Fill in the blanks
The reciprocal of 1 -1 is _ _ _ _.
2. Factorization:
x2-4 = _ _ _ _ _ _ _ _ _ _ _ _ _。
3. Waste batteries are a serious pollution source. A button cell can pollute 600,000 litres of water, which is expressed as _ _ _ _ _ litres of water by scientific notation.
4. In the donation activity of "holding hands and offering love", the number of donations in the three classes of a senior high school is 260, 220, 240, 280 and 290 respectively (unit: RMB), so the range of this set of data is _ _ _ _ _.
5. The purchase price of a commodity is 400 yuan. If it is sold after the price is increased by 20%, the profit of each commodity is RMB _ _ _ _.
6. Kobayashi writes a word on each side of a cube box, namely, I, Huan, Shu, Xue and Ban. The scheme is shown in the figure. Then, in the cube box, the word written opposite me is "".
7. As shown in the figure, △ABC is the inscribed triangle of ⊙O, AB is the diameter of ⊙O, point D is on ⊙O, ∠ BAC = 35, then ∠ ADC = degrees.
8. The solution of binary linear equations is.
9. As shown in the figure, point P is on the image of the inverse proportional function. If point P passes by, PA⊥x axis is at point A, PB⊥y axis is at point B, and the area of rectangular OAPB is 9, then the analytical formula of the inverse proportional function is.
10. It is known that the radius of the bottom surface of the cylinder is 2cm, the length of the bus bar is 3cm, and the area of the development diagram of the side surface of the cylinder is _ _ _ _ _ cm.
1 1. In an opaque box, there are four balls, all the same except the color, including three red balls and 1 white balls. After stirring, pull out two balls at the same time. Please write down a possible event in this experiment:
12. In a plane rectangular coordinate system, a point whose abscissa and ordinate are integers is called an integral point. Please observe the number of the whole points on the four sides of a square, a1b1d1,A2B2C2D2, A3B3C3D3…… ... and calculate the square A65438+.
Second, multiple choice questions
1. In the following operations, the correct result is []
A.x3？ x3 = X6 b . 3 x2+2 x2 = 5x4 c .(x2)3 = X5 d .(x+y)2 = x2+y2
2. Among the following surveys, [] is more suitable for general survey than sampling survey.
A. Investigate whether the pigment content of a food in the food market in the whole province meets the national standards.
B. investigate the service life of a batch of light bulbs
C. investigate the height of all the students in your class.
D. investigate the weekly pocket money of junior high school students nationwide.
3. Given that the radii of two circles are 1 and 4, respectively, and the center distance is 3, the positional relationship between the two circles is [].
A. externalization B. externalization C. intersection D. internalization
4. Xiaoming and Xiaohua both took the math test five times this semester (total score 100). The math teacher wants to judge which of them has more stable math performance. When doing statistical analysis, the teacher needs to compare the five math scores of the two students [].
A. mean b variance c mode d median
5. Among the following four propositions, the wrong one is []
A. A quadrilateral with four equilateral sides is a diamond.
B. A quadrilateral with three right angles is a rectangle.
A quadrilateral whose diagonals are perpendicular to each other and bisected and equal is a square.
D. A set of quadrangles with parallel opposite sides and another set of quadrangles with equal opposite sides are isosceles trapezoid.
Xiaoming's school is 2 kilometers away from home. One day, he rode home by bike after school. Drive for 5 minutes, stop for some reason 10 minutes, and ride home for 5 minutes. Which of the following images can roughly describe the relationship between the distance (kilometers) from home and the time (minutes) he spent on his way home []
Third, answer questions.
1. Calculation:
|- 1|-20060+3- 1
2. Simplify the following algebraic expression before evaluation:, where (the result is accurate to 0.0 1).
3. As shown in the figure, in ABCD, E and F are two points on the diagonal AC, AE = CF, and verification: Be = DF.
4. Every student in grade one of a school only uses one of three brand calculators, A, B and C. The figure below shows the frequency distribution histogram of the number of all students using three different brand calculators in that year.
