First, multiple-choice questions (this question ***5 small questions, 3 points for each small question, *** 15 points)
1, the calculation result is-1, and the formula is ().
a、-∣- 1∣ B 、(- 1)0 C 、-(- 1) D、 1- 1
2. It is known that the upper base of a trapezoid is 6 cm long and the middle line is 8 cm long, so its lower base length is ().
A, 8cm b,10cm c,12cm d,14cm.
3. Images with function y = and function y = x are in the same plane rectangular coordinate system, and the number of intersections is ().
A, a b, two c, three d and zero.
4. As shown in the figure, if the radian AB in ⊙O is 60 and AC is the diameter of ⊙O, then ∠BOC is equal to ().
a、 150 B、 130 C、 120 D、60
5. In △ABC, ∠ C = 90, and if ∠ A = 2 ∠ B, then cosB is equal to ().
A, B, C, D,
Fill in the blanks (this is entitled ***5 small questions, with 4 points for each small question and 20 points for * * *).
6. Nanometer is a unit of length, which is often used to measure the size of a substance atom. 1 nm = 10-9 meters. It is known that the spore diameter of a plant is 45,000 nanometers, and the spore diameter is _ _ _ _ _ meters by scientific notation.
7. If the average value of a set of data 8, 9, 7, 8, x, 3 is 7, then the mode of this set of data is _ _.
8. As shown in the figure, in △ABC, the bisector of the outer corner of ∠BAC and the extension line of BC intersect at point D. If ∠ ADC = ∠ CAD, ∠ABC equals _ _ _ degrees.
9. Calculation: = _ _ _ _.
10, a parabola passes through the origin, please write its resolution function _ _ _ _.
Three, solve the problem (this question 5 small problems, each small problem 6 points, ***30 points)
1 1, factorized first and then evaluated:, where a =-3 and b =+4.
12, as shown in the figure, AB‖CD, straight line EF intersects AB and CD at points E and F, and EG bisects ∠AEF, ∠ 1 = 40, so find the degree of ∠2.
13. Solve the inequality group: find the sum of its integer solutions.
14. Let the quadrilateral ABCD be a square with a side length of 1, make the second square ACEF with the diagonal AC of the square ABCD as the side, then make the third square AEGH with the diagonal AE of the second square as the side, and so on.
(1) Remember that the side length of the square ABCD = 1, and the side length of the square made by the above method is the value of,,,,.
(2) Write the expression of the side length of the nth square according to the above rules.
The scores of 40 students in Grade Three 15 (1) in a math test are as follows:
63,84,9 1,53,69,8 1,6 1,69,9 1,78,75,8 1,80,67,76,8 1,79,94,6 1,69,
89,70,70,87,8 1,86,90,88,85,67,7 1,82,87,75,87,95,53,65,74,77
The math teacher divides the students into groups according to the interval of 10, calculates the frequency of students' grades in each interval, and fills in the frequency paging table:
(1) Please complete the frequency distribution table and frequency distribution histogram;
(2) Ask the teacher to help you count the passing rate (above 60 points, including 60 points for passing) and excellent rate (above 90 points, including 90 points for excellent) of this math exam;
(3) Please explain which score has the largest number of students? Which students have the fewest scores?
Iv. Answering questions (this question has 4 small questions, 7 points for each small question and 28 points for * * *).
16, as shown in the figure, given a point outside the straight line MN and MN, please draw the following figure with a ruler:
(1) Make a circle whose center is tangent to MN;
(2) Find a point B on MN, so that ∠ ABM = 30 (drawing trace is reserved, and writing and proof are not needed).
17, Li Minghe and Wang Yun go in opposite directions from A and B respectively. If they start at the same time, they will meet in 80 minutes. If Li Ming leaves Wang Yun in 60 minutes, then 40 minutes later, the two meet. How many hours does it take for Li Minghe and Wang Yun to go to AB alone?
