Class name score

1. Multiple-choice questions (only one answer to each question is correct, with 3 points for each question and 36 points for * * *) 1. If the complete set U=R, A={- 1} and B={}, then () (A) AB (B) A (C) AB (D). What is not an even function is () (a) y = 2 (b) y = 2x+2-x (c) y = LG (d) y = LG (x+) 3. Figure 1 shows two function images made in the same coordinate system. Then these two functions are () (A)y=ax and y=loga(-x) (B)y=ax and y=logax- 1 (C)y=a-x and y=logax- 1 (D)y=a-x and y = Given that a2+a 12=3, then s13 = () (a)18 (b)19.5 (c) 21(d) 39 5. When x, the following function that is not increasing function is () (a) y = x+a2x-3 (b) y = 2x (c) y = 2x2+x+1(d) y = 6. If f (n+ 1) = f (n)+65438. Then the value of f( 100) is () (a)102 (b) 99 (c)1kloc-0/(d)1007. The following inequality holds () (a) log 3.

③{ }

④ {} {} = {} Then the above equation holds ().

(A)①③ (B)①② (C)②④ (D)③④

9. If series {an} is a geometric series, then the following four propositions: ① series {an3} is also a geometric series; ② The sequence {-an} is also a geometric series; ③ The sequence {} is also a geometric series; ④ The series {} is also a geometric series, in which the correct number is ().

1 (B)2 (C)3 (D)4。

10. in the mapping f: a → b, A={ 1, 2,3,k} and b = {4 4,7,a4,a2+3a}, where a and k correspond to the rule f: x → y = 3x+ 1.

a=2，k=5 (B)a=-5，k=2 (C)a=5，k=2 (D)a=2，k=4

1 1. Translate the image with function y=3x to the left by 1 unit to get the image C 1, translate C 1 up by one unit to get C2, and then make a symmetrical image C3 of C2 about the straight line y=x, then the analytical formula of C3 is ().

(A)y = log3(x+ 1)+ 1(B)y = log3(x+ 1)- 1

y = log3(x- 1)- 1(D)y = log3(x- 1)+ 1

12. The number of wrong propositions in the following propositions is ()

If log2x is true, then log2(x- 1) is meaningless. ② If the negative proposition of lgx+lg(x- 1)-lg2 is true; ③ "A number is 6" is a necessary and sufficient condition for "This number is the equal median of 4 and 9"; ④ "an = a1+(n-1) d" is a necessary and sufficient condition for "the sequence {an} is a arithmetic progression".

0 (B) 1 (C)2 (D)3。

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

13. The sum of all two positive numbers divisible by 6 is

14. Given that f(x)=x3+a, f(- 1)=0, the value of f- 1(2) is

15. The function y=-x2-4mx+ 1 is a decreasing function on [2,+], so the range of m is

16. The domain of function y= is

Iii. Answering questions (48 points for this question * * *)

17. (The full mark of this question is 8)

Judge the monotonicity of y= 1-2x3 on (-) and prove it by definition.

18. (The full mark of this question is 10)

It is known that in arithmetic progression {an}, a2=8, and the sum of the preceding 10 is S 10= 185.

(i) Find the general formula an of the sequence {an};

(ii) If the 2nd, 4th, 8th … 2n, … items are taken from the sequence {An} And arranged into a new sequence in the original order, try to find the sum of the first n items in the new sequence as an.

19. (The full mark of this question is 10)

Let the function f(x)= be the odd function on R.

(i) find the value of a;

(ii) Find the inverse function of f(x);

(iii) if k, the solution is not equal to: log2 >；; Log 2

20. (The full mark of this question is 10) The original fish in a fishing ground is 20,000 Jin, and the growth rate of fish raised in the first year is 200%, and the annual growth rate is half that of the previous year. Q:

1) What is the weight of fish after three years?

2) If the annual weight loss rate caused by environmental pollution is 10%, the weight of fish will start to decline in a few years.

2 1. (The full mark of this question is 10)

When the common ratio q of the defined geometric series is satisfied, it is called infinite inverse geometric series, which can prove that the sum of all terms of such a series is S=

1) If the sum of all terms of a geometric series is 6 and the common ratio is-,find the sum of the first six terms;

Senior 1 (1) Mathematics Final Exam (Volume B)

First, multiple choice questions

Title number

1

2

three

four

five

six

seven

eight

nine

10

1 1

12

answer

D

C

D

B

D

C

B

A

D

A

C

A

Second, fill in the blanks

13.8 10 14. 1 15 . m 16 . x(-0)(0，4)

Third, answer questions.

17.y = 1-2x3 is a monotone decreasing function on (-,+).

