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Beginning of the Semester Review Sheet - College Algebra | MATH 1021, Study notes of Algebra

Material Type: Notes; Professor: Hamid; Class: COLLEGE ALGEBRA; Subject: Mathematics; University: Temple University; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 09/17/2009

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Math 1021 โ€“ Beginning of the Semester Review
In 1 โ€“ 3, fill in the blanks to make each statement true.
1. The property abba +=
+
is called the _________________ of addition, and
is called the __________________ property.
() (
cbacba ++=++
)
2. The additive inverse of is __________, and the multiplicative inverse of is
______. 3โˆ’3/1
3. The additive inverse of 0 is __________, that is,
=
โˆ’
0__________; the multiplicative
inverse of 1 is __________, that is,
=
โˆ’1
1__________.
Evaluate each expression in 4 โ€“ 5.
4. (a)
()
()(
[]
24126 348 โˆ’รท+รท
)
)
)
(b)
()
[]
{}
24126 348 โˆ’รท+รท
(c)
[]
24126348 โˆ’รท+รท
(d)
24126348 โˆ’รท+โ‹…รท
5. (a)
()(
[]
339188 โ‹…รท+โ‹…
(b)
()
[]
339188 โ‹…รท+โ‹…
(c)
[]
339188 โ‹…รท+โ‹…
(d)
339188 โ‹…รท+โ‹…
In 6 โ€“ 9, fill in the blanks to make each statement true.
6. To compute when and are unequal and have opposite signs, we
_______________.
ba +ab
7. When there is a minus sign before parentheses, the parentheses can be removed by
___________ of each term inside the parentheses.
8. The subtraction is equal to the addition _________________.
ba โˆ’
9. The division is equal to the multiplication __________________.
ba /
In 10 โ€“ 15, evaluate each of the following.
10. 11.
(
27 โˆ’+โˆ’
(
)
44
โˆ’
+โˆ’ 12.
(
)
85
โˆ’
โˆ’
13.
()
83 โˆ’+
14.
()
15.
(
53 โˆ’โˆ’
)
6
24
โˆ’
1
pf3
pf4
pf5

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Math 1021 โ€“ Beginning of the Semester Review

In 1 โ€“ 3, fill in the blanks to make each statement true.

  1. The property a + b = b + a is called the _________________ of addition, and

( a + b ) + c = a +( b + c )is called the __________________ property.

  1. The additive inverse of is __________, and the multiplicative inverse of is ______.
  1. The additive inverse of 0 is __________, that is, โˆ’ 0 =__________; the multiplicative inverse of 1 is __________, that is, 1 โˆ’ 1 =__________.

Evaluate each expression in 4 โ€“ 5.

  1. (a) (^48 รท^3 )^ [(^6 +^12 )^ รท(^4 โˆ’^2 )]

(b) 48 รท{ 3 [ 6 + 12 รท( 4 โˆ’ 2 )]} (c) 48 รท 3 [ 6 + 12 รท 4 โˆ’ 2 ] (d) 48 รท 3 โ‹… 6 + 12 รท 4 โˆ’ 2

  1. (a) 8 โ‹…[( 18 + 9 ) รท( 3 โ‹… 3 ] (b) 8 โ‹…[ 18 + 9 รท( 3 โ‹… 3 )] (c) 8 โ‹…[ 18 + 9 รท 3 โ‹… 3 ] (d) 8 โ‹… 18 + 9 รท 3 โ‹… 3

In 6 โ€“ 9, fill in the blanks to make each statement true.

  1. To compute when and are unequal and have opposite signs, we _______________.

a + b a b

  1. When there is a minus sign before parentheses, the parentheses can be removed by ___________ of each term inside the parentheses.
  2. The subtraction a โˆ’ b is equal to the addition _________________.
  3. The division a / b is equal to the multiplication __________________.

In 10 โ€“ 15, evaluate each of the following.

14. (โˆ’^3 )^ (^ โˆ’^5 )^ 15.

In 16 โ€“ 20, express each of the following without parentheses or brackets.