18, as shown in the figure, the sum of two straight lines is known, and the area of the triangle enclosed by them and the y axis is found.
19, which is known, is two real roots of the equation. Solve the equation and find the following values:
( 1) ; (2) 。
V. Answering questions (there are 3 small questions in this question, with 9 points for each small question and 27 points for * * *).
20. As shown in the figure, in the isosceles trapezoid ABCD, AD‖BC, M and N are the midpoints of AD and BC, respectively, and E and F are the midpoints of BM and CM, respectively.
(1) Verification: quadrilateral MENF is a diamond;
(2) If the quadrilateral MENF is a square, please explore the quantitative relationship between the height of the isosceles trapezoid ABCD and the bottom BC to prove your conclusion.
2 1. Since this year, most areas in Guangdong have been short of electricity. In order to encourage citizens to save electricity, power companies have adopted the method of charging monthly electricity consumption. If the function image of a household's monthly electricity bill y (yuan) and electricity consumption x (degrees) is a broken line (as shown in the figure), the following problems can be solved according to the image:
(1) Write the functional relationship between Y and X when 0≤x≤ 100 and x≥ 100 respectively;
(2) Using the function relation, explain the charging standard adopted by the power company;
(3) If the user uses 62 kWh a month, how much should he pay? If the user pays 105 yuan a month, how many kwh does the user use this month?
22. As shown in the figure, the diameter of the semicircle O is known as AB = 4, and the right-angle vertex of the triangular plate is fixed on the center O. When the triangular plate rotates around the O point, the two right-angle edges of the triangular plate intersect with the circumference of the semicircle at C and D points respectively, and the connection points AD and BC intersect at E point .. (1) Verification: △ ace ∽△ BDE;
(2) Verification: BD = DE is established;
(3) Let BD = x, find the functional relationship between the area y of △AEC and X, and write the range of the independent variable X. ..
References:
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Responder: Butyl Corn-Magic Apprentice Level 1 2- 18 18: 19.
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Mathematics Examination Questions and Answers of College Entrance Examination in Guangdong Province in 2005 (Non-curriculum Reform Area)
First, multiple-choice questions (this question ***5 small questions, 3 points for each small question, *** 15 points)
1, the calculation result is-1, and the formula is ().
a、-∣- 1∣ B 、(- 1)0 C 、-(- 1) D、 1- 1
2. It is known that the upper base of a trapezoid is 6 cm long and the middle line is 8 cm long, so its lower base length is ().
A, 8cm b,10cm c,12cm d,14cm.
3. The number of images with function y = and function y = x intersecting in the same plane rectangular coordinate system is ().
A, a b, two c, three d and zero.
4. As shown in the figure, if the radian AB in ⊙O is 60 and AC is the diameter of ⊙O, then ∠BOC is equal to ().
a、 150 B、 130 C、 120 D、60
5. In △ABC, ∠ C = 90, and if ∠ A = 2 ∠ B, then cosB is equal to ().
A, B, C, D,
Fill in the blanks (this is entitled ***5 small questions, with 4 points for each small question and 20 points for * * *).
6. Nanometer is a unit of length, which is often used to measure the size of a substance atom. 1 nm = 10-9 meters. It is known that the spore diameter of a plant is 45,000 nanometers, and the spore diameter is _ _ _ _ _ meters by scientific notation.
7. If the average value of a set of data 8, 9, 7, 8, x, 3 is 7, then the mode of this set of data is _ _.
8. As shown in the figure, in △ABC, the bisector of the outer corner of ∠BAC and the extension line of BC intersect at point D. If ∠ ADC = ∠ CAD, ∠ABC equals _ _ _ degrees.
9. Calculation: = _ _ _ _.
10, a parabola passes through the origin, please write its resolution function _ _ _ _.
Three, solve the problem (this question 5 small problems, each small problem 6 points, ***30 points)
1 1, factorized first and then evaluated:, where a =-3 and b =+4.
