Class _ _ _ _ _ _ _ Name _ _ _ _ Student ID _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1. Multiple choice questions (3 points for each question, ***24 points) (60 minutes, full mark 100 points)
1. The number of integers whose absolute value is less than 3.5 is ()
A.8 B.7 C.6 D.5
2. The following statement is ()
A.B. C. D。
3. In -(-8), |- 1 |, | 0 |, the negative number in these four numbers is ().
A.4 B.3 C.2 D. 1
4. If sum is a rational number, the correct one of the following propositions is ().
A. If, then B. If, then
C. If, then D. If, not all of them are zero, then
5. If sum is opposite, the following conclusion is not necessarily correct ().
A.B. C. D。
6. The following median is negative ().
A.B. C. D。
7. The approximate value of three significant digits 4 1.0 is ().
a . 4 1. 12 b . 4 1.05 c . 40.95d . 40.94
8. The following statement is true ()
A. Positive and negative integers are collectively called integer b, and the smallest integer is 0.
C. any negative number is less than its opposite number d. The absolute value of rational number is positive.
2. Fill in the blanks (3 points for each question, ***30 points)
9. Save 500 yuan as +500 yuan, then-100 yuan is _ _ _ _.
10.|-6 | = _ _, and the reciprocal of |-5 | is _ _ _ _; The reciprocal of _ _ _.
1 1. If yes, then _ _; If so, then _ _; If so, then _ _.
12. The sum of non-negative integers with absolute values less than 3 is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
13. Calculate _ _ _ _ _ _ _.
14. If the number recorded by scientific notation is, the original number is _ _ _ _ _ _ _.
15. The number whose cubic number equals itself is _ _; The number whose square is equal to the cube is _ _ _ _.
16. Calculate _ _ _ _ _ _ _ _.
17. Calculation = _ _ _ _ _ _ _.
18. If,,, is known, then _ _ _ _ _ _ _.
Three. Calculation questions (6 points for each question, ***30 points)
19.
20.
2 1.
22.
23.
4. Solve problems (8 points for each question, *** 16 points)
24. If the rational number is satisfied, find the value of the formula.
25. When it is a rational number, the value of the algebraic expression is: (1) integer; (2) scores.
Exercise 2 Algebraic addition and subtraction
Class _ _ _ _ _ _ Student ID _ _ _ _ _ _ _ Name _ _ _ _ _ _ _ _
I. Right and wrong issues
The coefficient of 1 is 2 ().
2. and are similar projects ()
3. Algebraic expression is a quadratic trinomial expression ()
4. If,,, then ()
Second, multiple choice questions
1. The following operations are combined with similar items, and the correct result is ().
A.B.
C.D.
2. The following statements: ① and 0 are similar items; ② Sum is similar; ③ Sum is similar; (4) and are similar projects, and the correct one is ().
1。
3, in parentheses, the result is ()
A.B. C. D。
4. If, then the value of ()
A. equals 4 b equals C. D. can't be sure
5. If known, the value of is ()
80 BC
6. In the following brackets, the wrong one is ()
A.
B.
C.2
D.
7. If A= and B=, the relationship between A and B is ().
A.A & gtB B A & lt； Not sure.
Third, fill in the blanks
1, the coefficient of single item is _ _ _ _ _ _ _, and the degree is _ _ _ _ _ _ _.
2. If it is a cubic trinomial, it is = _ _ _ _ _ _ _ _ _ _ _.
3. The ascending order of polynomials is _ _ _ _ _ _ _ _ _ _ _ _,
4、
5. simplify.
6. If it is similar to 4, then.
7. When subtracting a polynomial A from it, the careless students copied the minus sign into a plus sign, and the result of the operation showed that the polynomial A was _ _ _ _ _ _ _ _ _ _ _ _ _.
8. If the digit of 10 is 2 less than the single digit, and the digit of 100 is half, then this three-digit number is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Fourth, simplify the problem.
1、
2、
3、
4、
Verb (abbreviation for verb) simplifies evaluation
1, where
2. When it is known, the value of the algebraic expression is 5, so find the value of the algebraic expression.
3, the value of: is known.
