017 Final Exam Topics

8/3/2019 017 Final Exam Topics

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Topics and sample problems for Math 017 Final Exam(long version)

Below there are 59 categories:9 arithmetic categories

13 easy algebra categories24 basic algebra categories9 difficult algebra categories4 very difficult algebra categories

Each version of the exam will be created as follows:First, 45 categories will be selected: All 9 arithmetic categories will be included. From thealgebraic categories, 8 categories will be selected at random from 13 easy categories, all24basic algebra categories will be represented, 3 out of the 9 difficult categories, and 1from thevery difficult category. After this process, we will have 45 categories. One questionout of each such category will be selected at random. Thus, the test will consist of 45 questions.

ARITHMETIC PART: 9 QUESTIONS

Select randomly one question from each category.

1AAddition, subtraction, multiplication, or division of integers (using both: and fraction bar as a division sign) - up to 3 integers.

Evaluate, if possible. Otherwise, write undefined: =+ 53

Compute, if possible. Otherwise, write undefined: = 17

Evaluate, if possible. Otherwise, write undefined: = 103

Compute, if possible. Otherwise, write undefined: =+ )11()2(3

Evaluate, if possible. Otherwise, write undefined: = )4)(1(

Compute, if possible. Otherwise, write undefined: = )1()1(2

Evaluate, if possible. Otherwise, write undefined:210


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Compute, if possible. Otherwise, write undefined: 210


Compute, if possible. Otherwise, write undefined: )3(3

Evaluate, if possible. Otherwise, write undefined: )7)(3(2

Compute, if possible. Otherwise, write undefined: 100)100(4

Evaluate, if possible. Otherwise, write undefined: 952 +

Compute, if possible. Otherwise, write undefined: )2)(1(6

Evaluate, if possible. Otherwise, write undefined: )100)(10(4

Compute, if possible. Otherwise, write undefined: )8)(1(5

Evaluate, if possible. Otherwise, write undefined: )8(6


Evaluate, if possible. Otherwise, write undefined: )9(2

Compute, if possible. Otherwise, write undefined: )3(10 +

Compute, if possible. Otherwise, write undefined:09

Evaluate, if possible. Otherwise, write undefined: 100



2AOrder of operations, integers only, two operations (only integers as an answer,no exponents).


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Compute, if possible. Otherwise, write undefined: =+ 327

Compute, if possible. Otherwise, write undefined: = )87(4

Evaluate, if possible. Otherwise, write undefined: =

5

105

Evaluate, if possible. Otherwise, write undefined: = )1(11

Compute, if possible. Otherwise, write undefined: ) 4(44

Evaluate, if possible. Otherwise, write undefined: ) 92)(16(

Compute, if possible. Otherwise, write undefined: )1212(4 +

Evaluate, if possible. Otherwise, write undefined: ) 31(2

Compute, if possible. Otherwise, write undefined: ) 3()54(2

Evaluate, if possible. Otherwise, write undefined: ) 2)](7(3[ +

Compute, if possible. Otherwise, write undefined: ) 231(4 +

Evaluate, if possible. Otherwise, write undefined: ) 2()7(4 +

Compute, if possible. Otherwise, write undefined: 8)2(8


+



Compute, if possible. Otherwise, write undefined: ) 29(8 +

Evaluate, if possible. Otherwise, write undefined: ) 52(4 +



Evaluate, if possible. Otherwise, write undefined: ) 22(4 +


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Compute, if possible. Otherwise, write undefined:)6(6

12

Evaluate, if possible. Otherwise, write undefined: 10)55( +

3AAddition and subtraction of fractions or of fractions and integers (positiveand negative).

Compute: =+54

32

Compute: =

65

53

Evaluate:43

2 +

Evaluate:34

1

Evaluate:

+

73

32

Evaluate:

5

3

4

5

Evaluate:12

594

+

Evaluate:29

143

Evaluate: ( )83

1

Evaluate: 365

Evaluate: 223

7+

Compute:

+

92

74

Compute:9

1043

Compute:

94

187


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Compute:

75

1

Compute:75

143

+

Compute:11

3

3

2

Compute:73

92

Compute: 632

Compute:12

594

+

4AMultiplication of fractions and of fractions and integers (positive andnegative).

