TEST No. ___ on the topic: “Derivative” 1. Find the derivative of the function f x A) B) C) D) E) cos x sin x ex sin x cos x ex cos x sin x ex cos x sin x x ex cos x sin x x ex 2. Find the derivative of the function f x sin x ex 1 cos x sin x A) 1 sin x 1 B) cos x 1 1 C) 1 sin x 1 D) 1 cos x E) 1 cos x 1 3 x 3x C) 2 1 3 x 3x D) 6 x 3 3x E) 2 x 3 3x , find f 2 2 С) 1 2 2 5x 1 D) 5 2 ln 2 5 x 1 E) 5 2 ln 2 5 x 1 D) 2 5x 1 E) 2 2 3 6. Find the derivative of the function f x e2x tgx e 2 x sin 2 x 1 A) sin 2 x e x sin x 1 B) sin 2 x e 2 x cos x 1 C) cos 2 x e 2 x cos x 1 D) sin 2 x e 2 x sin 2 x 1 E) sin 2 x 10 7. The function f x 4 1.5 x is given. Find f x A) 1.54 1.5 x 10 V) 1.54 1.5 x 9 C) 94 1.5 x 5 D) 6 4 1.5 x 9 Е) 1.54 1.5 x 9 yx cos x sin x 1. Find y x A) sin 2 x sin x B) sin 2 x sin x C) cos 2x cos x D) cos 2x sin x E) sin x cos 2x 9. Find the derivative of the function f x cos 2 x tgx 8. Given the function cos 2 x sin 2 2 x cos 2 x cos x sin 2 x B) cos 2 2 x sin 2 x cos 2 2 x C) cos 2 x sin 2 x cos 2 2 x D) cos 2 x sin x cos 2 x E) cos 2 2 x A) y x if y x log 5 x 5 x 1 5x A) ln 5 1 5x B) x ln 5 1 1 x C) x ln 5 5 ln 5 1 5 x ln 5 D) x ln 5 1 ln 5 E) x ln 5 10. Find TEST No. ___ on the topic: “Derivative” f x log 2 sin x 1. Find the derivative of the function 1 ctgx С) ctgx D) tgx E) ln 2 sin x 2. Derivative of the function f x ln ctg5x equals: 10 10 10 1 5 A) B) C) D) E) sin 10 x sin 5 x sin 10 x ctg5 x ctg5 x 3. Find the derivative of the function and simplify cos 2 x 4 cos 2 x A) B) C) -1 D) 1 E) 2 2 sin 2 x sin 2 x sin 2 2 x 2 4. The function f x tg 3x is given. Find f 0 A) B) ctgx A) 1 B) -1 5. The derivative of function C) 2 f x 5 D) 4 ln x E) 0 is 5 ln x C) 5 ln 5 5 ln x D) x ln 5 E) x A) 5 ln x f 1 x 1 D) 8 7. Given a function f x 4 x 1 x 1 . Find E) 3 f 5 1 1 3 D) 8 E) 1 3 4 4 8. Find the derivative of the function: f x x - 2 1 1 1 2 A) B) C) D) x -1 2 x2 x x2 x 9. Given a function f x , find f 1 2 x 3 1 5 1 3 1 A) B) C) D) E) 6 8 3 8 2 10. Find the derivative of the function: f x ln 1 0.2 x 5 5 1 1 A) B) C) D) 5 x x 1 5x 55 x A) 4 B) 12 11. Find at the point x C) 13 6 the value of the derivative of the function E) E) 1 x2 1 x5 f x cos 3x 3 2 1 D) E) 4 2 2 3 12. Given a function f x 3 x 2 x 12 x 1 . Find the derivative f x A) -3 B) 0 A) 3 3x 2 8 x 2 B) 3 3x 2 8 x C) 3 3x 2 4 x 3x 2 4 x 2 2 E) 3x 4 x D) C) TEST No. ___ on the topic: “Application of the derivative” 1. What angle does the tangent to the graph of the function f x 1 x , drawn at the point x \u003d 3 A) form with the direction of the Ox axis C) 30º C) straight line D) obtuse E) 0º 3 2. Find the extremum points of the function xmax 0, xmin 3 V) D) no extremum Е) xmax no, xmin 3 1 at the point with abscissa x 0 1 x2 С) y 2 x 3 D) y 2 x 3 Е ) y x 2 3. Write the equation of the tangent to the graph of the function y A) y x 2 B) y 3 x 2 4. Find the speed of a point moving rectilinearly according to the law A) 36 cm / s B) 12 cm / s C) 24 cm / s D) 26 cm / s 