Su ke printing plate ninth grade first volume mathematics final examination questions
Fill in the blanks (2 points for each question, ***24 points. )
1. When x, it is meaningful.
2. Calculation:.
3. If x= 1 is one root of the equation x2-5x+c=0, then the other root of the equation is.
4. The vertex coordinates of parabola are.
5. As shown in the figure, in □ABCD, AC and BD intersect at point O, point E is the midpoint of AB, and OE=3cm, then the length of AD is cm.
(Drawing No.5) (Drawing No.8) (Drawing No.0/kloc)
6. The upper bottom of the isosceles trapezoid is 4cm, the lower bottom is 10cm, and the bottom angle is 60? The waist length of an isosceles trapezoid is centimeters.
7. The length of two sides of a given isosceles triangle is 2 of the equation x2-6x+8=0, and the circumference of the triangle is.
8. The cross section of the drain pipe is as shown in the figure. It is known that the radius of the cross-sectional circle of the drainage pipe OB= 10, and the distance oc from the center o of the cross-sectional circle to the water surface is 6, then the water surface width AB is 0.
9. If the circumference of the bottom of the cone is 20? Is the central angle of the sector 120? The length of the generatrix of the cone is.
10. As shown in the figure, PA and PB are ⊙O is tangent, A and B are tangent points, and AC is the diameter of ⊙ O. If? BAC=25？ And then what? P=
Degree.
1 1. Xiao Zhang wants to draw an image of a quadratic function and take five values of the variable X. Please point out that this miscalculated y value corresponds to x=.
x -2 - 1 0 1 2
y 1 1 2 - 1 2 5
12. Fold a rectangular piece of paper () with a length of 1 and a width of a as shown in the figure, and cut out a square with a side length equal to the width of the rectangle (called the first operation); Fold the remaining rectangle as shown in the figure, and cut out a square whose side length is equal to the width of the rectangle at this time (called the second operation); If you do this again, if the remaining rectangle after the third operation is a square, the value of a is.
Second, multiple-choice questions: (This topic is entitled ***5 small questions, 3 points for each small question, *** 15 points)
13. Convert the quadratic function into the form of, and the result is correct.
A.B.
C.D.
14. Two students, A and B, took five tests in the 100 meter dash. Their scores are calculated as follows: A = B, S2 A =0.025, S2 B =0.026. The following statement is correct.
C.a is more stable than B.
15. If the equation about has two unequal real roots, the value range of is
Jiayihe
CD and
16. If the diameters of two circles are 2cm and 10cm respectively, and the distance between the center of the circle is 8cm, the positional relationship between the two circles is as follows
A. inscribed, intersected, circumscribed and separated
17. known quadratic function y=ax2+bx+c(a? 0) The image is as shown in the figure, and the following conclusions are drawn.
The correct one is 2.
A. when x> is at 1, y increases with the increase of x.
B.3 is the root of the equation ax2+bx+c=0.
C.a c & gt0
d . a+b+ c & lt； 0
Third, answer questions:
18. (5 points for this question) Calculation:
19. (5 points for this question) Simplification: ().
20. (This question 10, 5 points for each small question) Solve the following equations with appropriate methods:
( 1)x2-5x-6 = 0； (2)4x(2x- 1)=3( 1-2x)。
2 1. (6 points for this question)
(1) If five data 2,-1, 3, 5 have a value range of 8;
(2) Given the average value of six data -3, -2, 1, 3, 6, it is 1, and find the variance of this group of data.
22. (6 points in this question) As shown in the figure, in the parallelogram ABCD, the diagonal AC and BD intersect at the O point, AF? BD，CE？ BD, the vertical feet are e and f respectively;
(1) Connect AE and CF to get quadrilateral AFCE. Try to determine which of the following figures is a quadrilateral AFCE? ① parallelogram; ② diamond shape; ③ Rectangular;
(2) Please prove your conclusion;
23. (8 points in this question) It is known that the image of quadratic function has two intersections with the X axis.
