М. Өтемісов атындағы Батыс Қазақстан мемлекеттік университеті

Факультет: Физика-математикалық

Кафедра: Физика және математика

Шифр, мамандық: 5В010900- Математика

Пәні:

1 Variant

1. Find the interval on which = is decreasing.

1. ( ,3)

2. (-3,3)

3. (3, )

4. (0, )

5. (-

2. What are the solutions of the equation + 2x = 24?

1. 2 and 12

2. 4 and -6

3. 4 and -4

4. 4and 8

5. 5

is given. Find the value of the limit .

1. 2

2. 3

3. 4

4. 5x+1

5. 

Is given. Find the value of the limit .

1. 0

2. 1

3. e

4. e-1

5. e+1

5. Find the slope of tangent line to the curve at the point x=1.

1. 4

2. 5

3. 6

4. 10

5. 15

6. Find the equation of tangent line to the function at the point .

1. y=1

2. y=2

3. y=-4

4. y=x-2

5. y=-1

6. Specify therange of the function .

1. [-3;1]

2. [3;1]

3. (2;1]

4. [-1;3]

5. (-1;2)

6. Specify therange of the function .

1. [-1;1]

2. [-1;7]

3. (7;1]

4. [-7;-1]

5. (-7;2)

6. Specify therange of the function .

1. [3;7]

2. [1;7]

3. (1;-1]

4. [-7;-1)

5. (-2;2)

is given. Find .

1. 

2. 

3. 

4. 

5. 

11. Find

1. 

2. 

3. 

4. 

5. 

12. Find the derivative of the function

1. 

2. 

3. 

4. 

5. 

13. Findthe domain of thefunction

1. (0;7

2. (0;7)

3. (3; -

4. (0;4)

5. (3;

14. Solve an equation

1. 1

2. 2

3. 3

4. 4

5. 5

15. Find the range of the function

1. (2.5; ]

2. [2.75;

3. (-

4. [1.5;

5. (1.5;2.75)

is given. Find .

1. 

2. 

3. 

4. 

5. 

17. Given that and , find .

1. 3

2. 6

3. 15

4. 18

5. 20

is given. Find the value of the expression .

1. 10

2. 12

3. 14

4. 16

5. 18

19. is an arithmetic sequence such that a₃+a₄=23 and a₅+a₄=37. Find a₅.

A) 49

B) 47

C) 45

D) 44

E) 22

20. is an arithmetic sequence with first term , last term , and sum 9. How many terms are there in this sequence?

A) 9

B) 16

C) 32

D) 48

E) 64

21. In a triangle ∆ABC, a=12 cm, b=8 cm and h_a =6cm. Find the length of h_a.

A)4cm

B) 6cm

C)8cm

D)9cm

E)12cm

22. ABCD is a rectangle and ∆ABE is an equilateral triangle such that E lies on CD. The height of the equilateral triangle is 12 units. Find the area of the region between the equilateral triangle and the rectangle.

A) 24

B)36

C)23

D)48

E)

23. A triangle has sides of length 18, 12 and 10 units. Find the height to its shortest side.

A) 8

B)12

C)

D)

E)

24. Solve the equation .

А)

_B)

C)

D)

E)

25. Simplify the expression .

_A)

B)0

C)

D)

E) 1

26. Simplify the expression

A) 0.5

B)sin-6

C) 1

D)0

E)cos6

27. What is the primitive of the function f(x)=3cosx-4sinx?

1. 3sinx+4cosx+c

2. 3sinx-4cosx+c

3. -3sinx-4cosx+c

4. -3sinx+4cosx+c

5. -2sin2x+c

28. 

1. 

2. 

3. 

4. 

28. 

1. 

2. 

3. 

4. 

5. 

28. 

1. 

2. 

3. 

4. 

5. 

Control work

2. variant

1. Solve an equation

1. 2

2. 9

3. 1

4. 4

5. 5

2. Simplify an expression

1. 0

2. 2

3. 4

4. 1

5. 3

3. is given. Find .

1. 

2. 

3. 

4. 

5. 

4. and are given. Find the value of a.

1. 3

2. 4

3. 7

4. 11

5. 29

5. and are given. Find the derivative of .

1. 

2. 

3. 

4. 

5. 

6. is given. Find .

1. 0

2. 1

3. 2

4. 3

5. Does not exist

7.Specify the greatest value of the function .

1. 3

2. 1

3. 4

4. 3

5. 2

8. Solve the equation .

1. ,

2. 

3. 

4. 

5. _{правльный е}

9.Solve the equation .

1. 

2. 

3. 

4. 

5. ,

If the parametric function is given by the equations , , find .

1. 0

2. 1

3. -1

4. 

5. 

11. The implicit is given. Find .

1. 

2. 

3. 

4. 

5. 

12. is given. Find .

1. 

2. 

3. 

4. 

5. 

13. Findthe domain of thefunction

1. (0;7

2. (0;7)

3. (3; -

4. (0;4)

5. (3;

14. Solve an equation

1. 1

2. 2

3. 3

4. 4

5. 5

15. Find the range of the function

1. (2.5; ]

2. [2.75;

3. (-

4. [1.5;

5. (1.5;2.75)

If the curve is tangent to the straight line with the equation , then find the value of a.

