors with the same angle are parallel to each other; ② The bisectors of a pair of internal dislocation angles are parallel to each other; ③ A pair of bisectors at the inner corner of the same side are parallel to each other; (4) A pair of bisectors at the inner corner of the same side are perpendicular to each other. The correct conclusion is. (Note: Please fill in the serial numbers of all the correct conclusions you think)

⒛ If the circumference of an isosceles triangle is 24cm and the waist length is xcm, then the range of X is.

Third, do it seriously (this question is ***4 big questions, 26 points)

2 1. Calculation: (This big question ***3 small questions, 3 points for each question, 9 points)

⑴(2x- 1)(4x 2+ 1)(2x+ 1)；

⑵(2a-b+3)(2a-3+b)；

⑶4(a+2)2-7(a+3)(a-3)+3(a- 1)2。

22. Break down the following factors: (There are 3 small questions in this big question, 3 points for each question, 9 points)

⑴-36 x2+ 12xy-y2； ⑵9(2a+3b)2-4(3a-2b)2；

⑶(x2-2x)2+2(x2-2x)+ 1；

23. Simplify first, then evaluate: (4 points for this question)

2 (x-y) 2-(y-x) 2-(x+y) (y-x), where x = 3 and y =-2.

24. As shown in the figure, after a rectangular piece of paper is folded along EF, points D and C fall at points D' and C' respectively, and the extension line of ED' intersects with BC at point G. If ∠ EFB = 50, find the degrees of ∠ 1 and ∠2 (4 points for this question).

Four, independent inquiry (this ***4 big questions, 24 points)

25. When calculating the value of (x+y) (x-2y)-my (nx-y) (both m and n are constants), when substituting the values of x and y into the calculation, both the careless Xiaoming and Liang Xiao misread the value of y, but the results are all equal to 25. Careful Xiao Min substituted the correct values of X and Y into the calculation, and the result was exactly 25.

(1) According to the above situation, try to explore the mystery;

Can you determine the values of m, n and x? (Theme 1+3 = 4)

26. Observe the following series of equations:

① 1×2×3×4+ 1=52=( 12+3× 1+ 1)2;

②2×3×4×5+ 1= 1 12=(22+3×2+ 1)2;

③3×4×5×6+ 1= 192=(32+3×3+ 1)2;

④4×5×6×7+ 1=292=(42+3×4+ 1)2; ……

(1) Please indicate the above rules in letters:.

(2) Use the methods you have learned to prove the laws you have found. (This question is 2 points +4 points = 6 points)

27. Experiments show that the law of light reflected by a plane mirror is that the light incident on the plane mirror and the reflected light are equal to the acute angle sandwiched by the plane mirror, as shown in the figure, that is, ∠ 1 = ∠ 4, ∠ 5 = ∠ 6.

(1) As shown in the figure, a beam of light M hits the plane mirror A, which is reflected by A to the plane mirror B, and then reflected by B. If the light N reflected by B is parallel to the light M and ∠ 1 = 50, ∠ 3 = 0.

(2) In (1), if < 1 = 55, < 3 =; If ∠ 1 = 40, ∠ 3 = 0;

(3) From (1) and (2), please guess: When the included angle between two plane mirrors A and B is ∠ 3 = 0, any light M incident on plane mirror A can be made parallel to the reflected light N after being reflected by plane mirrors A and B twice. Can you explain the reason? (Subject 1+2+3 = 6)

28. Figure ① is a rectangle with a length of 2m and a width of 2n. Divide it into four small rectangles evenly along the dotted line in the figure, and then spell it into a square according to the shape of Figure ②.

(1) The shaded area in Figure (2) is:

(2) Look at Figure (2). Please write the equivalent relationship between three algebraic expressions (m+n) 2, (m-n) 2 and m+n)2.

(3) If X+Y =-6 and XY = 2.75, then X-Y =.

In fact, there are many algebraic identities that can be expressed by the area of a graph.

As shown in Figure (3), it represents.

5. Try to draw a geometric figure so that its area can be expressed as (m+n) (m+3n) = m2+4mn+3N2.

(Subject 1+ 1+2+2 = 8)

Reference answer

The title is 1 23455 6789 10.

Option b, a, d, c, c, b, c, b.

⒒ -4 ⒓ 1-a2 ⒔ 0，3 ⒕ 2(x-3)2 ⒖ ⒗ 9× 10-7

⒘ or 12x or-12x ⒙ 47 [6] ① ② ④ 93716 < x <12.