The first volume of the final exam of the third grade mathematics, the first volume, multiple-choice questions (24 points for this question, 3 points for each small question)
There are four options for each of the following questions, and only one is correct. Please fill in the following correct answers in alphabetical order.
Below the corresponding question number in the table.
The absolute value of 1 -3 Yes
3rd century BC to 3rd century BC.
2. As shown in the figure, the vertices of △ABC are all on the grid points of the grid paper, so the value of sinA is
A.B.
C.D.
3.20 1 1 10 Beijing Daily reported:? Since 1998, 3 million people in the city have participated in blood donation? The number 3 000 000 is expressed in scientific notation as
A.B. C. D。
4. As shown in Figure ⊙O, the length of the chord AB is 6cm, and the distance from the center of O to AB is 4cm.
Then the radius length of ⊙O is
A.3cm, B.4cm, C.5cm, D.6cm
5. In the plane rectangular coordinate system xoy, a circle with point () as the center and 4 as the radius.
A. intersect with the x axis and tangent to the y axis. B. separate from the x axis and intersect with the y axis.
C. Tangent to X axis, separated from Y axis D. Tangent to X axis, intersecting with Y axis
6. There are three balls of the same size in the bag, two of which are red and 1 is white. The probability that both balls are red when they are randomly drawn from the bag at the same time is
A. BC 1
7. As shown in the figure, in △ABC,? C=90？ , BC=6, D and E are on AB and AC respectively,
Fold △ABC along DE so that point A falls on a? Place, if one? Is the midpoint of CE,
The length of the crease is
A.B.2 C.4 D.5
8. As shown in the figure, in the isosceles trapezoid ABCD, the diagonal lines AC and BD intersect at O,
? ABD=30？ ，AC？ BC, AB=8cm, then the area of △COD is
A.B.
C.D.
II. Fill in the blanks (the score for this question is *** 15, with 3 points for each small question)
9. As shown in the figure, PA and PB are tangents of ⊙O, and A and B are tangents.
AC is the diameter ⊙O, P= 40? And then what? BAC= _？ . .
10. If the parabola intersects the X axis at two different points,
Then the range of m is _ _ _ _.
1 1. As shown in the figure, AB is the diameter of ⊙ O and CD is the chord of ⊙ O. If
? DAB=52？ And then what? ACD = _ _ _ _ _ _ _？ . .
12. An image with a known linear function and inverse proportional function.
The ordinate of the intersection is 2, so the value of b is _ _ _ _.
13. As shown in the figure, in the right triangle ABC,? ACB=90？ ，CA=4，
Point p is the midpoint of semi-circular arc AC, connecting BP, and the line segment BP is plotted.
APCB (figure composed of semicircle and triangle ABC) is divided into two parts.
Then the absolute value of the difference between the areas of these two parts is _ _ _ _ _.
Iii. Answer the question (9 points for this question, including 5 points for 14 and 4 points for 15).
14. Calculation:
Solution:
15. Known, find the value of algebraic expression.
Solution:
Fourth, answer the question (this question *** 15 points, 5 points for each small question)
16. As shown in the figure, in △ABC, AB=AC,? A= 120？ ,
BC=6。 Find the length of AB.
Solution:
17. As shown in the figure, in △ABC,? ABC=80？ ,? BAC=40？ AB perpendicular bisector.
Intersect with AC and AB at points D and E, respectively, and connect BD.
Proof: △ABC∽△BDC.
Prove:
18. As shown in the figure, it is known that point E is on the AB side of △ABC, and ⊙O with AE as the diameter is tangent to BC.
At point d, it's even with AD? BAC。
Proof: AC? BC.
Prove:
Five, answer (this question *** 15 points, 5 points for each small question)
19. As shown in the figure, in the plane rectangular coordinate system, the coordinates of points are as follows
Because.
(1) Please draw it in the picture, so it is the same as.
These points are centrosymmetric;
(2) Write the coordinates of the three vertices in (1) directly.
Solution:
20. The curve on the right is a branch of the inverse proportional function image.
(1) In which quadrant is the other branch of the inverse proportional function located? What is the range of the constant n?
(2) If the image of the linear function and the image of the inverse proportional function intersect at point a,
The area of △AOB intersecting with X axis at point B is 2. Find the analytic expression of inverse proportional function.
Solution:
2 1. As shown in the figure, in trapezoidal ABCD, AD//BC, BC=5, AD=3, diagonal AC? BD, what else? DBC=30？ .
Find the height of trapezoidal ABCD.
Solution:
Six, answer (this question *** 10, 5 points for each small question)
22. As shown in the figure, in Rt△OAB,? OAB=90？ , o is the origin of coordinates,
The edge OA is on the X axis, and OA=AB= 1 unit length. Put rt delta OAB.
△ After the positive translation of the X axis 1 unit length.
(1) Find the analytical formula of parabola with a vertex and passing through it;
(2) If the parabola in (1) intersects with OB at point C and with Y axis at.
Point d, find the coordinates of point d and point C.
Solution:
23. As shown in the figure, in △ABC, AB=AC, and ⊙O with the diameter of AB intersects BC.
At point d, pass point d for EF? AC is at point e, and the extension line of intersection AB is at point F.
(1) verification: EF is the tangent of ⊙O;
(2) When AB=5 and BC=6, find the length of DE.
(1) Proof:
Seven, answer (this question *** 12 points, 6 points for each small question)
24. As shown in the figure, the images of linear function and inverse proportional function y 1=? 3x images intersect at point a,
It intersects with the Y axis and the X axis at two points, B and C, respectively, C (2 2,0). When, linear function value.