Step 4 simplify
Half of the original passengers on the bus got off halfway and got on several people, so there were passengers on the bus. How many passengers are there? When and how many passengers were on board?
6. If the value of algebraic expression has nothing to do with the value of letters, find the value of algebraic expression.
Exercise 3: A Preliminary Understanding of Graphics
Grade: _ _ SeatNo.: Name: Achievement: _ _ _ _ _ _
1. Fill in the blank: (2 ′×14 = 28 ′)
1, two straight lines intersect and two adjacent angles are equal, then the two angles are summed separately.
2. Extend the line segment AB to C. If AB=, when the length of AB is equal to 2cm, the length of BC is equal to _ _ _ _ cm.
3. By knowing a point on (or outside of) a straight line, you can draw a straight line and intersect it. .
4 = degrees, minutes and seconds.
5, the complementary angle is 2 times, then = _ _ _ _ _ _.
6. If Xiao Li regards Xiao Zhang as 60 east of due north, then Xiao Zhang regards Xiao Li as _ _ _ _ _ _ _.
7. It is known that AC and BC are in a straight line. If AC = 8cm and BC=3cm, the distance between the midpoint of AC and BC is _ _ _ _ cm.
8. As shown in the figure, the straight line AB intersects with CD at O and OA, and bisects ∠EOD. Write all the diagonals in the diagram.
9. A three-dimensional figure with a quadrilateral top view can be:
10, as shown in the figure, there are two routes ① ② from A to B, so the first one is shorter; The relationship between the lengths of the other two roads is:
Second, multiple-choice questions: (3 ′× 7 = 21′) ①
1 1. The correct one in the following statement is ().
A, an angle with a common vertex is an antipodal angle;
B, there is one and only one straight line perpendicular to the known straight line;
C, the complementary angle of an angle must be greater than this angle;
D the length from a point outside the straight line to the vertical section of the straight line is called the distance from the point to the straight line.
12, given that the line segment AB= 1.8cm, the point C is on the extension line of AB, and AC=, then the line segment BC is equal to ().
A, 2.5cm b, 2.7cm c, 3cm d, 3.5cm.
13, two parallel lines are cut by a third straight line, and the bisectors are perpendicular to each other ().
A, dislocation angle b, ipsilateral internal angle c, congruent angle d, dislocation angle and congruent angle.
14, as shown in the figure, OA⊥OC, OB⊥OD, ∠BOC = а, then
∠AOD equals ()
a、2а B、90 + а
c、 180 - а D、90 +2а
15, it is known that ∠AOB = 30, and the light oc is led out from the vertex o of ∠AOB.
If ∠AOC: ∠AOB=4: 3, ∠BOC is equal to ()
A, 10 B, 40 C, 70 D, 10 or 70.
16, the following statement is true ().
(1) extended straight line ab; ②. Extend the line segment BA; ③. Prolonging ray OA;
④ backward extension ray OA; ⑤. Reverse extension of line segment AB; 6. make a straight line AB = CD.
a、4 B、3 C、2 D、 1
17, the known size is ()
a、 1 10、70 B、 105、75 C、 100、70 D、 1 10、80
Three. Drawings (5'+ 9'+ 10'= 24')
18. Given line segments A and B, please draw line segment AB=2a+b only with a ruler (without scale) and a compass (without writing, but with drawing traces).
19. As shown in the figure, draw the distance ad from A to BC; The distance is from b to AC; Distance CF from c to AB.
20. Please draw the front view and top view of the illustrated object.
Fourth, answer and prove questions. (9′+ 9′+ 9′= 27′)
2 1. straight line AB and CD intersect at point o, OE bisects ∠AOD, ∠ foc = 90,
∠ 1 = 40, find the degrees of∠ 2 and∠ 3.
22. As shown in the figure, ∞∠BAP+∠APD = 180, ∠BAE = ∠CPF.
Verification: ∠E = ∠F
Between 23: 00 and 7: 00 (1). When do the hour hand and minute hand form a right angle?
