1. Multiple-choice questions: (3 points for each question, ***21 points)
Question number 1 2 3 4 5 6 7
Answer
Each question gives four answers, only one of which is correct. Please fill in the selected answer number in the answer sheet above, otherwise no points will be given.
1. Known equation 3x+a =. Then the values of a are
A,-13b,-17c, 13 D, and 17
2. Given that the circumference of an isosceles triangle is 63cm, and the circumference of an equilateral triangle with one waist as its side is 69cm, then the length of the base of an isosceles triangle is
A, 23cm B, 17 cm C, 21 cm D, and 6. Take out the pocket money and count it. It is found that there are 15 * * * in 1 yuan and 2 yuan, and * * * in 2 yuan. Then there are
A, 5, 1 B, 1, 5 C, 8 D, 7 D, 8 p>4 in the following figures.
② the values of the modes and the median are not equal;
③ The median is equal to the average;
④ the value of average and mode is equal.
A, 1 b, 2 c, 3 d, 4
6. Among the following four regular polygons, those that can't be covered with the same figure are
A, regular triangle b, square c, regular pentagon d and regular hexagon
7. During the SARS period, a drugstore was in short supply of antiviral drugs in the market. If the price increase is limited to 1% of the original price, then the price reduction of the drug is
A, 45% B, 5% C, 9% D and 95%
2. Fill in the blanks: (4 points for each small question, ***32 points, please fill in the answer sheet)
Question No.8 9111.
9. in the isosceles right triangle ABC, ∠A=9o, BC=6cm, BD divides ∠A BC into AC days d, and DE⊥BC into e, then the circumference of △CDE is _ _ _.
1. If the sum of the internal angles of a polygon is 18o, the polygon is a polygon.
11. The speed of a ship sailing downstream is 2km per hour, and the speed of sailing upstream is 12km per hour, so the speed of the ship in still water is zero, and the current speed is zero.
12. In a basketball match, a main player made 22 shots, 14 of which scored 28 points. Besides 3-pointers, he also made 2 points and 3 free throws.
13. Given that 2x-y = 3, then 1-4x+2y =.
14. As shown in Figure 1, ∠1=8o, ∠F=15o, ∠B=35o,
Then ∠A=, ∠DEA=.
(Figure 1)
15. The diagonal line led by a vertex of a polygon divides this polygon into 1 triangles, so the sum of the internal angles of this polygon is.
Reference answers
1. Multiple choice questions
1, A 2, B 3, B 4, D 5, A 6, C 7, A
2. Fill in the blanks: (***1 small questions, 2 points for each question, ***2 points, please fill in the answers in the answer sheet)
9、6cm； 1, 8; 11, 16 km/4 km/hour when I was a child; 12、8 13、-5； 14、45? 85
1. When x=, the equation x+1=2 holds.
2. The solution of the equation -3x=3-4x is.
3. when x=, y1=x+3 and y2=2-x are equal.
the difference between 3 times of p>4.x and 2 is equal to 4, and x=.
5. The circumference of a book is 68cm, and the length is 6cm more than the width. Let the book be xcm in width and cm in length, then by solving the equation, we can find out that the width x= cm and the length is equal to cm.
6. The side of the pyramid is shaped.
7. cut a cube as shown in the figure, and the resulting figure has a face.
8. as shown in the figure, figure a is passed to get figure b.
9. Two identical right-angled triangular plates (3) can be spliced together to form a plane figure.
second, multiple-choice questions (3 points for each question, counting 24 points)
1. Among the following numbers, ()
A.2 B.3 C.4 D.5
11. If x=-2 is the solution of equation a(x+3)= a+x, then A2-+1 = ()
a.17b. B= ()
a.2b.1c.d.-1
13.3x+and 3(x-) are opposites, then x = ()
a.b.-c.d.-
14. The figure obtained is ()
16. The correct figure of the hollow cylinder from three directions is (the invisible part is indicated by dotted line) ()
17. The following figure cannot be folded into a cube is ()
with reference answer:
1.2 2.3.-4.2 5.x+6,2 [x+]
8. Fold, 9.6, 1.b, 11.c, 12.d, 13d, 14.c, 15.b, 16.a, 17.a,; 15、18? ;
multiple choice questions
1. If (x+y): (x-y) = 3: 1, then x: y = ().
A, 3∶1 B, 2∶1 C, 1∶1 D, 1 ∶ 2
2. If the solution of equation -2x+ m=-3 is 3, then the value of m is ().
A, 6 B, -6 C, d,-18
3. The number of equations solved in equation 6x+1=1, 2x=, 7x-1=x-1, 5x=2-x is ().
A, 1 b, 2 c, 3 d, 4
4. Equation () can be obtained according to the quantitative relationship of "the difference between the absolute value of 3 times a and -4 equals 9".
A, |3a-(-4)|=9 B, |3a-4|=9
C, 3 | a |-4 | = 9d, 3a-|-4 | = 9
5.
A, 2 B, 22 C, 1 D, -2
answers and analysis
answers: 1, B 2, A 3, B 4, D 5, C
analysis:
1.
from (x+y): (x-y) = 3: 1, we know that x+y=3(x-y), and we can simplify it to: x+y=3x-3y, and
2x-4y=, that is, x=2y and x: y = 2.
2. Analysis: ∵ 3 is the solution of the equation -2x+ m=-3,
∴-2x3+m =-3,
that is-6+m =-3,
∴ m=-3+6.
3. analysis: the solution of 6x+1=1 is , that of 2x= , that of 7x-1=x-1 is , and that of 5x=2-x is .
4. omitted.
5. analysis: because x=3 is the solution of equation =4(x-1), substituting x=3 into the equation satisfies the equation.