Is greater than the inverse proportional function, when the linear function is less than the inverse proportional function.
(1) Find the analytical formula of linear function;
(2) Let function y2= ax, y 1=? 3x(x & lt； 0) axis symmetry about y. When y2= ax
Take a point P on the image (the abscissa of the point P is greater than 2) and find PQ? X axis, vertical foot is q, if quadrilateral BCQP.
The area of is equal to 2. Find the coordinates of point p.
Solution:
25. the quadratic function of x is known (a >；; 0) passes through the point C(0, 1) and intersects the x axis at different angles.
Two points A and B, the coordinate of point A is (1, 0).
(1) Find the value of c;
(2) Find the range of a;
(3) The image of the quadratic function intersects with the straight line y= 1 at two points C and D, and it is a quadrilateral composed of four points A, B, C and D..
Diagonal lines intersect at point P, the area of △PCD is S 1, and the area of △PAB is S2. When,
The value.
Solution:
The answer to the final examination paper of the first volume of the third grade mathematics 1. Multiple choice questions (24 points for this question, 3 points for each small question)
Title 1 2 3 4 5 6 7 8
Answer A C D C D B B A
II. Fill in the blanks (the score for this question is *** 15, with 3 points for each small question)
9.； 10.； 1 1.38? ; 12.； 13.4.
Iii. Answer the question (9 points for this question, including 5 points for 14 and 4 points for 15).
14. Solution:
? .. 4 points
=..5 points
15. Solution:
∵ ,? Original formula =0.
Fourth, answer the question (this question *** 15 points, 5 points for each small question)
16. solution: AD? BC is at point D 1 point.
AB = AC，？ BAC= 120？ ,
B=30？ ，BD=？ .. 2 points
Yes,
∵ ? 3 points
? 5 points
17. Proof:
De is perpendicular bisector of AB,
? AD=BD。 ? .. 1 point
∵ ? BAC=40？ ,
ABD=40？ 2 points
∵ ? ABC=40？ ,
DBC=40？
DBC=？ BAC。 3 points
∵ ? C=？ C. 4 points
? △ABC∽△BDC。 ? .5 points
18. Proof: connect OD. . 1.
OA = OD，
1 =? 3.？ .. 2 points
∵ advertising split? BAC，
1 =? 2.
2 =? 3.
? OD∑AC。 ? .3 points
∵ BC is the tangent of⊙ O,
? OD？ BC. . ? 4 points
? AC？ BC. ? .. 5 points
Five, answer (this question *** 15 points, 5 points for each small question)
19.( 1) As shown in the figure ... 2 points.
(2) According to (1), the coordinates of the point are
. ? 5 points
20. Solution: (1) Another branch of the inverse proportional function is located in the fourth quadrant; ? 1 point
What is the range of the constant n? . ? .2 points
(2) set points A(m, n), make, get,
? B (2,0) .3 points
According to the question, what?
? , solution
? a()？ 4 points
.5 points
2 1. solution: for DE∑AC, the extension line of BC is at point e, for DF? Yes, the foot is F. .. 1 point
∫ AD ∨ BC,
? A quadrilateral is a parallelogram.
? AD=CE=3，BE=BC+CE=8。 .. 2 points.
∵ AC？ BD，
? De? BD。
? △BDE is a right triangle,
∵ ? DBC=30？ ，BE=8，
? ... four o'clock
How about in the right triangle BDF? DBC=30？ ,
? .5 points
Six, answer (this question *** 10, 5 points for each small question)
22. Solution: (1) A (1, 0), (2,0), (2,0/). 1 point
The analytical formula of parabola with vertex is
∫ This parabola passes (2, 1),? 1=a (2- 1)2。
? a= 1。
? The analytical formula of parabola is y=(x- 1)2. . ? 2 points
(2) When x=0, y=(0- 1)2= 1.
? The coordinates of point D are (0, 1) .3.
According to the meaning of the question, OB is on the bisector of the first quadrant, so C (m, m) can be set.
Substitute y=(x- 1)2 to get m=(m- 1)2.
The result is m 1 = 3-52.
? ... five points
23.( 1) Proof: Connect OD. ? . 1 point
AB = AC，
C=？ OBD
OD = OB，
1=? OBD。 2 points
1=? C.
? OD∑AC。
∵ EF？ Communication,
? EF? Oh, my god
? EF is the tangent of point ⊙0. 3.
(2) Solution: Connect AD.
∵ AB is the diameter⊙ O,
ADB=90？ . ? 4 points
AB = AC，
? . ? .
? , ? ...？ 5 points
Seven, answer (this question *** 12 points, 6 points for each small question)
24. Solution: (1) ∵ x; ? When 1, the value of the main function is less than
Inverse proportional function value.
? What is the abscissa of point A? 1,? One (? 1, 3) 1 point
Let a resolution function be y= kx+b, because a straight line passes through a and C.
Then the solution is:
? A resolution function is y=? X+2 .3 points
(2) The image of (2) y2 = ax and y 1=? 3x image is symmetrical about y axis,
? y2 = 3x？ .. 4 points
Point b is a straight line y=? The intersection of x+2 and y axis. B (0，2)？ 5 points
Suppose, n>2,
∵ ,
? Solve.
? (52,65) ... 6 points
25. Solution: Substitute (1) into point C (0, 1) to get ... 1.
(2) Substitute (1) into point A (1, 0).
, ?
? The quadratic function is .2 points.
∫ The image with quadratic function intersects the X axis at two different points.
? △& gt； 0. and
? The value range of is 0.3 points.
(3) ∵
? Symmetry axis is
4 points
substitute