Chapter I Evidence (2)

1. The base angle of an isosceles triangle is 15? , waist length is 10㎝, then its area is

2. In △ABC, ∠ A: ∠ B: ∠ C = 1: 2: 3, and the length of the middle line on the side of AB is 3, then its circumference is

3. The length of the base of an isosceles triangle is 7, and the difference between the center line of the waist dividing its circumference into two parts is 3, so the waist length is ().

A, 4 B, 10 C, 4 or 10 D, none of the above answers are correct.

4. Counterevidence "In a triangle, at least one inner angle is less than or equal to 60?" , the first step should assume that:

5. In △ABC, AB=AC, and DE is the median line on the side of AB.

(1) If ∠A=40? , then ∠CBE= (2) If the circumference of △CBE is 8 and AC-BC=2, then AB=

6. At the right angle △ABC, ∠C=90? , AC=BC, BD divided by ∠ABC, DE⊥AB in E, if CD=3, AD= AB=

7. Prove that a triangle with the same distance from the midpoint of one side to the other two sides is an isosceles triangle.

8. As shown in the figure, AB=AC, BD=BC, E and F are the midpoint of BD and CD respectively. Verification: AE=AF.

Chapter II Quadratic Equation in One Variable

1. Turn the equation into a general formula:

2. The sum and product of two roots of the quadratic equation x2=x are respectively

3. It is known that -2 is one root of the equation, so the value of k is, and the other root is.

4. Fill in the form by calculation and answer the questions:

x 1 2 3 4 5 6

x2-2x- 1

x

x2-2x- 1

( 1)

The first table shows that one root of the equation satisfies:

(2) Calculation with the second table shows that the tenth number of this root of the equation is

5. Solve the following equation:

(1) (matching method) (2) (factorization method)

(3) (formula method)

6. The previous annual output value of a company was 400,000 yuan, and the output value of last year and this year was * * * 924,000 yuan, seeking an average annual growth rate.

7. On average, 30 pieces of clothes can be sold every day, and each piece is profitable in 40 yuan. If the price of each piece is reduced by 1 yuan, you can sell 5 more pieces every day. If the daily profit increases by 50%, how much should the price of each piece be reduced?

8. At the right angle △ABC, ∠C=90? , AC=8㎝, BC=6㎝, Point P and Point Q start from Point A and Point B at the same time, and move to Point C at a constant speed along points AC and BC, with the speed of1m/s. After a few seconds, the area of △PCQ is half that of △ABC?

Chapter III Proof (III)

In 1.△ABC, the lengths of the three neutral lines are 3, 4 and 5 respectively, so the circumference of △ABC is and the area is.

2. In the right angle △ABC, the lengths of the two sides are 6 and 8 respectively, so the length of the middle line on the hypotenuse is

3. Connect the midpoints of the sides of the diagonal quadrilateral in turn to get a square.

4. If the circumference of a diamond is 20 and the ratio of two diagonal lines is 3: 4, then its area is

5. In the parallelogram ABCD, AB=4, BC=9, ∠B=45? , then its area is

6. In the rectangular ABCD, AB=4, AD=8, fold along AE so that point D falls on point F on BC, then ∠EFC=, DE=.

7. In △ABC, BE and CF are the high lines on both sides, and points P and Q are the midpoint between BC and EF.

Verification: PQ⊥EF

8. In right-angled trapezoidal ABCD, point P is the midpoint of AB, and ∠CPD=90? What conclusion can you draw? And prove it.

Chapter V Inverse Proportional Function

1. If the function is an inverse proportional function, the value of m is

2. If the rectangle has an area of 24, a length of X and a width of Y, then the functional relationship between Y and X is that its image is in the fourth quadrant.

3. As shown in the figure, there are points A, B,

AB passes through the origin O, AC⊥x axis, BD⊥x axis and quadrilateral.

If the area of ABCD is 8, then k=

4. There is a point (-2, 1) on the image of the inverse proportional function.

Then the coordinates of the intersection of hyperbola and straight line are

5. The voltage of the battery is constant. When the resistance is 9 ohms, the current is 4 amps. Relationship between current i and resistance r.

6. Explore a question: "Given any rectangle A, is there another rectangle B whose perimeter and area are three times that of the known rectangle?" Complete the following questions:

(1) If the length and width of rectangle A are 2 and 1 respectively, does rectangle B exist?

(2) If the length and width of rectangle A are m and n respectively, does rectangle B exist?

7. As shown in the figure, there is a point A on the function image, the axis A is AB⊥y, and there is a moving point P on the positive semi-axis of B and X. If AP intersects with OB, the value of k is C. (1); (2) If ∠ cab = 45, and c is the midpoint of OB, find the analytical formula of straight line AP;

Chapter IV Views and Prediction Chapter VI Frequency and Probability

1. As shown in the figure, a geometric figure composed of some identical small cubes has three views. So the number of small cubes that make up this geometry is

2. As the picture shows, Xiao Liang's classmates walk from street lamp A to street lamp B at night. When he reached point P, he found that the top of his figure just touched the bottom of street lamp B. At this time, he was 25 meters away from street lamp A and 5 meters away from street lamp B. If Xiao Liang's height is 1.6 meters, the height of street lamp is

3. The six faces of a uniform cube are marked with the numbers 1, 2, 3, 4, 5 and 6 respectively. The following figure shows the unfolded surface of the cube. When throwing a cube, the probability that the number of upper surfaces is exactly equal to the number of lower surfaces is

4. Zhang Ming wants to measure the height of trees on campus with the shadow of trees. At a certain moment, when he measured the height of small trees as 1.5m, the shadow length was1.2m. When he measured the shadow length of a big tree next to the teaching building, some shadows were on the wall because the big tree was close to the teaching building. After measurement, the shadow length on the ground is 6.4m, and the shadow length on the wall is 65438+.

There are eight black balls and several white balls in one pocket. Pick a ball at random and write down the color. Put it back in your pocket. Repeat. * * * touched 200 times, including 57 black balls, so it can be estimated that the number of white balls in the pocket is

6. The main reason for the staircase or downhill shape of the cinema is

7. There are several plates on the table. If you look at it from three directions and the three views are as shown below, then there are dishes on this table.

8. There are four seats beside the round table. A sits in the seat shown in the picture first, and B, C and D sit in the other three seats at random. Find the probability that A and B are not adjacent (illustrated by tree diagram or list method).