Compute: = )10(53

Evaluate: =34510

21

5345

Compute:

152

12

Evaluate: )18(98

Compute:111

34

711

x x

Evaluate:

354

64

25

Compute:

84

103

125

x

Evaluate:

324

61

724


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Compute: ( )

6

3212

3217

x

Evaluate:

152

12

Compute:2723

100

Evaluate:

819

324

Compute:

214

27

x

Evaluate:

522

1110

Compute:34

79

x

Evaluate:

106

45

Compute:158

25

Evaluate:9

1078

x

Compute:

32

37

x

Evaluate:

2

9

4

5

5ADivision (using both and fraction bar) of fractions and of fractions andintegers (positive and negative).


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Evaluate, if possible. Otherwise, write undefined:

2143

Compute, if possible. Otherwise, write undefined:

72

53



4


79


52

Evaluate, if possible. Otherwise, write undefined: ) 8(916


52

20


152



6598


13129


51

103


512


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8


973

14


14121

2


52

1


32

35


6

10

4

15

Compute, if possible. Otherwise, write undefined: ( )3139

6AZero category(number/0; 0/number; addition of opposite numbers;multiplication by 0). Ten category: Multiplication and division of decimalsand integers by powers of ten.

Compute, if possible. Otherwise, write undefined: = 1000234

Evaluate, if possible. Otherwise, write undefined: = 1013.0

Compute, if possible. Otherwise, write undefined: = 1002.0



Compute, if possible. Otherwise, write undefined: 26672667 +


Evaluate, if possible. Otherwise, write undefined: 102.0 Evaluate, if possible. Otherwise, write undefined: 10021.3 Evaluate, if possible. Otherwise, write undefined: 1006 Evaluate, if possible. Otherwise, write undefined: 10112


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Compute, if possible. Otherwise, write undefined: 2 (0.2) 0.03

8AExponential notation (fractions, integers, decimals)


Compute, if possible. Otherwise, write undefined: =3)1.0(

Evaluate, if possible. Otherwise, write undefined: =

2

32

Evaluate, if possible. Otherwise, write undefined: 2(0.9)Evaluate, if possible. Otherwise, write undefined: 3)4.0( Evaluate, if possible. Otherwise, write undefined: 2)1.1(

Evaluate, if possible. Otherwise, write undefined: 4)01.0( Evaluate, if possible. Otherwise, write undefined: 2)06.0( Evaluate, if possible. Otherwise, write undefined: 7)1.0( Evaluate, if possible. Otherwise, write undefined: 42 Evaluate, if possible. Otherwise, write undefined: 14)1( Evaluate, if possible. Otherwise, write undefined: 2)7( Evaluate, if possible. Otherwise, write undefined: 25)1( Evaluate, if possible. Otherwise, write undefined: 3)3(


2

89


21



32


52

Evaluate, if possible. If not possible, write undefined:4

21

9A


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Addition, subtraction, multiplication and division including mixed numberrepresentations. Order of operation (up to 3 operations).

Compute, if possible. Otherwise, write undefined: =65

131

2

Compute, if possible. Otherwise, write undefined: =+72

553

2

Compute, if possible. Otherwise, write undefined: =76

131

2

Evaluate, if possible. Otherwise, write undefined: = )91

1(32

1


Evaluate, if possible. Otherwise, write undefined: = )32

31

)(32(


53

21

53


17174

203


28

5

2


65


514

72

Evaluate, if possible. Otherwise, write undefined: 1 .2001.02.0

Evaluate, if possible. Otherwise, write undefined: )02.0)(3.07.0( Evaluate, if possible. Otherwise, write undefined: ) 3.0)(2.0()5)(2.0( + Evaluate, if possible. Otherwise, write undefined: 108.19.0 Evaluate, if possible. Otherwise, write undefined: ) 6.49.3(2.4


12

Evaluate, if possible. Otherwise, write undefined: = )2(31

5


22


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431

ALGEBRA PART: 36 QUESTIONS

EASY CATEGORY: select randomly 8 categories (1 question from each category)

1EWriting phrases (involving only one operation) as algebraic expressions.

Write a direct translation of the following phrases as an algebraic expression. DO NOTSIMPLIFY: The sum of a and b

Write a direct translation of the following phrases as an algebraic expression. DO NOTSIMPLIFY: x raised to m -th power

Write a direct translation of the following phrases as an algebraic expression. DO NOTSIMPLIFY: The product of a and b

Write a direct translation of the following phrases as an algebraic expression: The opposite of C

Let m represent mass, and c speed of light. Use m and c to write the following phrase as analgebraic expression: the product of mass and the square of speed of light.