(1) Find the value range of k;
(2) If k is the largest integer in the above conditions and the quadratic equation with one variable has the same root, find the value of the constant m. 。
24. (8 points in this question) It is known that the image C 1 of quadratic function has only one common point with the X axis.
(1) Find the vertex coordinates of C 1;
(2) Draw an approximate image of C 1 in the rectangular coordinate system as shown in the figure.
(3) After translating C 1 downwards by several units, the parabola C2 is obtained.
If the intersection of C2 and X axis is a (-3,0), find C2.
Function relation, and find the coordinates of another intersection point between C2 and X axis;
(4) If
The range of real number n.
25. (7 points in this question) As shown in the figure, A and B are two points on the arc, and D is the midpoint of the arc.
(1) verification: the quadrilateral AOBD is a diamond;
(2) Extend the line segment BO to point p, so that OP = 2OB, and OP intersects with another point c,
And link AC. Proof: AP is a tangent.
26. (7 points in this question) A carpenter can measure the radius of a circle with a square. R. close with the short side of the square, and the vertex b of the square (? B=90？ ) and make the long side tangent to point C.
(1) as shown in figure, AB
(2) If AB=8cm, assuming that the side BC of the square is long enough, if BC is pronounced long,
Is acm, then R is represented by an algebraic expression containing a. 。
27. (8 points in this question) A company sells a new type of energy-saving electronic small product, and now it is ready to choose one of the domestic and foreign sales schemes for sale. If it is only sold in China, the functional relationship between the sales price y (yuan/piece) and the monthly sales volume x (piece) is y = x+ 150, and the cost is 20 yuan/piece. No matter how much you sell, you still have to spend it every month.
If it is only sold abroad, the selling price is 150 yuan/piece. Due to various uncertainties, the cost is A yuan/piece (A normal, 10? Answer? 40), when the monthly sales volume is X (pieces), you need to add x2 yuan per month, and the monthly profit is W (yuan) (profit = sales-cost-addition).
(1) If it is only sold in China, when x= 1000, y= Yuan/piece;
(2) Find the functional relationships among w, w and x respectively (it is not necessary to write the range of x);
(3) When is the value of X, and the monthly profit of domestic sales is the largest? If the monthly maximum profit of foreign sales is the same as that of domestic sales, find the value of A;
(4) When A takes the value in (3), if all 5,000 products are to be sold in a month, please help the company to make a decision through analysis, and choose whether to sell at home or abroad, so as to obtain greater monthly profits.
28.( 1 1) As shown in the figure, it is known that the parabola intersects with the X-axis at two points A and B (point A is on the left of point B), intersects with the Y-axis at point C (0, -3), the symmetry axis is a straight line x= 1, and the straight line BC intersects with the parabola symmetry axis at point D. 。
(1) Find the function expression of parabola;
⑵ Find the functional expression of straight line BC;
(3) Point E is a fixed point on the Y-axis, the perpendicular line of CE intersects with the Y-axis at point F, and the parabola intersects with points P and Q, and intersects with point.
P is in the third quadrant.
① When PQ= AB, find the length of CE;
② When the triangle whose vertices are C, D and E is a right triangle, please write the coordinates of point P directly.
Reference answer to the final examination paper of ninth grade mathematics
I. Fill in the blanks (2 points for each question)
1、x？ 22,23,44, (5,3) 5,66,67, 10 8, 16 9,10,50 degrees 1 1, x = 2/kloc-.
Second, multiple-choice questions (3 points for each small question, *** 15 points)
13、C 14、C 15、B 16、D 17、B
Third, answer questions.
18, original formula = (3 points, one pair 1 minute)
=9 (5 points)
19, the original formula = (the first 2 points) = (5 points)
20. (1) (5 points) (2 points will be given for one, and points will be given gradually in combination with the scheme chosen by the students).