(2). When do the hour hand and the minute hand coincide? (3) When are the hour hand and the minute hand in a straight line?
Exercise 4: Representation of Data
1, as shown in the figure, is a statistical chart of hotline calls received by the People's Hotline of an evening newspaper within one week. Among them, there are 70 questions about environmental protection. Please answer the following questions: (1) This week, People's Hotline * * * received a hotline call _ _ _ _ _ _. (2) Calls about traffic problems are _ _ _ _ _.
2. Before the end of the semester, the school wanted to know students' satisfaction with the nutritious lunch provided by a food company this semester, and made a questionnaire survey to 600 students in the school. The results are as follows: 150 students are very satisfied; Satisfied with 200 people; Satisfied 1 10 people; Dissatisfied with 100 people; Very dissatisfied with 40 people.
According to the information in the question, draw: (1) bar graph; (2) Department statistics. (3) Please analyze it.
There are eight balls of the same size. Design a ball-touching game so that the probability of touching the white ball is 1/2, the frequency of touching the red ball is 1/4, the frequency of touching the yellow ball is 1/4, and the frequency of touching the green ball is 0. Then there are _ _ _ white balls, _ _ _ red balls and _ _ _ green balls.
The first line below shows five turntables that can rotate freely. Please use the language in the second line to describe the possibility of the pointer falling in the dark area when the turntable stops rotating, and connect them with lines.
Comprehensive exercise 1
I. Fill in the blanks (3 points for each small question, ***63 points)
The reciprocal of 1 and -2002 is _ _ _ _ _ _ _ _.
2. A school student sends 240 one-yuan books to Hope School, and the postage for each book is 5% of the book price, so the postage is _ _ _ _ _ _ _ _ _ _ _ _.
3. The population of China in the first census was about1.300 million, which was expressed as _ _ _ _ _ _ _ _ _ by scientific notation.
4. When the refrigerator is started, the internal temperature is 10℃. If the internal temperature of the refrigerator drops by 5℃, the internal temperature of the refrigerator will be _ _ _ _ _ _ _ _ _ _ _.
5. A building has * * * 12 floor and * * * 4 floor underground. Please use positive numbers and negative numbers to indicate the floors of the building _ _ _ _ _ _ _ _ _ _ _. Someone took the elevator from the second floor underground to the eighth floor above ground, and the elevator * * * rose _ _ _ _.
6. It is known that x=3 is the solution of the equation ax-6=a+ 10, then A = _ _ _ _ _ _ _ _ _ _ _ _ _ _
7. Throw an even number of dice, and both sides of the dice are marked with the numbers 1, 2, 3, 4, 5 and 6 respectively. The probability that you think "5" is up is _ _ _ _ _ _ _ _ _ _ _ _ _ _.
8. Which of the following events is certain? What are the uncertainties?
(1) Turn on the TV. The news it is broadcasting is _ _ _ _ _ _ _ _.
(2) You can see a big disc-shaped moon on New Year's Eve, which is _ _ _ _ _ _ _ _.
(3) The sun rises in the east every day is _ _ _ _ _ _ _ _ _ _ _ _.
9. There are four points on the straight line A, point A, point B, point C and point D, so there are _ _ _ _ _ _ _ _ line segments on the straight line A..
10, 2700〃=_______________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
1 1, make two straight lines through a point. If only the angle less than 180 is considered, then _ _ _ _ _ _ _ angles can be formed.
12. Draw a vertical line on both sides through the vertex of the acute angle. If the angle formed by two vertical lines is 136, then the acute angle is _ _ _ _ _ _ _ _ _ _.
13, 8: 20, the angle formed by the hour hand and the minute hand on the clock is _ _ _ _ _ _ _ _ _.
14, use a pair of triangles to draw angles greater than 0 and less than 180, and you can draw angles with different sizes. * * * is _ _ _ _.
15. A cube has _ _ _ _ _ _ vertices, _ _ _ _ _ edges and _ _ _ _ _ _ _ faces.
16. Cutting geometry with plane. If the cross section is circular, it is conceivable that the original geometric shape may be _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Two. (7 points)
The investigation team wanted to measure the height difference between A and B, and they found the middle point of D, E, F and G4. The measurement results are as follows: (unit m)
Can you determine which is taller, A or B? How much higher? What's your reason?