Use any letter to represent a number and write the following statement as an algebraicexpression: Double a number

Use any letter to represent a number and write the following statement as an algebraicexpression: Two thirds of a number

Use any letter to represent a number and write the following statement as an algebraicexpression: A number increased by 3

Write a direct translation of the following phrases as an algebraic expression. DO NOTSIMPLIFY: n subtracted from m .

Write a direct translation of the following phrases as an algebraic expression. DO NOTSIMPLIFY: The product of a and b .

Write a direct translation of the following phrases as an algebraic expression: n divided bym . Do not simplify.


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Write a direct translation of the following phrases as an algebraic expression: The sum of x , p and y.

Write a direct translation of the following phrases as an algebraic expression. DO NOT

SIMPLIFY: ab

raised to the tenth power.

Write a direct translation of the following phrases as an algebraic expression. DO NOTSIMPLIFY: ab2 squared.


SIMPLIFY: The opposite of 7

2a .


SIMPLIFY: The opposite of 7

2

a . Do not simplify.

Use the letter x to represent a number and write the following phrase as algebraic expression:One-eighth of a number

Use the letter x to represent a number and write the following phrase as an algebraic expression:A number multiplied by 3

Use the letter x to represent a number and write the following phrase as an algebraic expression:A number subtracted from 3

Use the letter x to represent a number and write the following phrase as an algebraic expression:The product of AB and a number.

Let a be a variable representing the length of the side of a square. Use a to write the followingstatement as an algebraic expression: Four times the side of a square.

Let a be a variable representing the length of the side of a square. Use a to write the followingstatement as an algebraic expression: The side of a square raised to the second power.

Let a be a variable representing the length of the side of a square. Use a to write the followingstatement as an algebraic expression: The side of a square doubled.

John has x dollars in his bank account. How much money will John have in the bank, after hewithdraws $100? Give your answer in the form of an algebraic expression.

Johns salary is x dollars. He got a new job and his salary doubled. How much does John earn inhis new job? Give your answer in the form of an algebraic expression.


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If a family has x children, and each of those children has 3 children of his own, how manygrandchildren are there? Give your answer in the form of an algebraic expression.

Let t be a variable representing temperature on a given day. Use the variable to write thefollowing statement as an algebraic expression: The temperature on the given day increased by 5degrees.

2EAbility to distinguish between an algebraic expression and equation.

Determine whether the following examples represent an equation or an algebraic expression.Circle ALL equations.

a) 24 x b) 724 = x c) 0= A

Determine whether the following examples represent an equation or an algebraic expression.Circle ALL equations.

a) x x x 924 = b) 724 = x c) x y x =+ 4322

Determine whether the following examples represent an equation or an algebraic expression.Underline the example that represents an equation.a) y x 524 + b) x x 23 c) 9524 = y x Determine whether the following examples represent an equation or an algebraic expression.Circle ALL algebraic expressions.a) 573 = y x b) 0= x c) 8379 ++ c y x

Determine whether the following examples represent an equation or an algebraic expression.Circle ALL algebraic expressions.a) 02 22 = y x b) z y x ++ 54 c) x

3ESolving linear equations (all variables on one side, no parentheses involved,no need for collecting terms, no fractions or decimals unless they appear as asolution).

Solve the following equation: x298 =

Solve the following equation: 27 =+ x

Solve the following equation: 473 = x


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Solve the following equation: 0= x

Solve the following equation: 52 = a


Solve the following equation: y+= 72


Solve the following equation: 23 =+ b


Solve the following equation: x= 2




Solve the following equation: 263 += w


Solve the following equation: 52 += x




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4ESolving a linear inequality (all variables on one side, no parentheses involved,no need for collecting terms, no fractions or decimals unless they appear as asolution). Solve the following inequality: x210 >

Solve the following inequality: 29 9

Solve the following inequality: x34 >

Solve the following inequality: x+ x

Solve the following inequality: 52 > x

Solve the following inequality: x+ 53

Solve the following inequality: 572 + a

Solve the following inequality: 132 x


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Solve the following inequality: x 46

,,,Solve the following inequality: 77 > x

Solve the following inequality: x+ 29

Solve the following inequality: 130 a

Solve the following inequality: 368 + x

Solve the following inequality: 16 + x

5EGraphing sets on a number line. Graph the following number set on a number line. Assume that the distance between all marks isthe same.

1 x

Graph the following number set on a number line. Assume that the distance between all marks isthe same.

3> x

Using inequality symbols, describe the set that is graphed below:

Graph the following inequality on the number line. Assume that the distance between all marksis the same.