5. Find the angle between the tangent to the graph of the function f x A) B) 3 C) 4 6. Examine the function for an extremum: 3 E) 4 2 2 f x x 7 x xt t 4 t 2 5 (cm) at time t 2c E) 28 cm/s 1 4 x at the point with abs cissus x0 1 and axis Ox 4 D) A) x 7, maximum point B) x 1, minimum point C) x 3.5, maximum point D) x 0, minimum point E) x 3, 5, minimum point 7. Find the smallest value of the function A) -2 B) C) f x 2 cos x cos 2x on the segment 0; D) 0 E) -3 x4 8 x 2 on the segment 1;2 4 3 3 3 A) 0;7 B) 0;28 C) 7 ;0 D) 32;7 E) 0;32 4 4 4 2 9. Find intervals of increasing function f x x 2 x 3 D) 1; E) 1;1 8. Find the smallest and smallest values of the function y 10. Find the equation of the tangent to the graph of the function f x x , which is parallel to the straight line given by the equation y x 5 1 С) y x 5 4 4 2 0, xmin 2 C) xmax 0, xmin 2 D) xmax 2, xmin 2 E) xmax 2, xmin 0 V) y x D) y x 1 2 E) y x 1
State Inspectorate for Supervision and Control in the Sphere of Education
Perm Territory
TEST ON algebra and the beginnings of analysis, grade 10
Topic: "Derivative of a function"
Target: Checking students' mastery of the topic "Derivative of a Function", the ability to apply the acquired knowledge to specific examples and problems of physics and geometry.
Difficulty level: base
Time to complete one test task: 1-4 min.
Work instructions
2 hours (120 minutes) are given to complete the work. The work contains 30 tasks with a choice of answers (one correct answer out of four proposed). The content checked by the tasks includes: the geometric meaning of the derivative, the physical meaning of the derivative, the table of derivatives, the study of a function using a derivative. With the help of tasks with a choice of answers, the basic level of preparation on the topic is checked.
It is forbidden to mark the correct answer in the test form. The selected answer must be marked on a separate answer sheet.
Complete the tasks in the order in which they are given. If a task is difficult for you, skip it. You can return to missed tasks if you have time.
One point is given for completing tasks. The points you get for completed tasks are summed up. Try to complete as many tasks as possible and score the most points.
We wish you success!
1. The derivative of the function is equal to:
1)12x 2 2) 12x 3)4x 2 4)12x 3
2. Specify the derivative of the function 
.
1) -5 2) 11 3) 6 4)6x
3. Determine the derivative of the function 
.
1)
2)
3)
4)
4. Find the derivative of a function 
.
1)
2)
3)
4)
5. The value of the derivative of the function is:
1)
2)
3)
4)
6. The value of the derivative of the function 
at the point X about =2
equals
:
1) 10 2) 12 3) 8 4) 6
7. Determine the derivative of the function 
.
1)
2)
3)
4)
8. Calculate the value of the derivative of the function 
at the point X about =
4.
1) 21 2) 24 3) 0 4) 3,5
9. The value of the derivative of the function
in
point 
equals:
1)
2
2)
3)
4
4)
10. Find the derivative of a function 
.