(2) (Give 2 points for one, and gradually give points according to the scheme selected by the students)
2 1, solution: (1)∫- 1, 2,3,5, the range is 6? & lt- 1, or >; 5( 1)
? 5 =8 or (-1)=8? =-3 or = 7.3 points (1 2 points)
(2) = 1 (4 points) (6 points)
22. solution: D 1 parallelogram (2 points) (2 points) proof: prove Rt△ABF≌ Rt△CDE (3 points) and get AF=CE (4 points) ∫AF∨CE(5 points)? Quadrilateral AFCE is a parallelogram (6 points)
23.( 1)∵ (2 points)? K<9 (3 points)
(2) ∵k is the largest integer satisfying the above conditions? K=8 (4 points)
When k=8, the root of the equation x2-6x+8=0 is x1= 2x2 = 4; (6 points)
Substitute x=2 into the equation x2+mx-4=0 to get 4+2m-4=0? M= 0 (7 points)
Substituting x=4 into the equation x2+mx-4=0 gives 16+4m-4=0? M= -3(8 points)
24.( 1) ( 1)
The axis has one and only one common point. The ordinate of the vertex is 0. The vertex coordinate of C 1 is (1, 0) (2 points).
(2) Drawing, roughly accurate (4 points)
(3) Let the functional relationship of C2 be a (3 3,0) and substitute it into the above formula. The functional relationship of C2 is (5 points) ∵ one intersection point of parabola symmetry axis is A (3 3,0), and the coordinate of the other intersection point of C2 and X axis is (1, 0). (6 points) (4) n > 1 or n
25. Solution: Prove: (1) connected OD.
Is the midpoint of the bad arc,
( 1) ∵OA=OD，OD=OB。
? △AOD and△△ DOB are equilateral triangles (2 points)? AD=AO=OB=BD？ Quadrilateral AOBD is a diamond (3 points)
(2)∫OP = 20b，OA=OC=OB？ PC=OC=OA(4 points) is an equilateral triangle (5 points).
? PC=AC=OCCAP=？ CPA again? ACO=？ CPA+？ Soft flat hat without eaves
(6 points) and the tangent of the radius (7 points)
26. Solution: (1) Add OC and OA as AD? OC, the vertical foot is D. Then in Rt△AOD, OD=r-8( 1), r2=(r-8)2+ 122.
(3 points) r= 13(4 points)
(2) When, when (7 points, 2 points into one)
27. Solution: (1) 140 (2 points)
(2) within w = x(y -20)- 62500 = x2+ 130 x, (3 points)
W = x2+( 150 )x.(4 points)
(3) When x = = 6500, it is the largest in W; (5 points)
Judging from the meaning of the question, (6 points)
The solution method is a 1 = 30 and a2 = 270 (irrelevant, omitted). So a = 30. (7 points)
(4) When x = 5000, W = within 337500, and W = outside. Choosing foreign sales can make the monthly profit bigger (8 points).
28.( 1) ∵ Parabolic symmetry axis is a straight line x= 1, and b=-2. ( 1)
∫ The parabola intersects the Y axis at point C(0, -3),? C=-3, (2 points)? The function expression of parabola is y=x2-2x-3.
(2) The parabola intersects the X-axis at point A and point B. When y=0, x2-2x-3=0.
? X 1 =- 1，x2 = 3。 Point a is to the left of point B. A (- 1, 0), B (3 3,0) (3 points)
Let the functional expression of the straight line passing through points b (3 3,0) and c (0 0,3) be y=kx+m,
Then, the functional expression of (4 points) line BC is y=x-3. (5 points)
⑷①∫AB = 4，PO= AB，？ PO=3(6 points) ∫PO? Y axis
? The abscissa of point p on the PO∑x axis can be obtained from the symmetry of parabola as follows,
? P (,) (7 points)? F(0，)，
? FC=3-OF=3- =。 ∫PO bisects CE vertically at point f,
? CE=2FC= (8 points)
②P 1( 1-，-2)，P2( 1-，)。 (1 1, write a right one to 1).