1. 5

2. 4

3. 3

4. 2

5. 1

17. If , then find the value of the expression .

1. 0

2. 1

3. 2

4. 3

5. 4

18. Find the shortest distance between the curve and the origin (0,0).

1. 8

2. 4

3. 2

4. 

5. 

19. Which terms can be the general term of a sequence?

I. II. 3 III. IV. V. VI.

A) I,II,III,IV

B) II, III, IV, VI

C) I, II, III, VI

D) II, III, V, VI

E) III, IV, V, VI

20. Which of the can be the general term of the sequence with the first four terms 3, 5, 7, 9?

A) 2n-1

B) 2n

C) 2n+1

D) n+1

E) n²+2

21. Given a₁=2 and for , find a₁₁?

A) 27

B) 25

C) 22

D)

E)

22. is an arithmetic sequence with a₁₁=8 and a₂₀=35. Find a_3.

A) -3

B) -6

C) -16

D) -22

E) -28

23. In a triangle ∆ABC, a=12 cm, b=8 cm and h_a =6cm. Find the length of h_a.

A)4cm

B) 6cm

C)8cm

D)9cm

E)12cm

24. The medians of a triangle are 3, 4 and 5 units long. Find the area of this triangle.

A) 6

B) 7

C) 8

D) 9

E) 12

25. One side of a square measures 6 units. Find the area of the region between theinscribed and circumscribed circles of this square.

A) 6

B) 8 π

C) 9

D)

E) 6 -36

26. Calculate .

A) 1

B) 0

C)

D)

_E)

27.

1. 

2. 

3. 5

4. 8

5. 0

28.

1. 9

2. 

3. 

4. 

5. 0

29.

1. 6

2. -4

3. 2

4. 4

5. -6

30.

1. 0

2. 4

3. 12

4. 16

5. -4

3 variant

1. Find .

1. 

2. 

3. 

4. 

5. 

2. is given. Find .

1. 1

2. 4

3. Which one of the following is correct for the tangent lines to the curve at the points x=a and x=-a?

1. They are perpendicular to each other.

2. They are parallel to each other.

3. The angle between them is .

4. They are parallel to x-axis.

5. They are parallel to y-axis.

4. is given. Find .

1. 

2. 

3. 

5. 

5. is given. Find the derivative of order n.

1. 

2. 

3. 

4. 

5. 

6. The tangent line to the curve at the point A(2,8) intersects the curve at another point B( ). Find .

1. 

2. 

3. -3

4. -4

5. -5

7. If the parametric curve is given by the equations , , find .

1. е

2. 2e

3. 

4. 

8. The implicit function is given. Find .

1. 1

2. 

3. 

4. 

5. 

9. Simplify an expression

1. 0

2. 2

3. 4

4. 1

5. -2

10. Findthe domain of thefunction

1. (0;7

2. (0;7)

3. (3; -

4. (0;4)

5. (3;

11. Solve an equation

1. 1

2. 2

3. 3

4. 4

5. 5

12. If f(x)= then what is f’(2)?

1. 1

2. 3

3. 

4. 

5. 5

13. 

1. 

2. 

3. 3

4. 6x-4+c

14. What is the primitive of the function

f(x)=

1. 

2. 

3. 

4. 

5. 5

15. 

1. 0

2. 1

3. -1

5. 

1. 9

5. 0

17. Simplify the expression .

_A)

B)0

C)

D)

E) 1

18. Simplify the expression

A) 0.5

B)sin-6

C) 1

D)0

E)cos6

19. Calculate .

A) 1

B) 0

C)

D)

E)

20. is an arithmetic sequence such that S₁₃=195 and a₁₃-a₁₁=24. Find a_1.

A) 2

B) 3

C) 4

D) 5

E) 6

21. is an arithmetic sequence such that a₃+a₄=23 and a₅+a₄=37. Find a₅.

A) 49

B) 47

C) 45

D) 44

E) 22

22. The roots of the equation 3x³+9x²+2x-a=0 form an arithmetic sequence. Find a.

1. -4

2. -2

3. -1

4. 2

5. 4

23. Solve 1+x+x²+…=x+3

1. 

2. 

3. 

4. 

5. 

24. is an arithmetic sequence with and . The sum of the first seven terms is 7. Find .

1. -3

2. -1

3. 0

4. 2

5. 4

25. One side of a regular hexagon measures 14 units. Find the area of this hexagon.

A)196

B)294

C)196

D)294

E)149

26.The radn of the circumscribed and inscribed circles of a regular polygon are 6 and 3 units respectivery. Find the area of this polygon.

A)54

B)36

C)72

D)18

E)96

27. a circle has circumference 18 cm. Findb its area.

A)81 cm²

B)36 cm²

C)81 cm²

D)324 cm²

E)162 cm²

28. one side of a square measures 6 units. Find the area of the region between the inscribed and circumscribed circles of this square.

A)6

B)8

C)9

D)10 /3

E)6 -36

29. The medians of a triangle are 3,4 and 5 units long. Find the area of this triangle.

A)6

B)7

C)8

D)9

E)12