First, multiple-choice questions (*** 12 small questions, 5 points for each question, only one of the four options meets the requirements)
1. All the elements in the following options can form a set ().
A. Students with higher basketball level in school B. There are tall trees on campus.
C.C. All EU countries in 2007 D. Economically developed cities in China
2. The solution set of equations is ()
A.B. Up to now, the most comprehensive and applicable math test for senior one (required test 1, 4)
C.( 1， 1)d。
3. Given the set A={a, b, c}, the following can be regarded as a subset of the set a ().
A.{a，b，c } C. { a，e } D. { a，b，c，d}
4. In the figure below, it means ()
5. The following statement is true ()
A.B. C. D。
6. Let A = {x | x freestyle swimmer} and B = {x | x breaststroke swimmer}. For "two participants"
Athletes plus freestyle and breaststroke "is expressed as () by set operation.
A.A∪B B B A B C A∪B D A B
7. Let A={x}, B={} and C={}
Then there is ()
A. (A+B) A B. (A+B) B C. (A+B) C D. (A+B) Any one of A, B and C. Let A = {1, 2, x} and B = {2, 4, 5}, if
A. 1 B. 3 C. 4 D. 5
9. The number of sets m satisfying the condition {1, 2,3} m {1,2,3,4,5,6} is ().
A.8b . 7c . 6d . 5
10. Complete works U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {3, 4, 5}, B = {1, 3,
6}, then the set {2,7,8} is ()
A.B. C. D。
1 1. Settings, ()
A.B. C. D。
12. If there is only one element in the set a = {x | ax2+2x+ 1 = 0}, the value of a is ().
A.0b.0 or1C.1D. Not sure.
Fill in the blanks (***4 small questions, 4 points for each question, and fill in the answers on the horizontal lines in the questions)
13. Describe the set of 1 divided by 3.
14. Fill in the blanks with appropriate symbols:
( 1) ; (2){ 1，2，3 } N；
(3){ 1} ; (4)0 .
15. A set containing three real numbers can be expressed as or, then.
16. Given set,, then set,,.
Third, the solution (***4 small questions, ***44 points, the solution should be written to prove the process or calculus steps)
17. The Set of values of set, set, if and real number A is known.
18. Known set, set, if satisfied, find the value of number A. 。
19. Known equation.
(1) If the solution set of the equation has only one element, find the relationship that the numbers A and B satisfy;
(2) If the solution set of the equation has two elements, 1 3, which are the values of real numbers A and B respectively.
20. If the known set,, satisfies, then the range of number A is realistic.
Properties of the required 1 function
First, multiple-choice questions:
1. The function that is not increasing function in the interval (0, +∞) is ().
a . y = 2x+ 1b . y = 3 x2+ 1 c . y = d . y = 2 x2+x+ 1
2. The function f (x) = 4x2-MX+5 is a increasing function in the interval [-2, +∞] and a decreasing function in the interval (-∞, -2).
Number, then f( 1) is equal to ()
A.-7b . 1c . 17d . 25
3. If the function f(x) is increasing function in the interval (-2,3), then the increasing interval of y = f (x+5) is ().
A.(3，8) B.(-7，-2) C.(-2，3)d .(0，5)
4. If the function f(x)= monotonically increases in the interval (-2, +∞), the range of the real number A is ().
A.(0，)b .(，+∞) C.(-2，+∞) D.(-∞，- 1)∞( 1，+∞)
5. If the function f(x) is monotonic in the interval [a, b] and f (a) f (b) is less than 0, then the equation f(x)=0 is in the interval [a, b] ().
A. At least one real root B. At most one real root
C. there is no real root. D. there must be a unique real root.
6. If satisfied, the value of is ()
5 6
7. If, and are set, then the set of real numbers ().
8. It is known that the function f(x) whose domain is r monotonically decreases (-∞, 5) in the interval. For any real number t, there exists f (5+t).
= f (5-t), then the following formula must hold ()
a . f(- 1)< f(9)< f( 13)b . f( 13)< f(9)< f(- 1)
c . f(9)< f(- 1)< f( 13)d . f( 13)< f(- 1)< f(9)
9. The increasing interval of the function is ()
A.B.