1. Multivariable
The application problem of solving multivariate linear equations refers to the application problem in which there are often multiple unknowns and multiple equal relationships. As long as one of these unknowns is X, the other unknowns can be expressed by an algebraic expression containing X according to the equality relation in the topic, and then a linear equation can be listed according to another equality relation.
Example 1: (Beijing People's Education in 25) In summer, in order to save electricity, two measures are often taken for air conditioning: raising the set temperature and cleaning the equipment. At first, a hotel raised the set temperature of air conditioners A and B by 1℃. As a result, air conditioner A saved 27 degrees more electricity than air conditioner B every day. Then clean the equipment of the second air conditioner, so that the total electricity saving of the second air conditioner is 1.1 times of that after the temperature is only raised by 1℃, while the regulated electricity of the first air conditioner remains unchanged, so that the two air conditioners can save 45 degrees of electricity every day. How many degrees of electricity can be saved by two air conditioners every day after the temperature is raised by 1℃?
analysis: there are four unknowns in this question: the regulated electric quantity of air A after raising the temperature, air B after raising the temperature, air A after cleaning the equipment, and air B after cleaning the equipment. The equal relationships are as follows: the adjusted power of air conditioner after temperature increase-adjusted power of air conditioner after temperature increase = 27, adjusted power of air conditioner after equipment cleaning = 1.1× adjusted power of air conditioner after temperature increase, adjusted power of air conditioner after temperature increase = adjusted power of air conditioner after equipment cleaning, adjusted power of air conditioner after equipment cleaning+adjusted power of air conditioner after equipment cleaning = 45. According to the first three equality relations, an unknown number is used to represent four unknowns, and then the equation is listed according to the last equality relation.
solution: suppose that only after the temperature is raised by 1℃, the second air conditioner saves X degrees of electricity every day, and the first air conditioner saves X degrees of electricity every day. According to the meaning of the question, it is:
Solution:
Answer: After only increasing the temperature by 1℃, the A-type air conditioner saves 27 degrees of electricity every day, and the B-type air conditioner saves 18 degrees of electricity every day.
second, piecewise
the application of piecewise linear equation refers to a kind of application problems with the same unknown quantity and different restrictions in different ranges. When solving this kind of problem, we must first determine the segment of the given data, and then solve it reasonably according to its segment.
Example 2: The price of bananas in a fruit wholesale market in Dongying City in 25 is as follows:
The number of bananas purchased
(kg) does not exceed
2 kg or more
but does not exceed 4 kg or more
The price per kg is 6 yuan, 5 yuan, 4 yuan
Zhang Qiang bought 5 kg of bananas twice.
analysis: because Zhang Qiang bought 5 kilograms of bananas twice (the second time was more than the first time), the second time he bought more than 25 kilograms of bananas, and the first time he bought less than 25 kilograms. Because 5 kilograms of bananas cost 264 yuan, the average price is 5.28 yuan, so it is inevitable that the price of bananas purchased for the first time is 6 yuan/kg, that is, less than 2 kilograms, and the price of bananas purchased for the second time may be 5 yuan or 4 yuan. We can discuss it in two situations.
Solution:
1) When the first banana purchase is less than 2kg and the second banana purchase is more than 2kg but not more than 4kg, let's say that the first banana purchase is x kg and the second banana purchase is (5-x) kg. Get:
6x+5 (5-x) = 264
Solution: x = 14
5-14 = 36 (kg)
2) When the first banana purchase is less than 2kg and the second banana purchase is more than 4kg, it is assumed that the first banana purchase is x kg, and the second banana purchase is x kg. Get:
6x+4 (5-x) = 264
Get: x = 32 (not in line with the question)
Answer: I bought 14 kilograms of bananas for the first time and 36 kilograms of bananas for the second time
Example 3: (Jingmen City, Hubei Province, 25) participated in the medical insurance of an insurance company and was hospitalized. The reimbursement rules formulated by the insurance company are as follows. The amount of reimbursement from the insurance company for someone after hospitalization is 11 yuan. Then this person's hospitalization medical expenses are ()
reimbursement rate of hospitalization medical expenses (yuan) (%)
no more than in 5 yuan
more than 5 ~ 6 in 1 yuan
more than 1 ~ 3 yuan, 8
...
A, B, 125 yuan C, 1 yuan. According to the meaning of the question:
5× 6%+(x-1) 8% = 11
Solution: x = 2
So the answer to this question is D.
Third, the scheme type
The scheme type one-dimensional linear equation often gives two schemes to calculate the same unknown quantity, and then connects the algebraic expressions representing the two schemes with an equal sign to form a one-dimensional linear equation.
example 4: (Quanzhou city, 25) The third-grade students of a school participated in social practice activities. It was originally planned to rent a number of buses with 3 seats, but there were still 15 people without seats.
(1) Suppose the original plan is to rent X buses with 3 seats, and try to express the total number of students in the third grade of the school with an algebraic expression containing X;
(2) Now it is decided to rent a 4-seat bus, which is one less than the 3-seat bus originally planned, and one of the 4-seat buses rented is not full, only 35 people are seated. Please find out the total number of students in grade three in this school.
analysis: there are two ways to express the total number of students in grade three. The number of buses with 3 seats is 3x+15
The number of buses with 4 seats is 4 (x-2)+35.
Solution: (1) The total number of students in grade three in this school is 3x+15
(2) It is derived from the meaning of the question:
3x+15 = 4 (x-2)+35
Solution: x = 6
3x+15 = 3x.
Fourth, data processing type
Data processing type One-dimensional linear equations often do not directly tell us some conditions, and we need to analyze the given data to obtain the data we need.
Example 5: Solving application problems (Haidian District, Beijing, 24): April, 24