Three. (6 points)
Give the numbers 1, 2, 3 12 ...1,12, and add a negative sign before some of them to make the sum of these numbers zero.
Four, (7 points)
Xiaoming started from home and went to the park by bike. When he realized that he had ridden too much, he had already walked 4.5 kilometers, and he rode back 1.2 kilometers to reach his destination.
(1) Use an addition formula to represent Xiao Ming's driving process.
(2) How far is Xiaoming's home from the park?
Verb (abbreviation of verb) (8 points)
Magic math game, try to play this game according to the following game guide, write a number you like, add 2 to this number, multiply the result by 5, subtract 10, and then divide it by 10, and you will get the original number.
List the final expressions according to each step in the game.
(1) Assuming that the number written at the beginning is n, list the final expression according to each step of the game.
(2) Simplify the expression in (1) and verify it with your results. Why does this game hold for any number?
(3) Write a math game by yourself and write a description (try to make your game amazing and not obvious. )
6.(8 points) Multiple playing cards are divided into three parts, which are placed on the left, middle and right respectively. Then take two from the left pile and put them in the middle pile, and then take one from the right pile and put it in the middle pile. Finally, take a few cards from the middle pile and put them on the left, so that the number of cards on the left is twice that of the original.
① If there are 8 cards in each hand at the beginning, how many cards are left in the middle pile?
② If each card starts with 12 cards, how many cards are left in the middle pile? If each hand starts with 16 cards, how many cards are left in the middle pile?
③ According to (1) and (2), what are the rules of your conclusion? Tell me your reasons.
Seven, (8 points) ① Use a rope with a length of 80 cm to form a rectangle, and the length of the rectangle is more than the width 10 cm. What is the area of this rectangle? Make a square with this rope. What is its area? Make a circle with this rope. What is its area? (л Take 3. 14)② Take ropes with lengths of 100 cm and 120 cm respectively, and repeat the above three questions (1). Comparing the three results, what guess can you draw?
8.(8 points) Last year, depositors deposited 46 million yuan in a savings office. Compared with last year, this year's time deposits increased by 20% and demand deposits decreased by 25%, but the total deposits increased by 65,438+05%. What time deposits and current deposits are there this year?
Comprehensive exercise 2
1. Fill in the blank: (65438+ 0 point per grid, ***22 points)
The reciprocal of 1 –5 is, and the minimum natural number is;
2. The elevations of A and B are 120m and-10m respectively, and B is lower than A1m;
3. There are about 28 million bacteria in the abdomen of a fly, which is accurate enough to be expressed by scientific notation;
4. Three times the sum of a and 5 is represented by algebra;
5. Polynomial xy2-9x3y+5x2y-25 is a secondary term, which is arranged in descending order of X as follows:
6. If, then;
7. It is known that 4amb3 and -3a2bn are similar terms, then-nm =;
8. If the difference between a polynomial and x2-6x-2 is 4x2-7x-5, then this polynomial is;
9. Given that X-Y = 3 and XY =-2, the value of 3x-5xy-3y is;
10. If ∠ 1 = 20 18', then the complementary angle of ∠ 1 = 0';
1 1. As shown in the figure, point C and point D are two points on the line segment AB. If AC = 3, CD = 5, and DB = 2, the sum of all the line segments in the graph is;
12. When paving the floor with square bricks, the master worker often hits two wooden stakes first, and then lays bricks along the tight line, so that the floor tiles are laid neatly. The principle explained by this fact is:
13. As shown in the figure, OA⊥OB, ∠ BOC = 40, OD ∠AOC,
Then ∠ BOD =;
15. As shown in the figure, if A ‖ B, ∠ 1 = (2x+36), then ∠ 2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
16. There are 10 white balls and 5 black balls in an opaque pocket, which are evenly mixed in the pocket. ① Take out 1 ball from your pocket, which happens to be a black ball. (2) Take out 1 1 balls from your pocket. There are both white balls and black balls, and this happens; (3) write an impossible event at will:
Second, multiple-choice questions (2 points for each question, ***24 points)
1. When x = 3 and y = 2, the value of the algebraic expression is ().
A.，B. 2，C. 0，D. 3，
2. It is known that after the polynomial mx+nx merges similar terms, the result is zero, so the following statement is correct ().
