Classic junior high school mathematics examination questions 1. Function analysis (solving the temperature drop per 100 meters above sea level), rational number multiplication, analytic function.
2. The concept of power sum polynomial of rational number.
3. The real problem is congruent triangles.
4. Use letters to express the quantitative relationship.
5. The nature of inequality.
6. Determination of diamonds.
7. The properties of parallelogram.
8. Draw with a ruler.
9. Prove the properties of parallelogram.
10. Solve the quadratic equation with one variable by formula method.
Multiplication of polynomials.
12. Three views (top view, front view and side view).
13. The concept of single item.
14.
15. Symmetry relation of original points in plane coordinates.
16. Multiply multiple rational numbers.
17. Weighted average and its application.
18. Inequality
19. Mixed operation of rational numbers.
20. Calculation of variance.
2 1. Use coordinates to indicate that two graphs are symmetrical about the origin.
22. The application of linear function.
23. Function analysis (solving the temperature drop per 100 meters above sea level).
24. Multiplication of rational numbers.
25. Resolution function.
26. The concept of polynomial.
27. Mixed operation of rational numbers.
28. A ruler can draw pictures to explain angles.
29. congruent triangles.
30. The circumference of the circle.
Example 1: There is a rectangular table, which is 6 feet long and 3 feet wide. Now there is a rectangular tablecloth on the desktop. If the tablecloth is twice the size of the desktop and the length hanging around it is the same, try to find out the length and width of this tablecloth. (Accurate to 0. 1 ft) Analysis: When the width hanging around is x feet, we can know that the length of the tablecloth is (2x+6) feet and the width is (2x+3) feet. We can draw a conclusion from the equation that the area of tablecloth is twice that of desktop.
Solution: If the width of hanging around is x feet, the equation can be listed as (6+2x)(3+2x)=2×6×3 according to the meaning of the question. Arrange the equations and get 2x2+9x-9=0. The solution is x 1≈0.84, x2≈-5.3. In other words, this tablecloth is about 7.7 feet long and 4.7 feet wide.
Example 2: If the sum of two right angles of a right triangle is 7 and the area is 6, the length of the hypotenuse is ().
Solution: 5
Example 3: Cut a rectangle with a width of 2cm from one side of the square iron sheet. If the area of the remaining rectangle is 48cm2, what is the area of the original square iron sheet?
Solution: Let the width of the lace be xm, and according to the meaning of the question (6+2x)(3+2x)=40, the result is X 1 = 1, x2 =-1/2 (omitted if not suitable for the meaning of the question), that is, the width of the lace.
Ex. 4: The purchase price of a certain kind of clothing is 60 yuan per piece. According to market research, when this kind of clothing is sold in 80 yuan, it can sell 400 pieces every month. If the sales price increases by 1 yuan, 5 pieces will be sold less. If the clothing store expects to make a monthly profit of 12000 yuan when selling this kind of clothing, what is the selling price of this kind of clothing, which will make customers more affordable?
Solution: If the sales price is increased by X 1 yuan, it should be sold 5 times less every month. According to the meaning of the question, the equation can be listed as (80+x-60)×(400-5x)= 12000. By solving this equation, we can get x 1 = 20 and x2 = 40. Obviously, when x=40, the selling price is 120 yuan, and when x = 40, the selling price is 120 yuan.