Proof: Take x 1, x2 R, and-

f(x 1)-f(x2)=( 1-2x 3 1)-( 1-2x 32)= 2(x32-x 13)= 2(x2-x 1)(x22+x 1x 2+x 2 1)= 2(x2-x / kloc-0/)[(x 1+x2)2+x 65438x 1∴x0-x 1>； 0 and (x1+x2) 2+x12 > 0，∴f(x 1)-f(x2)>； 0 is f(x 1)>F(x2). Therefore, f(x)= 1-2x3 is a monotonically decreasing function on (-,+).

18.(I) if the tolerance is d, a2 = a1+d = 810a1+

That is, a 1+d = 8, 2a 1+9d = 37, ∴ a 1 = 5, d = 3 ∴ an = a1(n-1) d =

(ⅱ)An = a2+a4+A8+…+a2n =(3×2+2)+(3×4+2)+(3×8+2)+…+(3×2n+2)= 3×(2+4+8+…+2n)+2n = 3×2n+ 1+2n-6

19. (I) f (x) is odd function, and f(-x)=-f(x).

that is

Namely: a-2x =1=1-a2x ∴ a+a2x =1+2x, ∴ A (1+2x) = 1+2x ∴.

(2) ∵ y = ∴ y+y2x = 2x-12x (y-1) =-1-y, ∝ 2x = f-1(x) = X. 1)

(ⅲ)log2 & gt； Log2 is equivalent to

(1)-1< 1-k & lt； 1, that is, 0

(2) When 1-K- 1, that is, k 2, {}

20. (1) meaning: A 1 = 2+2× 2 = 6, A2 = 2+2× 2+(2+2× 2) = 12, ∫ a2 = a1+a/kloc.

After three years of breeding, the weight of this fish has reached 80 thousand Jin.

(Ⅱ) Similarly: a4=a3+a3 ×, a5=a4+a4×, …

∴ An = An-1+ An-1 = An-1( 1+)

If the weight of fish is the largest in the n year, there are

that is

∴n=5 ∴ From the sixth year (five years later), the weight of fish began to decrease.

2 1.(I) The definition and formula given are 6= ∴a 1=8.

So S6= =

(2) Meaning: a2=6, S3=2 1.

That is, the solution of the equation is q= or q=2.

When q=, the sequence is an infinite inverse geometric series. At this time, a 1= 12, and the sum of all items is S=

When q=2, the sequence is not an infinite inverse geometric series, then a 1=3, then S 10=

Senior one last semester math final exam questions (B volume)

Class name score

1. Multiple-choice questions (only one answer to each question is correct, with 3 points for each question and 36 points for * * *) 1. If the complete set U=R, A={- 1} and B={}, then () (A) AB (B) A (C) AB (D). What is not an even function is () (a) y = 2 (b) y = 2x+2-x (c) y = LG (d) y = LG (x+) 3. Figure 1 shows two function images made in the same coordinate system. Then these two functions are () (A)y=ax and y=loga(-x) (B)y=ax and y=logax- 1 (C)y=a-x and y=logax- 1 (D)y=a-x and y = Given that a2+a 12=3, then s13 = () (a)18 (b)19.5 (c) 21(d) 39 5. When x, the following function that is not increasing function is () (a) y = x+a2x-3 (b) y = 2x (c) y = 2x2+x+1(d) y = 6. If f (n+ 1) = f (n)+65438. Then the value of f( 100) is () (a)102 (b) 99 (c)1kloc-0/(d)1007. The following inequality holds () (a) log 3.

③{ }

④ {} {} = {} Then the above equation holds ().

(A)①③ (B)①② (C)②④ (D)③④

9. If series {an} is a geometric series, then the following four propositions: ① series {an3} is also a geometric series; ② The sequence {-an} is also a geometric series; ③ The sequence {} is also a geometric series; ④ The series {} is also a geometric series, in which the correct number is ().

1 (B)2 (C)3 (D)4。

10. in the mapping f: a → b, A={ 1, 2,3,k} and b = {4 4,7,a4,a2+3a}, where a and k correspond to the rule f: x → y = 3x+ 1.

a=2，k=5 (B)a=-5，k=2 (C)a=5，k=2 (D)a=2，k=4

1 1. Translate the image with function y=3x to the left by 1 unit to get the image C 1, translate C 1 up by one unit to get C2, and then make a symmetrical image C3 of C2 about the straight line y=x, then the analytical formula of C3 is ().

(A)y = log3(x+ 1)+ 1(B)y = log3(x+ 1)- 1

y = log3(x- 1)- 1(D)y = log3(x- 1)+ 1

12. The number of wrong propositions in the following propositions is ()

If log2x is true, then log2(x- 1) is meaningless. ② If the negative proposition of lgx+lg(x- 1)-lg2 is true; ③ "A number is 6" is a necessary and sufficient condition for "This number is the equal median of 4 and 9"; ④ "an = a1+(n-1) d" is a necessary and sufficient condition for "the sequence {an} is a arithmetic progression".