(1) Find the total number of first-year students in this school;
(2) Which brand of calculator do you think is used most frequently? Find this frequency.
5. There is a right-angled trapezoid ABCD in the square grid below. Please draw numbers in the diagram according to the following requirements (drawing is not required):
(1) Translate the right-angled trapezoid ABCD downward by 3 units to obtain the right-angled trapezoid A1b1c1d1;
(2) Rotate the right-angled trapezoid ABCD counterclockwise around point D by 180 to obtain the right-angled trapezoid A2B2C2D.
6. When Party A and Party B play roulette, they divide roulette A and B into 4 equal parts and 3 equal parts respectively, and mark numbers on each part, as shown in the figure. The game stipulates that when the two roulette wheels stop rotating and the sum of the two numbers pointed by the pointer is odd, Party A wins; When it is an even number, B wins.
(1) Use the list method (or draw a tree diagram) to find the winning probability of A;
(2) Do you think the rules of the game are fair to both sides? Please briefly explain the reasons.
7. As shown in the figure, it is known that O is the origin, the coordinate of point A is (4,3), and the radius ⊙A is 2. Passing through a is a straight line parallel to the axis, and point P moves on the straight line.
(1) When point P is on ⊙O, please write its coordinates directly;
(2) Let the abscissa of point P be 12, try to judge the positional relationship between OP line and ⊙A line, and explain the reasons.
8. A community plans to buy and plant 500 saplings, and a sapling company provides the following information:
Message 1: There are three kinds of saplings to choose from: poplar, lilac, willow, and the number of poplar and lilac trees should be equal.
Message 2: The following table:
Suppose poplar and willow are purchased as X and Y plants respectively.
(1) y is represented by an algebraic expression containing x;
(2) If the total cost of purchasing these three kinds of saplings is W yuan, the sum of air purification indexes of these 500 saplings in this community after two years should not be less than 120, and try to find the range of W. 。
9. The construction team will build a highway tunnel with parabolic cross section, with a height of 6m and a width of 12m. Now establish a rectangular coordinate system, with point O as the origin and the straight line where OM is located as the X axis (as shown in the figure).
(1) directly write the coordinates of point m and parabola vertex p;
(2) Find the resolution function of this parabola;
(3) The construction team plans to build a rectangular "scaffold" CDAB at the entrance of the tunnel, so that points A and D are on the parabola, and points B and C are on the ground OM. In order to prepare materials, what is the maximum sum of the lengths of the three wooden poles AB, AD and DC of the scaffold? Ask the construction team to help calculate.
10. As shown in figure 1, a 4-meter-long ladder AB leans against the wall and is perpendicular to the ground OM, and the inclination angle α between the ladder and the ground is 60. .
(1) Find the length of AO and BO;
⑵ If the top A of the ladder slides down along NO, the bottom B slides to the right along om.
① As shown in Figure 2, suppose point A slides down to point C, point B slides to the right to point D, and AC:BD=2:3. Try to calculate how many meters the top of ladder A slides down along NO;
② As shown in Figure 3, when point A slides down to point A' and point B slides right to point B', the midpoint P of ladder AB also moves to point P'. If ∠ pop' = 15。 Try to find the length of AA'
Junior high school → mathematics → national entrance examination questions →2006 entrance examination questions → Quanzhou entrance examination questions in Fujian Province.
Fill in the blanks
The reciprocal of 1 -1 is _ _ _ _.
Test answer: 1 test analysis:
2. Factorization:
x2-4 = _ _ _ _ _ _ _ _ _ _ _ _ _。
Test answer: (x+2) (x-2) Test analysis:
3. Waste batteries are a serious pollution source. A button cell can pollute 600,000 litres of water, which is expressed as _ _ _ _ _ litres of water by scientific notation.