3 x


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21

> x


25

> x


21

x


2 x


31

x


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32

< x


2< x


3 x






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6EChecking if a given integer is a solution of a linear equation (inequality) in onevariable.

Is the number 5 a solution of the following inequality. 42


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Is the number 3 a solution of the following equation. 1974 = x .

Is the number 100 a solution of the following equation. 4320432 = x .

Is the number 1 a solution of the following equation 05

1=

+ x

Is the number 0 a solution of the following equation. 05

= x

Is the number 0 a solution of the following equation. 02

= x

7EUnderstanding , notation. Using it to describe sets of numbers (phrases like at least, at most, not less, not more).

Circle all of the numbers that satisfy the condition 2 x .1,0,9.0,2,1.2,4

Name three numbers that satisfy the condition: 1 x .

Write any inequality that is satisfied by 2 and 3.

Write any inequality that is not satisfied by 2 and 3.

Write any inequality that is satisfied by ,2 but not by 3.

Describe the following set of numbers using inequality signs: All numbers x that are positive

Describe the following set of numbers using inequality signs: All numbers x that are non-negative

Describe the following set of numbers using inequality signs: All numbers x that are at mostequal to 9.

Describe the following set of numbers using inequality signs: All numbers x that are at leastequal to 9.

Describe the following set of numbers using inequality signs: All numbers x that are not lessthan 9.


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Describe the following set of numbers using inequality signs: All numbers x that are not morethan 1 . Describe the following sets of numbers using inequality signs: All numbers x that are negative.

Describe the following sets of numbers using inequality signs: All numbers x that are non-positive.

Describe the following sets of numbers using inequality signs: All numbers x that are at leastequal to 6.

Describe the following sets of numbers using inequality signs: All numbers x that are at mostequal to 6.

Describe the following sets of numbers using inequality signs: All numbers x that are not morethan 6

Name three numbers that satisfy the condition: 4> x

Name three numbers that satisfy the condition: 3 x

Name three numbers that satisfy the condition:21

> x

Name three numbers that satisfy the condition: 5.0 x

Find a number that satisfies 8 x but does not satisfy 100> x

Circle all numbers that satisfy the following inequality 3> x 3 , 2 , 1 , 0, 1, 2, 3, 4, 5

Circle all numbers that do not satisfy the inequality: 3> x 3 , 2 , 1 , 0, 1, 2, 3, 4, 5

Circle all numbers that satisfy the inequality: 2 x :3 , 2 , 1 , 0, 1, 2, 3, 4, 5

8E


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Rewriting the expression by replacing the variable with its value (onlyintegers) and evaluating it, if possible. One operation needed for theevaluation.

Let 100= x . Rewrite the expression replacing the variable with its value and evaluate it, if

possible. Otherwise, write not defined : x3 Let 1= x . Rewrite the expression replacing the variable with its value and evaluate it, if possible. Otherwise, write not defined : 2 x


possible. Otherwise, write not defined : x4


possible. Otherwise, write not defined : 700 x


possible. Otherwise, write not defined : x0

Let 2= x . Rewrite the expression replacing the variable with its value and evaluate, if possible.Otherwise, write not defined : x3

Let 2= x . Rewrite the expression replacing the variable with its value and evaluate, if possible.Otherwise, write not defined : 3 x

Let 2= x . Rewrite the expression replacing the variable with its value and evaluate, if possible.Otherwise, write not defined : x x

Rewrite the expression A replacing the variable with its value and then evaluate if 2= A .

Substitute 6= x in the following expression and then evaluate, if possible. Otherwise, write notdefined : 8 x

Substitute 6= x in the following expression and then evaluate, if possible. Otherwise, write not

defined : x

10

Substitute 6= x in the following expression and then evaluate, if possible. Otherwise, write notdefined : x+ 4

Substitute 6= x in the following expression and then evaluate, if possible. Otherwise, write notdefined : 6 x


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Substitute 6= x in the following expression and then evaluate, if possible. Otherwise, write notdefined : 62 + x

Substitute 2= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : x+2

Substitute 2= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : x2

Substitute 2= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : x 2

Substitute 2= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : 45 + x

Substitute 2= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : 106 + x



Substitute 10= x in the following expression and then evaluate, if possible. Otherwise, write

not defined : x200

Substitute 10= x in the following expression and then evaluate, if possible. Otherwise, writenot defined :

