The final examination paper for the next semester of junior one mathematics 1998.7.

School _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Title number

one

two

three

four

five

six

seven

eight

nine

Total score

mark

1. Fill in the blanks: (2 points for each small question, * * * 20 points)

(1) The equation 2x-3y+4 = 0 is known. If x is represented by an algebraic expression containing y, it should be written as _ _ _ _ _ _ _ _.

(2) given that x=5 and y=7 satisfy KX-2Y = 1, then K = _ _ _ _ _ _ _ _

③ Inequality 2x-4

(4) 0.0987 is _ _ _ _ _ by scientific notation.

(5)__________。

(6) As shown in the figure, ∠1= _ _ _ _ _ _.

(7) As shown in the figure, the conformal angle of ∠3 is _ _ _ _ _ _.

(8) The northeast direction is _ _ _ _ _ _ _ due north by east.

(9) Rewrite "There is only one intersection point between two straight lines" as "If".

(10) It is known that all three points A, B and C are on the straight line L, and AB = 5cm and BC = 6cm, then the length of AC is _ _ _ _ _ _ _ _.

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

Of the four options given in each question, one and only one is correct. Please put the alphabetic code before the correct option in brackets.

The solution set of (1) unary linear inequality is ().

(A)x & gt； -8 (B)x<-8(C)x & gt； -2(D)x & lt； -2

(2) The following shows that the correct process of finding the solution set of inequality group is () on the number axis.

(3) The following calculation error is ().

① ②

③ ④

⑤ ⑥

Six (b) five (c) four (d) three

(4) The following multiplication formula is correct ().

①

②

③

④

(A)4 (B)3 (C)2 (D) 1。

(5) The correct one in the following drawing statement is ().

(a) extend the straight line PQ (B) as the midpoint o of the ray MN.

(c) The bisector MN (D) of the straight line AB is the bisector OC of ∠AOB.

(6) Among the following propositions, the straight proposition is ().

(a) The two acute angles must be complementary.

(b) Two complementary angles are adjacent complementary angles.

(c) The complementary angles of equal angles are equal.

(d) If AM = MB, point M is the midpoint of line segment AB.

(7) Angles smaller than right angles are divided into three categories according to size ().

(1) acute angle, right angle and obtuse angle (2) internal dislocation angle and internal angle on the same side.

(c) Round corners, right angles and right angles (d) Top angles, complementary angles and complementary angles.

(8) In plane geometry, the false proposition in the following propositions is ().

(a) Two lines parallel to the same line are parallel.

(b) There is only one straight line between two points.

(c) There is one and only one straight line parallel to the known straight line at one point.

(d) There is one and only one straight line perpendicular to the known straight line.

3. Calculate the following questions: (small questions (1)~(6)2 points, small questions (7) and (8)3 points, *** 18 points).

( 1)__________

(2)__________

(3)__________

(4)5x(0.2x-0.4 years) = _ _ _ _ _ _ _ _

(5)__________

(6)__________

(7)

Solution:

(8)

Solution:

Fourth, solve the following linear equations and linear inequalities of one variable: (5 points for each small question, *** 10).

( 1)

Solution:

(2)

Solution:

5. Drawing questions: (Draw with a scale, triangle, protractor or ruler, not writing, only requiring the picture to be accurate. ) (65438+ 0 point for each small question, ***3 points).

(1) The point where the parallel line M passes through A is BC;

(2) Point A is the vertical line of BC, and the vertical foot is point D;

(3) The length of the line segment _ _ _ _ _ _ is the distance from point A to BC.

6. Fill in the blanks in the following reasoning process, and fill in the blanks with the basis of this reasoning step (65438+ 0 points per space, ***7 points).

As shown in the figure, AD//BC (known),

∴∠DAC=__________().

∫∠BAD =∠DCB (known),

∴∠BAD-∠DAC=∠DCB-__________，

That is to say, ∞ _ _ _ _ _ = ∞ _ _ _ _ _ _.

∴AB//__________().

Seven, solve the problem of equations: (5 points for each small question, *** 10)

(1) I bought 10 stamps, 20 stamps and 50 stamps with 3 yuan 50 * *18 stamps. The total face value of 10 stamp is the same as that of 20 stamps. How many stamps did I buy each of these three stamps?

Solution:

(2) The complementary angle of ∠ABC is greater than that of ∠MNP, and the complementary angle of ∠ ABC is greater than that of ∠MNP. Find the degree of ∠ ABC and ∠MNP

Solution:

Eight. Proof question: (5 points for this question)

Known: as shown in figure ∠ BDE+∠ ABC =, BE//FG.