C.D
10. If the function is a decreasing function in the interval, the value range of the real number ().
a . a≤3 b . a ≥- 3c . a≤5d . a≥3
1 1. function, and then ()
12. If it is known that the even function defined on satisfies and is a decreasing function in the interval, then ()
A.B.
C.D.
Second, fill in the blanks:
13. The subtraction interval of the function y = (x- 1)-2 is _ _.
14. Function f (x) = 2x2-MX+3, when x∈? -2,+is increasing function, when x∈? -? ,-2? Time is a shortened letter.
Number, then f (1) =.
15. If the function is even, the decreasing interval of is _ _ _ _ _ _ _.
16. If the function f (x) = ax2+4 (a+ 1) x-3 decreases on [2, +∞], then the range of a is _ _.
Third, the solution: (the solution should be written in words to prove the process or calculation steps. )
17. Prove that the function f (x) = 2-xx+2 is in (-2,+? ) is an incremental function.
18. Prove that the function f (x) = monotonically decreases in [3,5], and find the maximum and minimum values of the function in [3,5].
19. Known functions
(1) to judge the monotonicity of the function and prove it;
⑵ Find the maximum and minimum values of the function.
20. The known function is an even function with an integer domain, which monotonically decreases in the interval, thus satisfying.
Collection of.
Required 1 function test questions
First, multiple-choice questions: (This question is entitled *** 12, with 5 points for each question and 60 points for * * *. Among the four options given in each question,
Only one item meets the requirements of the topic)
The domain of 1. function is ()
A B C D
2. The following groups of functions represent the same function ()
A.B.
C.D.
3. The range of the function is ()
0, 2 and 3 BC
4. If it is known, then f(3) is ()
A 2 B 3 C 4 D 5
5. In the quadratic function, the number of zeros of the function is ().
A 0 B 1 C 2 d cannot be determined.
6. If the function decreases in the interval, the value of the real number is the norm ().
A B C D
7. A student left home to go to school. Afraid of being late, he started running, and when he was tired, he walked the rest of the distance.
If the vertical axis represents the distance from home and the horizontal axis represents the time after leaving home, the following four figures are consistent with the students.
It is () that moves the law.
8. The image of the function f(x)=|x|+ 1 is ().
9. If the domain of a function is known, the domain of is ().
A.B. C. D。
10. If the function decreases in the interval, the range of real numbers is ().
A.B. C. D。
1 1. If the function is even, the value of is ().
A.B. C. D。
12. The range of the function is ()
A.B. C. D。
2. Fill in the blanks (***4 small questions, 4 points for each question, * *16 points, and fill in the answers on the horizontal lines in the questions)
13. The domain of the function is;
14. If
15. If the function, then =
16. The maximum value of the function is and the minimum value is.
Third, the solution (***4 small questions, ***44 points, the solution should be written to prove the process or calculus steps)
17. Find the domain of the following function:
( 1)y = x+ 1x+2(2)y = 1x+3+-x+x+4
(3)y = 16-5x-x2(4)y = 2x- 1x- 1+(5x-4)0
18. Point out the domain, range, monotone interval and monotonicity of the following functions.
( 1)y=x2？ x？ (2)y=x+？ x？ x
For quadratic functions,
(1) represents opening direction, symmetry axis equation and image vertex coordinates;
(2) Find the maximum or minimum value of the function;
(3) Analyze the monotonicity of the function.
20. it is known that A= and b =.
(i) If yes, the range of values to be found;
(ii) If yes, the range of values to be found.
Required 1 Chapter II Basic Elementary Functions (1)
First, multiple-choice questions:
The value is 1. ()
A B 8 C -24 D -8.
2. The domain of the function is ()
A B C D
3. Among the following functions, monotonically increasing is ().
A B C D
4. Image of function and ()
A about axial symmetry b about axial symmetry
C is symmetrical about the origin and d is symmetrical about the straight line.
