11 ALGEBRA

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Университет имени Сулеймана Демиреля

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2. x2 dx =?

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CHAPTER REVIEW TEST 1B

1. f (x)= d(x+1) and f(1) = 2 are given. What is f(2)?

A) 0

B) 1

C) 2

D) 3

E) –2

+4x2 3x

dx =?

+4x 3+ c

+4x 3 ln

+ c

4x3

3x2

4 +

+ c

D) x+4

+ c

E) x3 +4x2 3x

3.	f (x)		dx = x	3	+4x	2	+5x – 1 is given.
3.	x	2	dx = x		+4x		+5x – 1 is given.
	x
What is f(1)?
A) –7			B) 3				C) –2	D) 16	E) 20

4. (x2 +4x)5 (x+2) dx =?

A)	(x2 +4x)6		+ c				B)	(x2 +4x)6			+ c
A)	6		+ c				B)	12			+ c
	6							12
C)	(x2 +4x)6		+ c				D)	2x+4		+ c
	3							6
		x3			2	6	x2
			3	+ x				+ x
	E)		3				2		+ c
	E)					6			+ c
						6

dx =?

+ c

B) ñx + c

+ c

x x

+ c

6. sin3x dx =?
A) cos 3x + c			B)	1	sin3x + c
				3
C) –	1	cos 3x + c	D) sin 3x + c

3
			E) 0

7. xsin x dx =?
A) x cos x + sin x + c	B) x cos x – sin x + c
C) x2 cosx + x sin x + c	D) –xcosx + sinx + c

E) x cos x – sin x + c

8. ex cos x dx =?

A) ex (cos x+sin x)+ c 2

B) x arccos x + 1 x2 + c

C)arccosx + x arccos x + c

D)sec 2x + c

E) x arccos x + 1+ x2 + c

Chapter Review Test 1B

9. sin3 x cos5 x dx =?

A) 15sin2xcos4 x + c

B) 8sin2x + 8cos4x + c

sin4 x

cos5

+ c

cos8 x

cos6

+ c

sin7

sin5

+ c

10. sin2x cos4x dx=?

A)cos2x cos6x + c 4 12

B)sin2x cos6x + c 12

C)sin2 2x + cos4 4x + c 2 4

D)	sin6x	cos2x	+ c
	6	2
E)	cos2x 2sin4x			+ c
		4

11. x2 f (x) dx 5x4 + 2x2 – 1 is given. What is f(x)?

A) 20x +			4		B) 20x3 + 4x + c
			x
C)	5x3	– 2x + c			D) 5x2 + 2 + c
	3
			E)	2	+ 5x + c
				x

12.		3	dx =?

	1	9x2

A) arcsin x + c				B) arccos x + c
C) arcsin 3x + c				D) arctan 3x + c
			E) arccos 3x + c

13.

1– cos x

dx ?

sin

2tan x

+ c

tan x

+ c

2tan

+2sin

+ c

D) sin x + cos x + c

E) sin

+cos

+ c

14.cos(cos x) sin2x dx=?

A)cos x + c

B)sin(cos x) + cos(sin x) + c

C)sin x + c

D)sin(cos x) +cos(sin x) + c

E)–2(cos(cos x) + cos x sin(cos x)) + c

80	Algebra 11

CHAPTER REVIEW TEST 1C

1.In the figure, A, B and C are areas such that A = 3 unit2, B = 6 unit2, and C = 5 unit2.

What is f (x) dx?

a	B	b	x

A) 27

B) 14

C) 4

D) 2

E) 8

3.	/ 2 sin x dx =?
	0
	A) 0	B) 1	C) –1	D)	1	E)	3
	A) 0	B) 1	C) –1	D)	2	E)	2
					2		2

4.		d	7	(4x2
		d			+3x – 4) dx	=?
					+3x – 4) dx	=?
		dx 2
	A) –5			B) 3 C) 3x – 4 D)			1	E) 0
	A) –5			B) 3 C) 3x – 4 D)			x – 2	E) 0

3
5. x3	dx =?
0
A) 9	B)	9	C)	81	D)	17		E) 0
A) 9	B)	2	C)	4	D)		3	E) 0
		2		4			3

6. (2x+1)(x2 + x – 4) dx=?

0
A) 6	B) –4	C) 2	D) 4	E) –6

7.	/ 6 sin2x dx =?
	0
	A) 1	B) 0	C) –	1	D)	3	E)	1
	A) 1	B) 0	C) –	2	D)	2	E)	4
				2		2		4

2
8. (3x 1)2	dx =?
1
A) 13	B)	7	C)	17	D)	31	E)	321
		6		3		3		5

3		1
9.		1	dx =?

		3
1	(2x 1)
A)		2	B)	6	C)	1	D)	1	E)		7
A)			B)	6	C)	7	D)	25	E)	125
		13	25			7		25		125

	x2
10. F(x)= cos(3t) dt is given. What is F (0)?
	3
A) 0	B) 1	C)	1	D)	2	E)	1
A) 0	B) 1	C)	3	D)	2	E)	4
			3		2		4

Chapter Review Test 1C

CHAPTER REVIEW TEST 1D

1.y

In the figure, f (x)

dx =18 and f(x) dx=10.