Test answer:
6× 105 test analysis;
4. In the donation activity of "holding hands and offering love", the number of donations in the three classes of a senior high school is 260, 220, 240, 280 and 290 respectively (unit: RMB), so the range of this set of data is _ _ _ _ _.
Test answer: 70 Test analysis:
5. The purchase price of a commodity is 400 yuan. If it is sold after the price is increased by 20%, the profit of each commodity is RMB _ _ _ _.
Test answer: 80 Test analysis:
6. Kobayashi writes a word on each side of a cube box, namely, I, Huan, Shu, Xue and Ban. The scheme is shown in the figure. Then, in the cube box, the word written opposite me is "".
Test answer: Test analysis:
7. As shown in the figure, △ABC is the inscribed triangle of ⊙O, AB is the diameter of ⊙O, point D is on ⊙O, ∠ BAC = 35, then ∠ ADC = degrees.
Test answer: 55 Test analysis:
8. The solution of binary linear equations is.
Test answer: Test analysis:
9. As shown in the figure, point P is on the image of the inverse proportional function. If point P passes by, PA⊥x axis is at point A, PB⊥y axis is at point B, and the area of rectangular OAPB is 9, then the analytical formula of the inverse proportional function is.
Test answer: Test analysis:
10. It is known that the radius of the bottom surface of the cylinder is 2cm, the length of the bus bar is 3cm, and the area of the development diagram of the side surface of the cylinder is _ _ _ _ _ cm.
Test answer: 12π test analysis:
1 1. In an opaque box, there are four balls, all the same except the color, including three red balls and 1 white balls. After stirring, pull out two balls at the same time. Please write down a possible event in this experiment:
Test answer: such as test analysis "touch out two red balls";
12. In a plane rectangular coordinate system, a point whose abscissa and ordinate are integers is called an integral point. Please observe the number of the whole points on the four sides of a square, a1b1d1,A2B2C2D2, A3B3C3D3…… ... and calculate the square A65438+.
Test answer: 80 Test analysis:
Second, multiple choice questions
1. In the following operations, the correct result is []
A.x3？ x3 = X6 b . 3 x2+2 x2 = 5x4 c .(x2)3 = X5 d .(x+y)2 = x2+y2
Test answer: Test analysis:
2. Among the following surveys, [] is more suitable for general survey than sampling survey.
A. Investigate whether the pigment content of a food in the food market in the whole province meets the national standards.
B. investigate the service life of a batch of light bulbs
C. investigate the height of all the students in your class.
D. investigate the weekly pocket money of junior high school students nationwide.
Test answer: C test analysis:
3. Given that the radii of two circles are 1 and 4, respectively, and the center distance is 3, the positional relationship between the two circles is [].
A. externalization B. externalization C. intersection D. internalization
Test answer: D Test analysis:
4. Xiaoming and Xiaohua both took the math test five times this semester (total score 100). The math teacher wants to judge which of them has more stable math performance. When doing statistical analysis, the teacher needs to compare the five math scores of the two students [].
A. mean b variance c mode d median
Answer to the question: analysis of question b:
5. Among the following four propositions, the wrong one is []
A. A quadrilateral with four equilateral sides is a diamond.
B. A quadrilateral with three right angles is a rectangle.
A quadrilateral whose diagonals are perpendicular to each other and bisected and equal is a square.
D. A set of quadrangles with parallel opposite sides and another set of quadrangles with equal opposite sides are isosceles trapezoid.
Test answer: D Test analysis:
Xiaoming's school is 2 kilometers away from home. One day, he rode home by bike after school. Drive for 5 minutes, stop for some reason 10 minutes, and ride home for 5 minutes. Which of the following images can roughly describe the relationship between the distance (kilometers) from home and the time (minutes) he spent on his way home []
Test answer: D Test analysis:
Third, answer questions.
