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Advanced Algebra: Final Exam Review - Equations, Inequalities, and Quadratic Functions, Exams of Calculus

Birla Institute of Technology and ScienceCalculus

A final exam review for advanced algebra, covering various topics such as solving equations, graphing quadratic functions, and working with inequalities. Students are expected to be able to solve equations in one variable and systems of equations, graph quadratic functions using completing the square, and identify the domain and range of functions. Additionally, they should be able to identify the solution to quadratic equations and describe the roots using the discriminant.

Typology: Exams

2012/2013

Uploaded on 01/31/2013

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bg1
Name:
Advanced Algebra: Final Exam Review
Solve the following equations.
1)
2x 5 3โˆ’=
2)
2 3x 2 3 7โˆ’+=
3)
2 x 5 14โˆ’ +=
4)
2 13
x
3 24
โˆ’=
5)
( ) ( )
6 2x 1 2 3 x 4โˆ’+=โˆ’ +
6)
7)
( ) ( )
3 5 2x 3 2 4 2x 3โˆ’ +=โˆ’ +
8)
( )
1
5x 1 2x 6
2
โˆ’=โˆ’ +
9)
( )
2
x 2 9x 12
3
+= โˆ’
Solve and graph each inequality.
10)
3x 2 5โˆ’<
11)
2x 4 8+โ‰ฅ
12)
2x 3 1+<
13)
3y 2 10โˆ’ +โ‰ฅ
14)
( )
3 2x 3 4x 4x 1+โˆ’ < +
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Advanced Algebra: Final Exam Review - Equations, Inequalities, and Quadratic Functions and more Exams Calculus in PDF only on Docsity!

Name:

Advanced Algebra: Final Exam Review

Solve the following equations.

  1. (^) 2x โˆ’ 5 = 3 2) (^) 2 3x โˆ’ 2 + 3 = 7 3) (^) โˆ’2 x + 5 = 14

x 3 2 4

  1. (^) 6 2x( โˆ’ (^1) ) + 2 = โˆ’ 3 x( + (^4) ) 6) (^1 ) x 3 4 5
  1. (^) 3 5( โˆ’ 2x (^) ) + 3 = 2 โˆ’ 4 2x( + (^3) ) 8) ( ) 5x 1 1 2x 6 2

( ) x 2 2 9x 12 3

Solve and graph each inequality.

  1. (^) 3x โˆ’ 2 < 5 11) (^) 2x + 4 โ‰ฅ 8 12) 2x + 3 < 1

  2. โˆ’3y + 2 โ‰ฅ 10 14) (^) 3 2x( + (^3) ) โˆ’ 4x < 4x + 1

  1. (^) Given g x( ) = (^) ( 3x + (^1) ) 2 โˆ’ 5, find g (^) ( โˆ’2 .)

  2. (^) Given f (^) ( x (^) ) = x^2 โˆ’ 3x +2, find f (^) ( 4 .)

  3. State the domain and range of the following relation. Is the relation a function?

{ ( โˆ’1,3 , 5,^ ) ( โˆ’^ 2 ,) (^ โˆ’1, 6 , 7, 4) ( )}

Domain___________________ Range_____________________ YES or NO

Write an equation of a line in slope intercept form that has the following conditions.

  1. (^) Passes through the points (^) ( 5,8) and (^) ( โˆ’1, โˆ’ (^2) )

  2. (^) Passes through the points (^) ( 6, โˆ’ (^2) )and (^) ( 4, โˆ’ (^2) )

  3. (^) Passes through the point (^) ( 1, โˆ’ (^5) )and is parallel to the line 2x โˆ’ 3y = 1

Solve by graphing:

y x 1 x y 4 x 5

  1. (^) Graph using slope-intercept form: 4x โˆ’ 6y = 12

Solve the system of equations using substitution method.

  1. y 4x 2x y 2
  1. x 3y 7 2x 7y 12

Solve the system of equations using elimination method.

  1. (^) 2x 5y 14 3x 2y 17
  1. (^) 4x 3y 2 3x 5y 7

Solve the system of equations.

  1. (^) 2x y 3z 7 x 2z 3 3x 2y 2z 5
  1. (^) x y z 5 3x y 2z 1 4x 2y 3z 10

Write the equation that represents the function.