11. The root of the equation f ´(x)=0, if f(x)=(x-1)(x²+1)(x+1) is:
1)-1 2)1 3)±1 4)0
12. Solve the inequality f ´(x)>0 if f(x)=-x²-4x-2006
1) (-∞; -2) 2) (-2;+∞) 3) (-∞;2) 4) (2;+∞)
13. What angle does the tangent to the graph of the function y=x 2 -x form with the x-axis at the origin?
1)45° 2)135° 3)60° 4)115°
14. The equation of the tangent to the graph of the function y \u003d -1 / x, drawn at the point (1; 1), has the form;
y \u003d x 2) y \u003d - x-2 3) y \u003d x + 2 4) y \u003d -x + 2
15. Determine the slope of the tangent drawn to the graph of the function y \u003d sin2x at its point with abscissa 0.
2 2) 1 3)0 4) -1
16. The tangent of the slope of the tangent drawn to the graph of the function y \u003d 6x-2 / x at its point with the abscissa (-1) is:
1) -4 2) 1 3)0 4)-1
17. Indicate the interval on which the function f(x) =5x²-4x-7 only increases .
1)
(-1;+∞)
2)
3)
4)
(0;+∞)
18. The figure shows a graph of the function 
.
How many minimum points does the function have?
1) 4 2) 5 3) 2 4) 1
19. The maximum point of the function is:
1) -4 2) -2 3) 4 4) 2
20. How many critical points does a function have f(x)=2x³+x²+5?
1)
2
2)
1
3)
4
4)
3
21. The figure shows a graph of the derivative y=f ´(x).
Find the maximum point of the function y=f(x).
1) 1 2) 3 3) 2 4) -2
22. Minimum point of a function 
is equal to:
1
)
-2
2)
-0,5
3)
0,5
4)
2
23. The graph of the function y \u003d f (x) is shown in the figure. Specify the largest value of this function on the segment 
1) 2 2) 3 3) 4 4) 6
24. Determine the smallest value of a function 
on the segment 
25. Which of the functions increases on the entire coordinate line?
1)y=x³+x 2)y=x³-x 3)y=-x³+3 4)y=x²+1
26. Function y=4x²+ 23 on the segment [-2006; 2006] has the smallest value at x equal to...
2005 2)0 3) 23 4)2005
27. Indicate the maximum point of the function f(x) if f´ (x)=(x+6)(x-4)
5 2)6 3)-6 4)-5
28. The body moves in a straight line so that the distance S (in meters) from it to point B in this straight line changes according to the law S (t) \u003d 2t³-12t² + 7 (t-time of movement in seconds). After how many seconds after the start of motion, the acceleration of the body will be equal to 36 m/s²?
1) 3 2) 6 3)4 4)5
29. The body moves in a straight line so that the distance from the starting point changes according to the law S = 5t + 0.2t³-6 (m), where t is the time of movement in seconds. Find the speed of the body 5 seconds after the start of motion.
1)10 2) 18 3) 20 4)26
30. The straight line passing through the origin touches the graph of the function y=f(x) at the point (-2;10). Calculate f ´(-2).
1)-5 2)5 3)6 4)-6
Instructions for checking the test task.
For each correctly completed task, the student receives 1 point. The maximum number of points is 30. The score is determined based on the following indicators:
From 27 to 30 points - score "5"
From 22 to 26 points - score "4"
From 16 to 21 points - grade "3"
15 or less points - score "2"
Formanswers
Tests in algebra and the beginnings of analysis. Grade 10. To the textbook Kolmogorov A.N. and etc. Glazkov Yu.A., Varshavsky I.K., Gaiashvili M.Ya.
M.: 2010. - 112 p.
The collection contains 16 tests for the current and thematic control of students' knowledge in the course of algebra and the beginning of the analysis of the 10th grade. Each test is presented in 4 versions and contains multi-level tasks.
Estimated time to complete each test is 25-30 minutes. At the end of the collection are answers to all tasks. The collection also contains recommendations for scoring and marking.