What is the total area of the shaded region?

A) 28

B) 8

C) 10

D) 12

E) 26

(3x2 4x) dx = ?

A) 0

B) 4

C) 12

D) 16

E) –4

/ 2 cos x sin x dx = ?

/ 4

C) 1

E) 0

4. (x+2)

dx 10 and a – b = 2. What is a?

A) 2

B) –6

C) –4

D) 5

E) 6

(sin x+cos x) dx ?

A) 0

B) 1

C) 2

D) 4

E) –1

7. / 3 sin3 x cos3 x dx=?

0
A)	17	B)		9	C)		58
A)	43	B)	128		C)	161
	43		128			161

/ 4

8.cos xsin3 x dx =?

0
A) 0	B) 1	C)		1
A) 0	B) 1	C)	16
			16

D)	7	E)	128
	4		5

D)	1	E) –1
	2

D)	1	E)	1
	4		2

9. What is	the mean		value	of	the	function
f(x) = 2x2 +1 on the interval [0, 5]?
A) 27	B) 48	C)	53	D)	62	E)	17
4	5		3		7		5

10. What is the mean value of the function f(x) = cos x

on the interval				,		?
on the interval			4	,	2	?
			4		2
A) 0				B)		2			C)	1 3	2
A) 0				B)		2			C)
						2
D)	4 2	2					E)		(1 2)
								4

82	Algebra 11

CHAPTER REVIEW TEST 1E

1. y

–3	–1		3	6	x

		O
		O

In the figure, f (x) dx =12 cm2 and

f (x) dx = 5 cm2.

What is the total area of the shaded region in cm2?

A) 7

B) 12

C) 17

D) 19

E) 21

2.What is the area of the region bounded by the graphs of y = 2x – 3, the x-axis, and the lines x = 2 and x = 4?

A) 6

B) 9

C) 10

D) 16

E) 21

3.What is the area of the region bounded by the graphs of y = –x + 5, the x-axis, and the lines x = 3 and x = 5?

A) 27

B) 13

C) 7

D) 3

E) 2

4.What is the area of the region bounded by the graph of y = x2 – 9 and the x-axis?

A) 27

B) 36

C) 28

D) 40

E) 49

5.What is the area of the region bounded by the graphs of y = x2 – 3x + 2, the x-axis, and the lines x = 1 and x = 3?

A)	1	B)	5	C) 1	D)		7	E)	21
	6		6			12
									5

6.What is the area of the region bounded by the graph of y = x3, the y-axis, and the line y = 8?

A) 12	B)	8	C)	16		D) 8	E) 17
		3			3

7.What is the area of the region bounded by the graph of y = x2 – 7x + 10 and the line y = x + 3?

A) 33

B) 27

C) 18

D) 36

E) 42

8.What is the area of the region bounded the graphs of y = x2 – x + 1 and y = –x2 + 2x + 3?

A)	146		B)	68	C)	125		D)	17		E) 49
		7					24			2
				3

Chapter Review Test 1E

9.What is the area of the region bounded by the graph of y = sin 2x and the x-axis on the interval [0, ]?

A) 2

B) 4

C) 5

D) 3

E) 4

10.What is the area of the region bounded by the graph of y = 3x – 4, the y-axis, and the lines y = 1 and y = 4?

A)	7	B)	13		C)	8	D)	43	E) 10
	3			2		5		7

11.What is the volume of the solid figure generated by rotating the area between y = x and the x-axis around the x-axis on the interval [0, 3]?

A)		B) 27	C)	27	D) 27	E) 9
	3			2

12.What is the volume of the solid figure generated by rotating the area between y = x2 + 1, the x-axis, and the lines x = 0 and x = 1 around the x-axis?

A)	B)	19	C) 4	D)	28	E)	17
		2			15		3

13. What is the volume of the solid figure generated by rotating the area between the graphs of y = x2 + 2 and y = 3 around the x-axis?

A)	27		B)	104		C)	48
	5	163		15			5

	D)				E)	32
		15				3

14. What is the volume of the solid figure generated by rotating the area between the graphs of y = 3x + 2 and y = x + 8 around the x-axis on the interval [0, 1]?

A) 65		B) 27		C)	178
					3
	147		63
D)		E)
	3		3

15. What is the volume of the solid figure generated by rotating the area of the region between y = 3x – 1, the y-axis, and the lines y = 1 and y = 2 around the y-axis ?

A)	19				B)				C)	47
		27				3				9
				17				2
			D)				E)
				5				3

16.What is the volume of the solid figure generated by rotating the area of the region between the graph of y = 2x – 1 and the x-axis through 180° on the interval [0, 2]?