0 (B) 1 (C)2 (D)3。

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

13. The sum of all two positive numbers divisible by 6 is

14. Given that f(x)=x3+a, f(- 1)=0, the value of f- 1(2) is

15. The function y=-x2-4mx+ 1 is a decreasing function on [2,+], so the range of m is

16. The domain of function y= is

Iii. Answering questions (48 points for this question * * *)

17. (The full mark of this question is 8)

Judge the monotonicity of y= 1-2x3 on (-) and prove it by definition.

18. (The full mark of this question is 10)

It is known that in arithmetic progression {an}, a2=8, and the sum of the preceding 10 is S 10= 185.

(i) Find the general formula an of the sequence {an};

(ii) If the 2nd, 4th, 8th … 2n, … items are taken from the sequence {An} And arranged into a new sequence in the original order, try to find the sum of the first n items in the new sequence as an.

19. (The full mark of this question is 10)

Let the function f(x)= be the odd function on R.

(i) find the value of a;

(ii) Find the inverse function of f(x);

(iii) if k, the solution is not equal to: log2 >；; Log 2

20. (The full mark of this question is 10) The original fish in a fishing ground is 20,000 Jin, and the growth rate of fish raised in the first year is 200%, and the annual growth rate is half that of the previous year. Q:

1) What is the weight of fish after three years?

2) If the annual weight loss rate caused by environmental pollution is 10%, the weight of fish will start to decline in a few years.

2 1. (The full mark of this question is 10)

When the common ratio q of the defined geometric series is satisfied, it is called infinite inverse geometric series, which can prove that the sum of all terms of such a series is S=

1) If the sum of all terms of a geometric series is 6 and the common ratio is-,find the sum of the first six terms;

Senior 1 (1) Mathematics Final Exam (Volume B)

First, multiple choice questions

Title number

1

2

three

four

five

six

seven

eight

nine

10

1 1

12

answer

D

C

D

B

D

C

B

A

D

A

C

A

Second, fill in the blanks

13.8 10 14. 1 15 . m 16 . x(-0)(0，4)

Third, answer questions.

17.y = 1-2x3 is a monotone decreasing function on (-,+).

Proof: Take x 1, x2 R, and-

f(x 1)-f(x2)=( 1-2x 3 1)-( 1-2x 32)= 2(x32-x 13)= 2(x2-x 1)(x22+x 1x 2+x 2 1)= 2(x2-x / kloc-0/)[(x 1+x2)2+x 65438x 1∴x0-x 1>； 0 and (x1+x2) 2+x12 > 0，∴f(x 1)-f(x2)>； 0 is f(x 1)>F(x2). Therefore, f(x)= 1-2x3 is a monotonically decreasing function on (-,+).

18.(I) if the tolerance is d, a2 = a1+d = 810a1+

That is, a 1+d = 8, 2a 1+9d = 37, ∴ a 1 = 5, d = 3 ∴ an = a1(n-1) d =

(ⅱ)An = a2+a4+A8+…+a2n =(3×2+2)+(3×4+2)+(3×8+2)+…+(3×2n+2)= 3×(2+4+8+…+2n)+2n = 3×2n+ 1+2n-6

19. (I) f (x) is odd function, and f(-x)=-f(x).

that is

Namely: a-2x =1=1-a2x ∴ a+a2x =1+2x, ∴ A (1+2x) = 1+2x ∴.

(2) ∵ y = ∴ y+y2x = 2x-12x (y-1) =-1-y, ∝ 2x = f-1(x) = X. 1)

(ⅲ)log2 & gt； Log2 is equivalent to

(1)-1< 1-k & lt； 1, that is, 0

(2) When 1-K- 1, that is, k 2, {}

20. (1) meaning: A 1 = 2+2× 2 = 6, A2 = 2+2× 2+(2+2× 2) = 12, ∫ a2 = a1+a/kloc.

After three years of breeding, the weight of this fish has reached 80 thousand Jin.

(Ⅱ) Similarly: a4=a3+a3 ×, a5=a4+a4×, …

∴ An = An-1+ An-1 = An-1( 1+)

If the weight of fish is the largest in the n year, there are

that is

∴n=5 ∴ From the sixth year (five years later), the weight of fish began to decrease.

2 1.(I) The definition and formula given are 6= ∴a 1=8.

So S6= =

(2) Meaning: a2=6, S3=2 1.

That is, the solution of the equation is q= or q=2.

When q=, the sequence is an infinite inverse geometric series. At this time, a 1= 12, and the sum of all items is S=

When q=2, the sequence is not an infinite inverse geometric series, then a 1=3, then S 10=