1. Calculation:
|- 1|-20060+3- 1
Test answer:
Test analysis:
2. Simplify the following algebraic expression before evaluation:, where (the result is accurate to 0.0 1).
Test answer:
Test analysis:
3. As shown in the figure, in ABCD, E and F are two points on the diagonal AC, AE = CF, and verification: Be = DF.
Test answer:
Test analysis:
4. Every student in grade one of a school only uses one of three brand calculators, A, B and C. The figure below shows the frequency distribution histogram of the number of all students using three different brand calculators in that year.
(1) Find the total number of first-year students in this school;
(2) Which brand of calculator do you think is used most frequently? Find this frequency.
Test answer:
Test analysis:
5. There is a right-angled trapezoid ABCD in the square grid below. Please draw numbers in the diagram according to the following requirements (drawing is not required):
(1) Translate the right-angled trapezoid ABCD downward by 3 units to obtain the right-angled trapezoid A1b1c1d1;
(2) Rotate the right-angled trapezoid ABCD counterclockwise around point D by 180 to obtain the right-angled trapezoid A2B2C2D.
Test answer:
Test analysis:
6. When Party A and Party B play roulette, they divide roulette A and B into 4 equal parts and 3 equal parts respectively, and mark numbers on each part, as shown in the figure. The game stipulates that when the two roulette wheels stop rotating and the sum of the two numbers pointed by the pointer is odd, Party A wins; When it is an even number, B wins.
(1) Use the list method (or draw a tree diagram) to find the winning probability of A;
(2) Do you think the rules of the game are fair to both sides? Please briefly explain the reasons.
Test answer:
Test analysis:
7. As shown in the figure, it is known that O is the origin, the coordinate of point A is (4,3), and the radius ⊙A is 2. Passing through a is a straight line parallel to the axis, and point P moves on the straight line.
(1) When point P is on ⊙O, please write its coordinates directly;
(2) Let the abscissa of point P be 12, try to judge the positional relationship between OP line and ⊙A line, and explain the reasons.
Test answer:
Test analysis:
8. A community plans to buy and plant 500 saplings, and a sapling company provides the following information:
Message 1: There are three kinds of saplings to choose from: poplar, lilac, willow, and the number of poplar and lilac trees should be equal.
Message 2: The following table:
Suppose poplar and willow are purchased as X and Y plants respectively.
(1) y is represented by an algebraic expression containing x;
(2) If the total cost of purchasing these three kinds of saplings is W yuan, the sum of air purification indexes of these 500 saplings in this community after two years should not be less than 120, and try to find the range of W. 。
Test answer:
Test analysis:
9. The construction team will build a highway tunnel with parabolic cross section, with a height of 6m and a width of 12m. Now establish a rectangular coordinate system, with point O as the origin and the straight line where OM is located as the X axis (as shown in the figure).
(1) directly write the coordinates of point m and parabola vertex p;
(2) Find the resolution function of this parabola;
(3) The construction team plans to build a rectangular "scaffold" CDAB at the entrance of the tunnel, so that points A and D are on the parabola, and points B and C are on the ground OM. In order to prepare materials, what is the maximum sum of the lengths of the three wooden poles AB, AD and DC of the scaffold? Ask the construction team to help calculate.
Test answer:
Test analysis:
10. As shown in figure 1, a 4-meter-long ladder AB leans against the wall and is perpendicular to the ground OM, and the inclination angle α between the ladder and the ground is 60. .
(1) Find the length of AO and BO;
⑵ If the top A of the ladder slides down along NO, the bottom B slides to the right along om.
① As shown in Figure 2, suppose point A slides down to point C, point B slides to the right to point D, and AC:BD=2:3. Try to calculate how many meters the top of ladder A slides down along NO;
② As shown in Figure 3, when point A slides down to point A' and point B slides right to point B', the midpoint P of ladder AB also moves to point P'. If ∠ pop' = 15。 Try to find the length of AA'
Test answer:
Test analysis: