Tests on algebra and principles of analysis. 10th grade. To the textbook by A.N. Kolmogorov. etc. Glazkov Yu.A., Varshavsky I.K., Gaiashvili M.Ya.
M.: 2010. - 112 p.
The collection contains 16 tests for current and thematic control students' knowledge in the algebra course and began analysis of the 10th grade. Each test is presented in 4 versions and contains multi-level tasks.
The planned execution time for 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
Size: 2.3 MB
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CONTENT
Preface 7
Test 1. Definitions and properties of sine, cosine, tangent, cotangent, Radian measure of angle. Table values 9
Option 1 9
Option 2 10
Option 3 11
Option 4 12
Test 2. Relationships between trigonometric functions of the same angle. Application of basic trigonometric formulas to transforming expressions 14
Option 1 14
Option 2 15
Option 3 16
Option 4 17
Test 3. Formulas for reduction, addition, double angle 19
Option 1 19
Option 2 20
Option 3 21
Option 4 22
Test 4. Converting the sum of trigonometric functions into a product, product into a sum. Conversion 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 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 the graph of function 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. Sign of increasing (decreasing) function. Critical points, maximums and minimums 80
Option 1 80
Option 2 81
Option 3 83
Option 4 84
Test 14. Application of the derivative to the study of functions. The largest and smallest values of the function 87
Option 1 87
Option 2 88
Option 3 89
Option 4 90
Test 15. Final repetition. Converting trigonometric expressions and solving equations. Derivatives of trigonometric functions 92
Option 1 92
Option 2 93
Option 3 95
Option 4 96
Test 16. Final review of the algebra course and beginning of analysis for grade 10 98
Option 1 98
Option 2 99
Option 3 100
Option 4 102
Replies 104
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 3. Find the derivative of the function A) f x x 3 3x 3x 2 3 2 x 3 3x 1 2 x 1 3 B) x 2 3x 1 3 x 3x C) 2 1 3 x 3x D) 6 x 3 3x E) 2 x 3 3x 4. The function f x sin A) 2 8 B) 3 2 8 3 x , find f 2 2 C) 1 5. Find the derivative of the function f x log 2 A) 5 ln 2 5 x 1 B) 5 ln 2 2 C) 5x 1 ln 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. Given the function f x 4 1.5 x . Find f x A) 1.54 1.5 x 10 B) 1.54 1.5 x 9 C) 94 1.5 x 5 D) 6 4 1.5 x 9 E) 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 the TEST No. ___ on the topic: “Derivative” f x log 2 sin x 1. Find the derivative of the function 1 ctgx C) ctgx D) tanx E) ln 2 sin x 2. Derivative of the function f x ln ctg5x is equal to: 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 f x tgx ctgx 4 cos 2 x 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. Given the function f x tan 3x. Find f 0 A) B) ctgx A) 1 B) -1 5. The derivative of the function C) 2 f x 5 D) 4 ln x E) 0 is equal to ln 5 x ln x B) 5 ln 5 ln x C) 5 ln 5 5 ln x D) x ln 5 E) x A) 5 ln x 6. Given a function f x A) 2 B) 1 x2 3 C) 4 2x, find 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 the 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 make with the direction of the Ox axis, drawn at point x = 3 A) acute B) 30º C) straight D) obtuse E) 0º 3 2. Find the extremum points of the function A) f x 0.5x 4 2 x 3 xmax 3, xmin 0 xmax 0, xmin no C) xmax 0, xmin 3 B) D) no extremum E) xmax no, xmin 3 1 at the point with abscissa x 0 1 x2 C) y 2 x 3 D) y 2 x 3 E ) 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 its extremum: 3 E) 4 2 2 f x x 7 x xt t 4 t 2 5 (cm) at time t 2s E) 28 cm/s 1 4 x at the point with abscissa x0 1 and the Ox axis 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 the intervals of increase of the function f x x 2 x 3 A) 1; B) ;1 C) ;1 D) 1; x 5 1 C) y x 5 4 4 2 11. Find the extremum points of the function f x x 8 x 6 A) xmax 2, xmin 0 A) y x 5 V) xmax 0, xmin 2 C) xmax 0, xmin 2 D) xmax 2, xmin 2 E) xmax 2, xmin 0 B) y x D) y x 1 2 E) y x 1
Testing and measuring materials. Algebra and beginnings of analysis: 10th grade / Comp. A.N. Rurukin. - M.: VAKO, 2011. - 112 p. - (Testing and measuring materials).
The manual presents test and measurement materials (KIM) on algebra and the beginnings of analysis for grade 10: tests in the format of Unified State Examination tasks, as well as independent and tests on all topics studied. Answers are provided for all tasks. The proposed material allows you to test your knowledge using various shapes control.
The publication is aimed at teachers, schoolchildren and their parents.
Content
From the compiler........................................ 3
Requirements for the level of students' preparation ............... 4
Completing assignments and assessing them.................................... 4
Test 1. Function. Domain of definition and range of values of a function...... 6
Test 2. Basic properties of the function.................................... 8
Test 3. Function graphs.................................................... .............10
Test 4. Generalization of the topic “Numerical functions and their properties”....................................12
Test 5. Meanings of trigonometric expressions................16
Test 6. Basics trigonometric identity. Reduction 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. Arccosine and arcsine. Solving the equations cosx = a and sinx = a...........28
Test 11. Arctangent and arccotangent. Solving the equations tgx = a and ctgx = a...........30
Test 12. The simplest equations and inequalities..................................32
Test 13. Generalization of the topic “Trigonometric equations”..................................34
Test 14. Functions of sum and difference of arguments....................................38
Test 15. Double argument formulas.................................................40
Test 16. Converting sums of trigonometric functions into products.................................42
Test 17. Converting trigonometric expressions... 44
Test 18. Trigonometric equations, systems of equations, inequalities......46
Test 19. Generalization of the topic “Transformation of trigonometric expressions”................................48
Test 20. Consistency limit. Sum of an infinite geometric progression........52
Test 21. Function limit. Definition of derivative.... 54
Test 22. Calculation of derivatives...................................................56
Test 23. Equation of a tangent to the graph of a function......58
Test 24. Application of the derivative to study functions for monotonicity and extrema....60
Test 25. Using the derivative to find the largest and lowest values magnitudes....62
Test 26. Generalization of the topic “Derivative”................................................64
Test 27. Final according to the 10th grade program.................................68