The book is addressed to 10th grade mathematics teachers and schoolchildren for self-control of knowledge.
Format: pdf
The size: 2.3 MB
Watch, download: drive.google
CONTENT
Preface 7
Test 1. Definitions and properties of sine, cosine, tangent, cotangent, Radian measure of an angle. Table values 9
Option 1 9
Option 2 10
Option 3 11
Option 4 12
Test 2. Relations between trigonometric functions of the same angle. Application of basic trigonometric formulas to expression conversion 14
Option 1 14
Option 2 15
Option 3 16
Option 4 17
Test 3
Option 1 19
Option 2 20
Option 3 21
Option 4 22
Test 4. Converting the sum of trigonometric functions into a product, products into a sum. Converting trigonometric expressions 24
Option 1 24
Option 2 25
Option 3 27
Option 4 28
Test 5. Definitions and properties of trigonometric functions 30
Option 1 30
Option 2 31
Option 3 33
Option 4 34
Test 6. Basic properties of functions 36
Option 1 36
Option 2 37
Option 3 39
Option 4.41
Test 7. Inverse trigonometric functions. Trigonometric equations 43
Option 1 43
Option 2 44
Option 3 45
Option 4 47
Test 8. Trigonometric equations, inequalities and their systems 49
Option 1 49
Option 2 50
Option 3 52
Option 4 54
Test 9. The concept of a derivative. Rules for calculating derivatives 56
Option 1, 56
Option 2 57
Option 3 59
Option 4 60
Test 10. Derivative of a complex function. Derivatives of trigonometric functions 63
Option 1 63
Option 2 64
Option 3 65
Option 4 66
Test 11. Applications of continuity. Tangent to function graph 68
Option 1 68
Option 2 69
Option 3 71
Option 4 72
Test 12. Derivative in physics and technology 74
Option 1 74
Option 2 75
Option 3 77
Option 4 78
Test 13 Critical points, highs and lows 80
Option 1 80
Option 2 81
Option 3 83
Option 4 84
Test 14. Application of the derivative to the study of functions. Maximum and minimum function values 87
Option 1 87
Option 2 88
Option 3 89
Option 4 90
Test 15. Final repetition. Transformation of trigonometric expressions and solution of equations. Derivatives of trigonometric functions 92
Option 1 92
Option 2 93
Option 3 95
Option 4 96
Test 16
Option 1 98
Option 2 99
Option 3 100
Option 4 102
Answers 104
Control and measuring materials. Algebra and the beginning of analysis: Grade 10 / Comp. A.N. Rurukin. - M.: VAKO, 2011. - 112 p. - (Control and measuring materials).
The manual presents control and measuring materials (KIM) in algebra and the beginnings of analysis for grade 10: tests in the format of USE tasks, as well as independent and test papers on all topics studied. All questions are answered. The proposed material allows you to test knowledge using various forms of control.
The publication is aimed at teachers, schoolchildren and their parents.
Content
From the compiler ........................................ 3
Requirements for the level of preparation of students ............... 4
Assignment completion and assessment .............................. 4
Test 1. Function. Domain of definition and range of values of the function ............... 6
Test 2. Main properties of the function ............................. 8
Test 3. Graphs of functions............................................... .............ten
Test 4
Test 5
Test 6. Basic trigonometric identity. Casting Formulas...................18
Test 7. Functions y = sinx and y = cosx ....................................... ...20
Test 8. Functions y = tgx and y = ctgx .............................................. .....22
Test 9. Generalization of the topic "Trigonometric functions" ... 24
Test 10 Solution of the equations cosx = a and sinx = a ........... 28
Test 11 Solution of the equations tgx = a and ctgx = a......................30
Test 12
Test 13
Test 14
Test 15
Test 16
Test 17
Test 18
Test 19
Test 20 The sum of an infinite geometric progression ........ 52
Test 21 Definition of derivative.... 54
Test 22
Test 23
Test 24
Test 25
Test 26
Test 27