A.m=n=0，B. m=n，C. m-n=0，D. m+n=0，
3. If the algebraic expression is equal to ()
A.5x B. 9x C. 12x D. 16x
4.–[a-(b-c)] The brackets should be ().
A.-a+b+c B- a+b-c c-a-b-c d-a-b+c
5. As shown in the figure, three straight lines intersect at one point, and there is a diagonal angle in the figure.
A.3 B. 4 C. 5 D. 6
6. Given the value of x2+3x+5 as 7, the value of algebraic expression 3x2+9x-2 is ().
A.0 B. 2 C. 4 D. 6
7. The circumference of a rectangle is 6a+8b, one side is 2a+3b, and the other side is ().
A.4a+5b B. a+b C. a+2b D. a+7b
8. As shown in the figure, expand the plan of the cube, and each face is marked with numbers. If 2 is on the left side of the cube and 3 is below, then the previous number is ().
A. 1 B. 4 C. 5 D. 6
9. In the figure below, there is an intersection ().
10. In the figure below, ∠ 1 and ∠2 are inscribed angles ().
1 1. As shown in the figure, the following judgment is correct ()
A. ∠1and ∠ 5 are conformal angles.
B ∠ 5 and ∠2 are internal angles.
C ∠ 3 and ∠4 are ipsilateral internal angles.
D.∠2 and ∠4 are antipodal angles
12. As shown in the figure, it is known that DE BC and CD are bisectors of ∠ACB.
∠ b = 72, ∠ ACB = 40, then ∠ ∠BDC is equal to ().
A. 78 BC to 90 BC
Three. Simplified calculation (4 points +4 points +5 points +3 points +5 points, ***2 1 minute)
1.– 12002-( 1+0.5)× ÷(-4);
2.2(2 x2-5x)-5(3x+5-2 x2)；
3.3x3-[x3+(6x2-7x)]-2 (x3-3x2-4x) where x =-2;
4. Is it true that "the sum of two cubic polynomials must still be a cubic polynomial"? Please give an example;
5. A classmate did a dice-throwing experiment and threw it 40 times, and recorded the results in the table below. Please complete the missing data in the form.
Yes 1 min, 2, 3, 4, 5 and 6.
Frequency 4 8 10 6
Frequency 10%
Iv. Drawing questions: (4 points +3 points +3 points, *** 10 points)
1.( 1) Draw the height of the BC side in the triangle ABC; (2) Draw a straight line MN through point A to make Mn ‖ BC;
2. As shown in the figure, translate the figure in the square paper 4 squares to the right, and then translate it 3 squares upwards to draw the translated figure;
3. Draw three views of the picture below;
Verb (abbreviation of verb) completes the following reasoning: (9 points +4 points, *** 13 points)
1. As shown in the figure, if ∠ 1 = ∠ d, then according to the available ∠;
If ∠4 =∞, press Available ‖;
If AF‖BD, then according to _ _ _ _ _ _ _ _ Available ∠2 =∞,
According to available ∠ a +∞ =180;
2. Lines A, B, C and D are shown in the figure, if ∠1=17, ∠ 2 =117 ∠ 3 =1.
6.(4 points) Observe the following equations and answer the questions:
; ; ; ; …
(1) Fill in the blanks: (n is a positive integer);
(2) Calculation: …
Seven. (6 points) Taxi charging standards vary from place to place in China. A city starting price 10 yuan, price per kilometer after 3 kilometers 1.2 yuan; B: The starting price is 8 yuan, and the price per kilometer after 3 kilometers is 1.4 yuan. Fill in the following table according to the above conditions:
Cycling mileage (km) 16x (x > 3)
Charge for a city (yuan)
B city charge (yuan)
Price difference between the two places (yuan)