5. If it is known, it is expressed as ()
A B C D
6. If known, then ()
A B C D
7. If the function f(x)=2x, the image of f (1-x) is ().
A B C D
8. There are four conclusions as follows: ① LG (LG 10) = 02LG (LNE) = 0③ If 10=lgx, then x= 10 ④ If e=lnx, then
X=e2, where the correct one is ().
A.① ③ B.② ④ C. ① ② D. ③ ④
9. if y=log56? log67？ log78？ log89？ Log9 10, with ()
A.y (0， 1) B . y ( 1，2 ) C. y (2，3 ) D. y= 1
10. Given that f(x)=|lgx|, f (), the relationship between f () and f(2) is ().
A.f(2)>f()& gt； f()b . f()& gt； f()& gt； Female (2)
C.f(2)>f()& gt； f()d . f()& gt； f()& gt； Female (2)
1 1. If f(x) is an even function, it is a decreasing function, and f (lgx) >; F( 1), then the value range of x is ()
A.(， 1) B. (0)，( 1，)c .( 10)d .(0， 1) ( 10，)
12. if a and b are arbitrary real numbers and A >；; B, then ()
A.a2 & gtb2 B.< 1 degree centigrade. 0d . & lt；
Second, fill in the blanks:
13. When x [- 1, 1], the value range of the function f(x)=3x-2 is
14. The known function is _ _ _ _ _ _ _ _.
15. As we all know, it is a decreasing function on, so the value range of _ _ _ _ _ _ _ _.
16. If the even function f(x) whose domain is r is a increasing function on [0, +∞), and f () = 0, then the inequality.
The solution set of f (log4x) > 0 is _ _ _ _ _ _ _ _.
Third, answer questions:
17. Known functions
(1) to make its image;
(2) Monotonous intervals are represented by images;
(3) It is pointed out from the image that the function has a minimum value when it takes any value. What is the minimum value?
18. It is known that f (x) = log a (a >; 0, and a ≠ 1)
(1) Find the domain of f(x)
(2) find f (x) >; The value range of x is 0.
19. It is known that the maximum value of the function in the interval [1 7] is greater than the minimum value. Find the value of a ..
20. Known
(1), the maximum and minimum values of;
(2) Maximum value and minimum value;
Required 1 Chapter II Basic Elementary Functions (2)
First, multiple-choice questions:
The range of 1 and the function y = log x+3 (x ≥ 1) is ().
A.B.(3，+∞) C. D.(-∞，+∞)
2, known, then = ()
a、 100 B、C、D、2
3, known, it is expressed as ()
A, B, C, D,
4. It is known that the function is continuous in the interval, and the following statement is affirmative.
It is ()
A. The function has a zero point in the interval or.
B the function has a zero point in the interval and a zero point in the upper interval.
C this function has at most two zeros in the interval.
D the function may have 2006 zeros in the interval.
5. Hypothetically, the process of finding an approximate solution in an equation by dichotomy.
Take the midpoint of the interval, and the next rooted interval is ()
A.( 1, 2) B. (2,3) C. (1,2) or (2,3) D. Not sure.
6. The image of the function passes through the fixed point ()
A.( 1，2)b .(2， 1)c .(2， 1)d .( 1， 1)
7. If, then the size relationship between A and B is ()
a . b < a < 1B。 a < b < 1 c . 1 < b
8. Among the following functions, the function whose range is (0, +∞) is ().
A.B. C. D。
9. The three elements of the equation,,, in which
Answer. B . ( 0， 1 ) C . ( 1，)D .(2)
10. The function with the range of (0, +∞) is ().
A, B, C, D,
1 1. The image of the function y= | lg(x- 1)| is ().
12. The monotonic increasing interval of the function is ()
a、B、C 、( 0，+∞) D、
Second, fill in the blanks:
13. Calculation: =.
14. The image passing point (2, 32) of the power function is known, and its analytical formula is.
15. The domain of the function is.
16. The monotone decreasing interval of the function is _ _ _ _ _ _ _ _.
Third, answer questions.
17. Find the domain of the following function:
( 1) (2)
18. Known function, the domain of (1);
(2) The range of values.
19. Find the domain, range and monotone interval of function y=3.
20. if 0≤x≤2, find the maximum and minimum values of the function y=