Proof: ∠ Deb = ∠ GFC.

Prove:

Nine, it is known that the solution of the equation about x and y is the same as the solution of the equation, and the values of m and n are found. (3 points for this question)

Solution:

Reference answers and equal division criteria

Fill in the blanks

(2 points for each small question, ***20 points)

( 1) (2)3

(3)x & lt； 2 (4)

⑸4xy⑹ 100

(7)& lt； 7 (8)45

(9) If two straight lines intersect, there is only one intersection point, (1 0) 1cm or1cm (if only one of them is written,1minute can be given).

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

BBAD·DCAC

Three. Calculate the following questions: (2 points for minor questions (1) ~ (6), 3 points for minor questions (7)(8), *** 18.

( 1) (2) (3) (4)

(5) (6)

(7) (If the result is wrong and the process is correct, you can give 1 minute)

(8) Original formula .......................................... 1 min.

Three points

Four, solve the following linear equations and linear inequalities (5 points for each small question, *** 10).

(1) Answer:

Correctly exclude 2 points.

Correctly solve the value of an unknown .............................................................................................. 4 points.

Complete the solution of the equation 5 points.

(2) answer:.

2 points for correctly solving the solution set of each inequality in the inequality group.

Get the correct answer and get 1 point.

The solution set of the first inequality is written as x < 8, or finally get -3, otherwise it is correct, get 4 points.

Fifth, drawing questions. (65438+ 0 point for each small question, ***3 points)

Six, (per grid 1 minute, ***7 points)

∠BCA, (two straight lines are parallel with equal internal angles)

∠BCA∠BAC∠DCA，

DC, (offset angle is equal, two straight lines are parallel)

Seven. Solving application problems with equations: (5 points for each small question, *** 10)

(1) Solution: Suppose 10 bought x stamps, y stamps for 20 stamps and z stamps for 50 stamps. ................. 1 point

So ... three points.

The solution is 4 o'clock.

A: 10 bought 10 stamps, 5 stamps for 20 and 3 stamps for 50. Five points.

(2) Solution: Let ∠ABC be and ∠MNP be. ................................ 1 min.

So ... three points.

The solution is 4 o'clock.

A: ABC is, MNP is. Five points.

Eight, proof questions. (5 points for this question)

Proof: ∫∠BDE+∠ABC =,

∴DE//BC, 2 points

∴∠DEB=∠EBF。 Three points

∵BE//FG，

∴∠EBF=∠GFC, 4 points.

∴∠DEB=∠GFC。 Five points.

9. Solution: The solution of the equations is the same as that of the equations.

The solution of ∴ is the same as that of the equation.

The fraction of solving the equation is

Substitution equation

To understand this system of equations, you must get

Replace in my =- 1

∴,。 Three points

See the figure below.

References:

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Line AB CD intersects with point O, angle AOE=30 degrees, angle BOC=2* angle AOC, and find angle DOF.

Supplement: f is the reverse extension of e (two rays drawn on the same straight line)

There are two ideas about this problem:

Since angle BOC = 2, angles AOC and AOB are flat angles of 180 degrees, which is equivalent to dividing the flat angle into three parts, angle AOC accounting for 60 degrees and angle BOC accounting for two parts, that is 120 degrees.

(1) Point E is between A and C, and the angle AOE = 30 degrees, then OE is the bisector of the angle AOC. That is to say, angle AOE= = angle COE = 30 degrees. Because the angles DOF and COE are diagonal, the angle DOF = 30 degrees.

Steps: ∵∠ AOB =180 ∠ BOC = 2 ∠∴∠ AOC = 60 and ∵∠ AOE = 30 ∴∠ COE.

(2) point e is between a and d. Because the angle AOD is the antipodal angle of the angle BOC, the angle AOD = 120 degrees. Because the angle AOE = 30 degrees and the angle DOE = 120-30 = 90 degrees. That is, the straight line EF is perpendicular to CD, so the angle DOF = 90 degrees.

Steps: ∵∠ AOB =180 ∠ BOC = 2 ∠∴∠ AOC = 60 and ∵∠ AOE = 30.

∴∠COE=90 EF⊥CD ∴∠DOF=90

A math problem about "angle" in grade one.

Within the angle AOB, draw three rays OC, OD and OE through the vertex O. How many angles does this figure have? What if you draw four rays? What if you draw (n-2) rays (n is greater than or equal to 2)?

The first problem is the 10 angle.

The second problem is the angle of 15.

What's the third question? 3 1+2

4 1+2+3

5 1+2+3+4

Article N-21+2+3+...+(n-3) = n (n-1)/2