Reference answers to math test questions
First, multiple choice questions
The title is 1 23455 6789 10.
Answer A B D C B C B C A D
Second, fill in the blanks
The title is112131415.
answer
42 2 1 ( 16,0)
Third, answer questions.
16 (7 points for each small question, *** 14 points)
(1) solution: original formula
(2) Solution: Original formula
17, (7 points for each small question, *** 14 points)
(1) Proof: ∴. ab‖de
In △ABC and △DEF,
∴△ABC≌△DEF
(2) As shown in the figure, the rectangle is what you need to do.
(0,2), (3,2) (3,0)
18 (in 12)
(1) as shown in the figure.
(2) 180
(3) 120
(4) Solution:
Answer: The probability of pumping into the refrigerator is.
19, (in 1 1)
Solution: (1) Proof: ∫∴.
Once again: Ⅷ
∴CB‖PD
(2) Connect the AC power supply
∵AB is the diameter⊙ O,
It's ∴ CD ∵ AB again.
∴ ,
In Rt△ABC,
∵ ,∴
Say it again,
That is, the diameter of ⊙O is 5.
20. (Full score 12)
(1) Solution: If the price of each schoolbag is yuan, then the price of each dictionary is yuan. According to the meaning of the question:
Solution:
∴
A: The price of each schoolbag is 28 yuan, and the price of each dictionary is 20 yuan.
(2) Solution: Buy a dictionary when you buy a schoolbag. According to the meaning of the question, you will get:
Solution:
Because it is an integer, the value of is 10 or 1 1 or 12.
So there are three purchase schemes, namely: ① 10 schoolbag and 30 dictionaries.
② schoolbag 1 1, 29 dictionaries.
③ 0/2 schoolbags and 28 dictionaries.
2 1, (in 13)
Solution: (1)∵ quadrilateral EFPQ is a rectangle, ∴EF‖QP.
∴△AEF∽△ABC
And ∴AH⊥EF. ∵AD⊥BC.
∴
(2) From (1), ⅷ
∴
∴
At the right time, there is a maximum value, and this maximum value is 20.
(3) As shown in figure 1, obtained from (2),
△ FPC is an isosceles right triangle.
∴ ,
Discuss in three situations:
① As shown in Figure 2, when,
Let EF and PF intersect AC at point m and point n, respectively, and then △MFN is an isosceles right triangle.
∴
∴
② As shown in Figure 3, if, then,
∴
(3) As shown in Figure 4, when, let EQ intersect with AC at K point.
rule
∴
To sum up: the functional relationship between s and t is
22. (Full score 14)
The solution (1) is substituted into O (0 0,0) and A (5 5,0) respectively.
Get, get
∴ The analytical formula of parabola is
(2) Point C is on a parabola.
Reason: the intersection point C makes the CD⊥ axis at point D, connects OC, and sets the AC intersection point OB at point E.
Point b is on a straight line, ∴ B (5, 10)
Points a and c are symmetrical about a straight line.
∴OB⊥AC、,BC⊥OC、
It is also the ∵AB⊥ axis, which is obtained by Pythagorean theorem.
∵
∴ ,∴
* ,∴△cda∽△oab
∴ 。
∴ , ,
∴C(-3,4)
When,
Point c is on a parabola.
(3) There is a point Q on the parabola, which makes the circle with PQ as its diameter tangent to ⊙.
The passing point P is the PF⊥ axis of point F, and the connecting point P is the ⊥ axis of point H.
∴CD‖ ba
∫ c (-3,4), b (5, 10) and is the midpoint of BC.
Viewing Ⅶ from the Proportional Theorem of Parallel Lines
The same is true.
∴ The coordinate of this point is (1, 7).
∴oc ∵bc⊥oc is the tangent of ⊙.
And ∵OP is the tangent of ∵∴.
∴ A quadrilateral is a square, ∴, ∴
Once again: ∴△POF≌△OCD
∴ ,
∴P(4,3)
Let the analytical formula of a straight line be ()
Substitute (1, 7) and p (4, 3) respectively,
Get, get
The analytical formula of ∴ straight line is
If the circle with the diameter of PQ is tangent to ⊙, then point Q is the intersection of a straight line and a parabola, and the coordinates of point Q can be set to (,).
Yes,
arrange
Solve.
The abscissa of point q is or