2 x


Substitute 10= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : 4 x



not defined :6 x



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not defined :12

6+ x


Substitute 12= x in the following expression and then evaluate, if possible. Otherwise, writenot defined : 2 x

9ESolving literal equations (variable one is seeking will not appear in thedenominator). One operation needed. No simplification needed at the end. Solve for x : b

a

x=

Solve for x : ba x =+

Solve for x : cax =

Solve for x : 0= d x

Solve for the indicated variable: cab

7= for b

Solve for the indicated variable: 4=+ ba for a

Solve for m : xm

=4

Solve for x : Z Y x =+

Solve for x : c x =

Solve for x : z

v

x=

Solve for x : z x y =+

Solve for x : m x += 4

Solve for x : xy=3


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Solve for x : x y =

Solve for the indicated variable: z yb = 7 for b

Solve for the indicated variable: msa = for a

Solve for m : m xy 3=

Solve for x : ca x

=

10EIf possible, rewriting algebraic expressions with the use of exponential laws

(non-negative exponents; only one law used) .Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 153aa

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 153 aa +

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, just

rewrite the expression: ( )24b

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: a 43 b

If possible, eliminate parentheses by applying an exponential law. If it is not possible to simplify, just rewrite the expression: 7)(ab

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 153ba

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 3

7

aa

Simplify, using one of the exponential laws, if possible, If not possible, write not possible :

( )210m


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Simplify, using one of the exponential laws, if possible, If not possible, write not possible :mmm 43

If possible, eliminate parentheses by applying an exponential law. If not possible, write not

possible:

7

nm

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 15 xx


rewrite the expression: 314

s

s

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: ( )315t

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 43 mm

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: 157 x x

Simplify, using one of the exponential laws, if possible, If it is not possible to simplify, justrewrite the expression: aaa 3



q

q



qq


rewrite the expression:q

q 5

11E


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Removing parentheses in multiplication of a monomial by a polynomial (up to3 terms). Performing numerical operations might be required but no use of exponential laws needed. No fractions, no decimals.

Eliminate parentheses in the following expression: )3(4 z y x +

Eliminate parentheses in the following expression: )2( y x +

Eliminate parentheses in the following expression: )( d cba ++ .

Eliminate parentheses in the following expression: ( ) 2103 x

Eliminate parentheses in the following expression: ( )W L +2

Eliminate parentheses in the following expression: ( ) x R 1

Eliminate parentheses in the following expression: ( ) Ar R 22 .

Eliminate parentheses in the following expression: ( )rt P +13

Eliminate parentheses in the following expression: ) 2)(7( 2 z x

Eliminate parentheses in the following expression: ) 2( 2 + aa

Eliminate parentheses in the following expression: )3( xy+ .

Eliminate parentheses in the following expression: )2( cad +

Eliminate parentheses in the following expression: )2)(( w y x

Eliminate parentheses in the following expression: y x x 4)1( 23 ++

Eliminate parentheses in the following expression: ))(( d gba + .

Eliminate parentheses in the following expression: )10( 3a

12ECollecting like terms (2 terms only), if possible. No fractions, no decimals.


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If possible, collect like terms. If not possible, just rewrite the expression x x 43 +

If possible, collect like terms. If not possible, just rewrite the expression 22 6aa

If possible, collect like terms. If not possible, just rewrite the expression mmn

If possible, collect like terms. If not possible, just rewrite the expression yx xy

If possible, collect like terms. If not possible, just rewrite the expression x x 24

If possible, collect like terms. If not possible, just rewrite the expression aa 2

If possible, collect like terms. If not possible, just rewrite the expression y y

If possible, collect like terms. If not possible, just rewrite the expression yx xy

If possible, collect like terms. If not possible, just rewrite the expression aba +

If possible, collect like terms. If not possible, just rewrite the expression tsst +

If possible, collect like terms. If not possible, just rewrite the expression x x 9

If possible, collect like terms. If not possible, just rewrite the expression 22 94 y y

If possible, collect like terms. If not possible, just rewrite the expression 33 mm +

If possible, collect like terms. If not possible, just rewrite the expression zyx xyz 6

If possible, collect like terms. If not possible, just rewrite the expression dcscd 43

If possible, collect like terms. If not possible, just rewrite the expression baab 2

If possible, collect like terms. If not possible, just rewrite the expression y x x 33 43 +

If possible, collect like terms. If not possible, just rewrite the expression22222 63 aa

If possible, collect like terms. If not possible, just rewrite the expression t st

If possible, collect like terms. If not possible, just rewrite the expression kmnmnk 52

13E


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Factoring an indicated expression (a variable or an integer). No use of exponential laws needed. No instances when an entire term is factored andthus 1 becomes a term after factorization.