  1. ๐‘‰๐‘’๐‘Ÿ๐‘ก๐‘’๐‘ฅ ( 1 , โˆ’ 9 ); ๐‘…๐‘œ๐‘œ๐‘ก๐‘  ๐‘ฅ = โˆ’ 2 , 4 35) ๐‘‰๐‘’๐‘Ÿ๐‘ก๐‘’๐‘ฅ ( 0 , โˆ’ 1 ); ๐‘…๐‘œ๐‘œ๐‘ก๐‘  ๐‘ฅ = โˆ’ 1 , 1

State the domain of the function.

Simplify.

  1. 3 2 7 5 3

12x y z 8x y z

โˆ’ โˆ’

39) ( โˆ’3x y 2 3 ) (^3 2x y 2 ) 40) ( )

2 3 3 2 0 2

2x y 4x โˆ’y

41) ( 6x 2 + 3x โˆ’ 5 ) โˆ’ ( 4x 2 โˆ’ 7x + 3 ) 42) 24 + 4 27 โˆ’ 3 48 43) 2

Multiply.

58) ( 2y โˆ’ 4 )^2 59) ( 3 + 2 i )^2 60) ( x โˆ’ 3 ) ( x 2 โˆ’ 5x + 2 )

Use synthetic division to divide.

61) ( 4x 4 โˆ’ 3x 3 โˆ’ 8x 2 โˆ’ 3 ) รท ( x โˆ’ 2 )

Use the discriminant to describe the roots of the equation.

  1. (^) 2x 2 โˆ’ x โˆ’ 4 = 0

Solve.

  1. (^) 5x โˆ’ 1 = 2x + 21 64) (^3) 2x + 1 + 6 = 3 65) (^) 3x โˆ’ 1 โˆ’ 2 = 3

  2. (^3) + x = 2 67) (^) 3x 2 + 36 = 0 68) (^) x 2 โˆ’ 7x โˆ’ 18 = 0

  1. (^) 2x 2 โˆ’ 4x = 3 70) (^) 24x 2 โˆ’ 15 =2x

Solve the inequality.

  1. (^) x 2 โˆ’ 6x โˆ’ 16 โ‰ค 0 72) (^) 6x 2 +13x โˆ’ 5 > 0

Graph the following quadratic functions. Use completing the square when necessary.

  1. (^) y = 3x 2 โˆ’ 6x + 1 74) (^) y = โˆ’ x 2 โˆ’ 1

Graph the following quadratic inequalities. Use completing the square when

necessary.

  1. (^) y > 2 x( + (^4) )^2 โˆ’ 3 76) (^) y โ‰ค โˆ’ 4x 2 + 16x โˆ’ 11

  1. ๐‘ฆ = (๐‘ฅ โˆ’ 1)^2 โˆ’ 9

  2. ๐‘ฆ = ๐‘ฅ 2 โˆ’ 1

  3. [1, โˆž)

  4. (โˆ’โˆž, 2]

3 4 2

3y 2x z

  1. โˆ’54x y^8

x^10 y^9 2

  1. 2x 2 +10x โˆ’ 8

  2. 2 6

  3. 2 5 5

  4. 28 7 3 13

  1. (^11) + 10 i

  2. 2xy z^3 2 3 5xy^2

  3. 2xy z^3 2 4 x z^3

  4. 56 6

  5. 27

  6. 18 13 17

  • i

52) ( 2x โˆ’ 5 )( x + 3 )

53) ( x โˆ’ 2 ) ( x 2 + 2x + 4 )

54) ( 7x โˆ’ 5 )( 7x + 5 )

55) ( 4x + 3 ) ( 16x 2 โˆ’12x + 9 )

56) ( 5x + 3 )( 2x โˆ’ 7 )

57) ( 4x โˆ’ 9 )( 4x + 9 )

  1. 4y 2 โˆ’16y + 16

  2. (^5) + 12 i

  3. x^3 โˆ’ 8x 2 +17x โˆ’ 6

  4. 4x 3 5x 2 2x 4 5 x 2

  1. 2 real roots

  2. x 22 3

  1. (^) x = โˆ’ 14
  2. x 26 3

  1. no solution

  2. ยฑ 2 i 3

  3. x = 9, โˆ’ 2

  4. x 2 10 2

=^ ยฑ

  1. x 5 ,^3 6 4

71) [ โˆ’2,8]