Seek the comprehensive examination paper at the end of last semester of senior one mathematics.

The new curriculum senior one last semester's comprehensive mathematical simulation test paper 1 (required 1.2).

First, multiple-choice questions (5 points for each question, * * 60 points, each question has only one correct answer)

1, if the set A = {1, 3, x}, B = {1, 0}, A ∪ B = {1, 3, x}, then the number of real numbers x satisfying the condition is ().

1 (B) 2 (C)3 (D) 4。

2. In the orthographic drawing shown on the right, the area of the original plane figure is ().

a、4 B、4 C、2 D、8

3, the following images can't represent the image function is ()

y y y

o x x o x o x

(A) (B) (C) (D)

4. There are four propositions:

1) Determine a plane through three points 2) A rectangle is a plane Figure 3) Three straight lines intersect to determine a plane.

4) Two intersecting planes divide the space into four areas, in which the serial number of the wrong proposition is ().

(A) 1) and 2) (B) 1) and 3) (C)2) and 4) (D)2) and 3)

5. The straight line L 1: AX+3Y+ 1 = 0, L2: 2x+(A+ 1) Y+ 1 = 0. If L 1‖L2, then a= ().

A.-3 b.2 c.-3 or 2 d.3 or -2

6. the number of products produced by a factory in the first five months of this year is c (pieces), and the time is about C.

The function image of t (month) is shown in the figure, so this factory is () for this product.

One two three four five t

(a) The monthly output increases from 1 month to March, and decreases in April and May.

(b)1-The monthly output increased month by month, and the output in April and May was the same as that in March.

(d) The monthly production of1month to March remains unchanged, and production is stopped in April and May.

7. As shown in the figure, the plane cannot be represented by ().

(a) plane α (B) plane AB

8. Let f(x)=3ax+ 1-2a have x0 in (-1, 1), so f(x0)=0, then the range of a is

(a):-1< a <1/5 (b): a >1/5 (c): a >1/5 or a.

9. As shown in the figure, if MC⊥ diamond ABCD is in the plane.

Then the positional relationship between MA and BD is ()

A. Parallel B. Vertical crossing

C. Different planes D. Intersecting but not perpendicular

10, the straight line passing through point m (1, 1) and having the same intercept on both axes is ().

A.x+y = 2b.x+y =1c.x =1or y = 1d.x+y = 2 or x = y.

1 1, where n N, then f(8)= ().

6 (B)7 (C) 2 (D)4

12, circle x2+y2+4x–4y+4 = 0 The equation of a circle symmetrical about the straight line L is ().

a . x2+y2 = 4 b . x2+y2–4x+4y = 0

c . x2+y2 = 2d . x2+y2–4x+4y–4 = 0

Fill in the blanks (4 points for each small question, 16 * * * 4 small questions)

13. It is known that three points A(a, 2) B(5, 1) C(-4, 2a) are on the same straight line.

Then a =

14. In the equilateral triangle ABC with side length A, AD⊥BC is in D,

After folding into dihedral angle b-AD-c along ad, BC= 12 a,

At this time, the size of dihedral angle B-AD-C is

15, exponent: function y=(a+ 1)x is the increasing function on R, so the range of a is

16, there are four propositions:

① the function f (x) = (a > 0 and a≠ 1) has the same domain as the function g (x) = (a > 0 and a≠ 1);

② The function f(x)=x3 has the same range as the function g(x)=;

③ Functions f(x)= and g(x)= are increasing function in (0, +∞);

④ If the function f(x) has the inverse function f- 1 (x), the inverse function of f(x+ 1) is f- 1 (x+ 1).

The incorrect question number is.

Third, answer questions.

17, calculate the following

( 1)(lg2)2+lg5？ lg20- 1

(2)

18. The function y= f(x) defined on the real number r is an even function. When x≥0.

(1) Find the expression of f(x) on r;

(2) Find the maximum value of y=f(x) and write the monotonous interval of f(x) on r (without proof).

19, as shown in the figure, there is a hemisphere on the empty conical cup.

If the ice cream melts, will it overflow the cup?

Please explain the reason with your calculation data.

20. It is known that the three vertices are,,.

(i) Find the equation of the straight line where the BC side midline AD is located;

(ii) Find the distance from point A to BC.

2 1. When a brand of sweater is sold in a shopping mall, the number of buyers is a linear function of the sweater price. The higher the bid price, the fewer buyers. The lowest bid price when the number of buyers is zero is called invalid price, and the known invalid price is 300 yuan per piece. At present, the cost price of this sweater is 100 yuan/piece, and the mall sells it at the same price (marked price) higher than the cost price. Q:

(1) How much should the price of each sweater be set to maximize the profit of the shopping mall?

(2) Under normal circumstances, getting the maximum profit is only an "ideal result". What is the price of each sweater if the mall wants to get the maximum profit of 75%?

22. Known straight lines: y=x+b and circle x2+y2+2x―2y+ 1=0.

(1) If the straight line is tangent to the circle, find the equation of the straight line; (2) If b= 1, find the chord length of the intersection of a straight line and a circle;

Bachelor of Arts

Two, 3.5 or two, 60? (0,+∞ ) 2,3

Three. 17.( 1) solution: the original formula = 0 ——— 6 points.

(2) Solution: The original formula =4*27+2-7-2- 1.

= 100- 12 points.

18 solution: (1)f(x)= -4x2+8x-3 x≥0.

-4x 2-8x-3x & lt； o - 6#

(2) when x= 1 or-1, the maximum value of y = 1-8 #

Increase the interval (-∞,-1) (0, 1)-10 #

Negative interval (1, +∞)-12 #

19 solution: v hemisphere =? √×π×43= 128π/3 - 5#

V-cone =? ×π×42× 12 = 64π& gt； V hemisphere-10 #