12, as shown in the figure, AB‖CD, straight line EF intersects AB and CD at points E and F, and EG bisects ∠AEF, ∠ 1 = 40, so find the degree of ∠2.
13. Solve the inequality group: find the sum of its integer solutions.
14, let the quadrilateral ABCD be a square with a side length of 1, make the second square ACEF with the diagonal AC of the square ABCD as the side, then make the third square AEGH with the diagonal AE of the second square as the side, and so on? .
(1) Note that the side length of the square ABCD = 1, and the side length of the square made by the above method is,,,? Find the value of.
(2) Write the expression of the side length of the nth square according to the above rules.
The scores of 40 students in Grade Three 15 (1) in a math test are as follows:
63,84,9 1,53,69,8 1,6 1,69,9 1,78,75,8 1,80,67,76,8 1,79,94,6 1,69,
89,70,70,87,8 1,86,90,88,85,67,7 1,82,87,75,87,95,53,65,74,77
The math teacher divides the students into groups according to the interval of 10, calculates the frequency of students' grades in each interval, and fills in the frequency paging table:
(1) Please complete the frequency distribution table and frequency distribution histogram;
(2) Ask the teacher to help you count the passing rate (above 60 points, including 60 points for passing) and excellent rate (above 90 points, including 90 points for excellent) of this math exam;
(3) Please explain which score has the largest number of students? Which students have the fewest scores?
Iv. Answering questions (this question has 4 small questions, 7 points for each small question and 28 points for * * *).
16, as shown in the figure, given a point outside the straight line MN and MN, please draw the following figure with a ruler:
(1) Make a circle whose center is tangent to MN;
(2) Find a point B on MN, so that ∠ ABM = 30 (drawing trace is reserved, and writing and proof are not needed).
17, Li Minghe and Wang Yun go in opposite directions from A and B respectively. If they start at the same time, they will meet in 80 minutes. If Li Ming leaves Wang Yun in 60 minutes, then 40 minutes later, the two meet. How many hours does it take for Li Minghe and Wang Yun to go to AB alone?
18, as shown in the figure, the sum of two straight lines is known, and the area of the triangle enclosed by them and the y axis is found.
19, which is known, is two real roots of the equation. Solve the equation and find the following values:
( 1) ; (2) 。
V. Answering questions (there are 3 small questions in this question, with 9 points for each small question and 27 points for * * *).
20. As shown in the figure, in the isosceles trapezoid ABCD, AD‖BC, M and N are the midpoints of AD and BC, respectively, and E and F are the midpoints of BM and CM, respectively.
(1) Verification: quadrilateral MENF is a diamond;
(2) If the quadrilateral MENF is a square, please explore the quantitative relationship between the height of the isosceles trapezoid ABCD and the bottom BC to prove your conclusion.
2 1. Since this year, most areas in Guangdong have been short of electricity. In order to encourage citizens to save electricity, power companies have adopted the method of charging monthly electricity consumption. If the function image of a household's monthly electricity bill y (yuan) and electricity consumption x (degrees) is a broken line (as shown in the figure), the following problems can be solved according to the image:
(1) Write the functional relationship between Y and X when 0≤x≤ 100 and x≥ 100 respectively;
(2) Using the function relation, explain the charging standard adopted by the power company;
(3) If the user uses 62 kWh a month, how much should he pay? If the user pays 105 yuan a month, how many kwh does the user use this month?
22. As shown in the figure, the diameter of the semicircle O is known as AB = 4, and the right-angle vertex of the triangular plate is fixed on the center O. When the triangular plate rotates around the O point, the two right-angle edges of the triangular plate intersect with the circumference of the semicircle at C and D points respectively, and the connection points AD and BC intersect at E point .. (1) Verification: △ ace ∽△ BDE;
(2) Verification: BD = DE is established;
(3) Let BD = x, find the functional relationship between the area y of △AEC and X, and write the range of the independent variable X. ..