16. โˆ’ ( โˆ’ x โˆ’ 7 ) 17. โˆ’ ( 6 โˆ’ y ) 18. โˆ’[ โˆ’( โˆ’ x ) โˆ’( โˆ’ y )]

19. (โˆ’ 4 ) b 20. [ โˆ’ ( โˆ’ 5 )]( โˆ’ y )

  1. Express each of the following as a product of a power of 2 by a power of 3. (a) 2 3 โ‹… 32 โ‹… 6 (b) 4 โ‹… 6 โ‹… 12 โ‹… 6 (c) 18 2 โ‹… 243

In 22 โ€“ 28, simplify each of the following. Leave your answer in exponential notation.

22. ( 2 2 )^4 23. 7 2 โ‹… 73 โ‹… 75 24. (โˆ’ 5 ) ( โˆ’ 5 ) (^2 โˆ’ 5 )^3

25. x^2 โ‹… x โ‹… x^3 โ‹… x โ‹… x^4 โ‹… x 26. ( )

23 4 (^4) โŽฅ โŽฆ

โŽก (^) 27. ( 2 ab )^6

28. ( a^2 b )^5 ( ac ) (^3 b 2 c^3 ) โˆ’^4 ( ab )^2 put some in with quotients where you get positive

exponents in numerator

In 29 โ€“ 30, accompany each of the following with an appropriate diagram.

  1. On a coordinate plane, locate and clearly label each of the following points.

(a) ( 5 , 2 ) (b) (โˆ’ 4 , 3 ) (c)( โˆ’ 6 , โˆ’ 5 ) (d) ( 5 , โˆ’ 8 )

  1. If a < 0 and b > 0 , determine the quadrant of each of the following points.

(a) ( a , b ) (b) (โˆ’ a , b ) (c) ( a ,โˆ’ b ) (d) (โˆ’ a ,โˆ’ b )

31. Find two points P 1 and P 2 such that P 1 , P 2 ,( โˆ’ 4 , โˆ’ 2 ), and ( 5 , 3 )are the vertices

of a rectangle whose sides are parallel to the coordinate axes.

  1. Add. (a) 15

(b) 15

(c) 3 1

  • x

x x

x

(d) 2

t t

  1. Find the slope, x โˆ’and y โˆ’intercepts of the following equations. (a) y = 2 x + 1

(b) 2 x + 3 y = 6

  1. Solve the following equations. (a) 7 x + 7 =โˆ’ 14

(b) ( z + 5 ) โˆ’ 7 =( z โˆ’ 7 ) + 5

(c) โˆ’ ( y + 5 ) โˆ’( 2 + 7 y ) + 8 y = 3 y โˆ’ 8

(d) โˆ’ 8 b + 6 + 6 b =โˆ’ 3 b + 11 + b

  1. Write an expression for the area of the figure shown.

2 x + 3

x โˆ’ 1

  1. Write an expression for the difference of 4 and the quotient of x and 6.
  2. Check to see if โˆ’ 1 is a solution of the equation, 3 x^2 โˆ’ 2 x =โˆ’ 5 x.

For problems 42 and 43, solve by first finding an equation.

  1. Five times the sum of a number and ten is the same as three times the number. Find the number.
  2. The length of a rectangular area is 10 feet more than twice the width. The perimeter of the rectangle is 338 feet. Find the length and the width of the rectangle.
  1. Factor completely the following polynomials: (a) x^2 โˆ’ 12 x + 35

(b) 2 y^3 โˆ’ 22 y^2 + 48 y

(c) 6 y โˆ’ 18

(d) x^2 โˆ’ 81

(e) 4 x^2 y^3 โˆ’ 12 x^3 y^2

(f) 10 a^2 โˆ’ 19 a + 6

(g) โˆ’ 4 x^2 + 64

(h) 3 x (^6 x โˆ’^5 )^ โˆ’^4 (^6 x โˆ’^5 )

  1. Combine the following polynomials and simplify: (a) ( 3 x^2 โˆ’ 8 x + 2 ) +( 4 x^2 โˆ’ 2 x โˆ’ 9 )

(b) (โˆ’ 5 x^2 + 7 x โˆ’ 9 ) โˆ’( โˆ’ 2 x^2 โˆ’ 8 x + 6 )

(c ) โˆ’ 3 x^3 ( 2 x^4 + 5 x โˆ’ 7 )

(d) ( 3 x โˆ’ 5 )(^4 x + 7 )

(e) ( 7 x โˆ’ 4 )^2

(f) (^) โŽŸ โŽ 

(^1) x x