A)	21			B)	21	C)	14
	3		7		4		3

		D)				E) 5
			3

84	Algebra 11

CHAPTER REVIEW TEST 1F

1.What is the area of the region bounded by the graphs of y = 3x – 1 and the lines x = 0 and y = 2?

A)	3	B)	3	C) 2	D) 1	E)	7
	7		2	3			3

2.What is the area of the region bounded by the graph of y = 3x2 + 4, the x-axis, and the lines x = 1 and x = 3?

A) 34

B) 29

C) 21

D) 16

E) 9

3.The figure shows the graph of f(x) = x2.

Given 2S1 = S2, find a.

	S2
	S1	x
	a 3	x
	a 3

A) 2 B) 23 2

C) 3 9

D) 3 8

E) 13

4.What is the area of the region bounded by the graph of y = 5x + 1 and the x and y-axes?

A) 1

B) 3

C) 0.3

D) 0.2

E) 0.1

5.What is the area of the region bounded by the graphs of y = 2x + 1 and y = 5 – 2x and the x-axis?

A)	1	B)	5	C)	9	D)		7	E)	21
	6		6		2		12			5

6.What is the area of the region bounded by the graph of y = x3 – 4x and the x-axis?

A) 12	B)	8	C)	16	D) 8	E) 16
		3	3

7.What is the area of the region between the graphs of y = x2 – 6x and y = –9 and the y-axis?

A) 32

B) 27

C) 18

D) 9

E) 4

8.What is the area of the region between the graphs of y = x2 – x + 1 and y = –x2 – 4x + 3?

A)	145	B)	125	C)	127		D)	17		E) 49
						25			2
8		24

Chapter Review Test 1F

9.What is the area of the region bounded by the graphs of y = cos 2x and x = and the x-axis?

A) 2

B) 4

C) 5

D) 3

E) 4

10.What is the area of the region bounded by the graphs of y = cos2x and y = sinx on the interval [0, ]?

A) 3ñ3 – 2	B) ñ3 – 2	C) 12 – 2
D) 6ñ3 + 2	E) 6ñ3 – 2

11.What is the area of the region bounded by the graphs of x = y2 + 1, y-axis, y = 1 and y = 3?

A)	17		B)	32	C) 9	D)	28	E)	17
		3					3			6
				3

12.What is the volume of the solid generated by rotating the area between the graphs of y = 3x – 1, x = 2 and x = 3 around the x-axis?

A)	27	B) 16	C) 22	D) 42	E) 43
	5

13.What is the volume of the solid figure generated by rotating the area between y = x2 – 2x and the x-axis around the x-axis ?

A) 2	B)	19	C) 7	D)	28	E)	16
		3			15		15

14.What is the volume of the solid figure generated by rotating the area between the graphs of y = 5x – 1, x = 1, x = 2 and the x-axis around the y-axis?.

A)	35		B) 27		C)	71
	3					3

	D)	147	E)	63
		3		2

15. What is the volume of the solid figure generated by rotating the area between the graphs of y = x2 – 3x – 4, x = 2, x = 5 and the x-axis around the x-axis?

A)	197	B)	28	C)	441	D)	17	E)	2
27			3		10		3		3

16. What is the volume of the solid figure generated by rotating the area between the graphs of y = 2x – 1 , x = 1, x = 2 and the x-axis through 180° around y-axis?

A)	64	B)	41	C)	14	D)	96	E) 5
	3		12		5		5

86	Algebra 11

CHAPTER 2

A. RADICAL EXPRESSIONS

				1. nth Root of a Number
				Up to now we have studied exponential expressions of the form an, where n is any integer
				and a is a real number. We have learned how to evaluate numbers like 24, 3–5 and 90. But what
				do expressions such as 31/2 and 82/3 mean? In this section we will extend our study of
				exponents to include rational exponents. But before doing this, we need to understand the
				concept of nth root.
				Square roots are a special case of nth roots for n = 2. More generally, the nth root of a is the
				number which gives a as a result when it is raised to the nth power.

				principal nth root
	Definition			principal nth root
	Definition
				Let a and b be real numbers, and let n be a natural number different from 1 such that bn = a.
				n
				Then b is called the principal nth root of a, denoted by b = ña.
				For example,
				2 9 3 (‘3 is the square root of 9’) since 32 = 9.
				3 8 2 (‘–2 is the cubic root of –8’) since (–2)3 = –8.
				4 625 5 (‘5 is the fourth root of 625’) since 54 = 625.
				5 243 3 since 35 = 243.
				6 64 since there is no real number whose sixth power is negative.

Note

1.An even root is always non-negative, but there is no restriction for an odd root.

2.An even root of a negative number is undefined, but an odd root is defined for any number.


Definition	radical expression, radicand, index
Definition
		n
	A radical expression is an expression of the form ña. a is called the radicand and n is called
			2
	the index. We do not write the index for square roots: ña =ña.
	index	n
	index	n
		ña		radicand
				radicand

radical sign

88	Algebra 11

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