30. Solve the equation .

_А)

_B)

C)

D)

E)

4 Variant

1. , a, b, form an arithmetic sequence. Find .

1. 

2. 

3. 

4. 

2. is a geometric sequence with fourth term and tenth term . Find the seventh term.

3. is a geometric sequence with first term and common ratio . Find the general term.

1. 

2. 

3. 

4. 

5. 

4. is a geometric sequence such that b₃-b₄= and b₈-b₃= . Which one of the following can be the ratio?

3. 1

5. 2

5. Seven numbers are inserted between 16 and to form a monotone geometric sequence. Find the fourth term of this sequence.

1. 4

2. 2

6. , , are the three terms of a geometric sequence. Find the eighth term.

1. 

2. 

3. 

4. 

5. 

7. The numbers x-3, 3, y+5 form both an arithmetic and a geometric sequence. Find x-y.

1. 0

2. 2

3. 4

4. 8

5. 16

8. is given. What is ?

1. -7

2. 3

3. -2

4. 16

5. 20

9. and are given. What is

1. 

4. 21

5. 13

10.

A)

B)

3. 5

4. 8

5. 0

11.

1. 0

2. 1

3. -1

12.

1. 9

5. 0

13.

1. 6

2. -4

3. 2

4. 4

5. -6

14.

1. 0

2. 4

3. 12

4. 16

5. -4

15. 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

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

1. 0

2. 1

3. 2

4. 3

5. 4

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

1. 8

2. 4

3. 2

15. is given. Find the derivative of the function at the point .

1. does not exist

2. 0

3. 1

4. 2

5. 18

15. Find .

1. 

2. 

4. 

5. 

15. is given. Find .

1. 9

2. 3

5. 

15. is given. Find .

2. E

3. 

15. Find .

1. 

2. 

3. 

4. 

5. 

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

1. 20

2. 12

3. 6

4. -20

5. -30

15. Findthe domain of thefunction

1. (0;7

2. (0;7)

3. (3; -

4. (0;4)

5. (3;

15. 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)

15. Specify therange of the function .

1. [-3;1]

2. [3;1]

3. (2;1]

4. [-1;3]

5. (-1;2)

15. Specify therange of the function .

1. [-1;1]

2. [-1;7]

3. (7;1]

4. [-7;-1]

5. (-7;2)

15. Specify therange of the function .

1. [3;7]

2. [1;7]

3. (1;-1]

4. [-7;-1)

5. (-2;2)

15. Specify the greatest value of the function .

1. 3

2. 1

3. 4

4. 3

5. 2

5. Variant

1. Twelve numbers are inserted between 16 and 81 to form an arithmetic sequence. What is the sum of the twelve numbers?

1. 682

2. 679

3. 582

4. 579

5. 485

2. Given an arithmetic sequence with S_n=n(2n+7), find the general term.

1. 4n+3

2. 4n+5

3. 5n-4

4. 4n-13

5. 5n+13

3. 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

4. a terms are inserted between 1+a and a³+1 to form an arithmetic sequence. Find the common difference of the sequence.

1. a²+a

2. a²-a

3. -a²+a

4. a²-1

5. a-1

5. is an increasing arithmetic sequence with positive terms. The sum of a₆, a₇, and a₈ is 36 and the sum of the squares of these terms is 450. Find the nineteenth term.

1. 39

2. 42

3. 48

4. 49

5. 54

6. 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

7. Solve 1+x+x²+…=x+3

A)

B)

C)

D)

E)

8.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

9. 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 π

C) 9

D)

E) 6 -36

10. ABCDEFGH is a regular octagon with side length 4 units. Find the area of ABC

A) 8+4

B)4+4

C)16

D)6+8

E)6+8

11. 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

12.The radian 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

13. 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

14. 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