Factor x from the following expression: xy x 23

Factor 4 from the following expression: x y 84 2 +

Factor 5 from the expression: y x 55 +

Factor 7 from the expression: a4921 Factor c from the expression: cac 23

Factor y from the expression: y xy 78 +

Factor 2 from the whlhlw 222 ++

Factor x from the expression: x yx xz 54 +

Factor x from the following expression: vx zx yx +

Factor 10 from the following expression: v yxz 10100

Factor 9 from the expression: y x 2718

Factor 2 from the expression: ba 2420 +

Factor c from the expression: ccd 23

Factor y from the expression: xy y 14+

Factor 2 from the expression bc yz x 122 4

Factor x from the expression: x xy xz 547 +

Factor x from the following expression: xy xy 82

Factor 4 from the following expression: z xy 412 2 +

Factor m from the expression: mmn 35 +

Factor s from the expression: sst 49


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BASIC CATEGORY: 1 question from each category of 23 categories

1BSimplifying an expression by performing numerical operations when possible.(may need to change the order of terms or factors). Performing an operationon fractions or on decimals might be needed.

Simplify if possible. If no numerical operation can be performed, write not possible:12 ++ x

Simplify if possible. If no numerical operation can be performed, write not possible:

Y +61

32

Simplify if possible. If no numerical operation can be performed, write not possible:8

4 x

Simplify if possible. If no numerical operation can be performed write not possible: x312 +

Simplify if possible. If no numerical operation can be performed, write not possible:m)32(

Simplify if possible. If no numerical operation can be performed, write not possible:m

32

Simplify if possible. If no numerical operation can be performed, write not possible: y x )3(2

Simplify if possible. If no numerical operation can be performed, write not possible:)( x

Simplify if possible. If no numerical operation can be performed, write not possible:03.02.0 + x


x

Simplify if possible. If no numerical operation can be performed, write not possible:)8(4 a


8a


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21

21

x

Simplify if possible. If no numerical operation can be performed, write not possible: acbd

93

Simplify if possible. If no numerical operation can be performed, write not possible: y x )3(2


x52

4

Simplify if possible. If no numerical operation can be performed, write not possible: xz y

212


21

2 2 x


510

x

Simplify if possible. If no numerical operation can be performed, write not possible:)10(1.0 2 y x

Simplify if possible. If no numerical operation can be performed, write not possible:)3.0(5.0 m

Simplify if possible. If no numerical operation can be performed, write not possible:m+ 6.05.0


02.04.0

y

2B


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Simplifying algebraic expressions by applying exponential laws (only non-negative exponents; one variable, up to 2 types of operations. Performing anoperation on fractions or on decimals might be needed.

Simplify x x 32 )(2

Simplify: 23

aaa

Perform the indicated operation and simplify: )4)(3( 25 x x

Perform the indicated operation and simplify: 24

63 x x

Perform the indicated operation and simplify: )4(3 2 x x

Perform the indicated operation and simplify: 36 )2( x


68 x

x


x

x x


a

a

a


1v

v

Perform the indicated operation and simplify: 432 )3(

x x


)3(3 x x

Simplify 22 )3( aa

Simplify: 23

aa

a

Perform the indicated operation and simplify: x

x

3)4(


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2)(

a

a

Perform the indicated operation and simplify: 752 )( x x

Perform the indicated operation and simplify: 36 )2( x

Perform the indicated operation and simplify: )4)(3( 52 x x x

Perform the indicated operation and simplify: ))(2)(3( 3 x x

3BThe Distributive Law: removing parentheses in multiplication of a monomialby a polynomial with up to 3 terms. No collecting terms needed at the end butnumerical operations or application of exponential laws needed in the process.Performing an operation on fractions or on decimals might be needed.

Use the Distributive Law to eliminate parentheses in the following expression. Simplify, if possible. )2( 2 x x

Use the Distributive Law to eliminate parentheses in the following expression. Simplify, if possible. )( 43 aaaa + .

Use the Distributive Law to eliminate parentheses in the following expression. Simplify, if

possible. x x 221

3

Use the Distributive Law to eliminate parentheses in the following expression. Simplify, if possible. )43(2 z y x +

Remove parentheses and simplify: 42 )2( x x x

Remove parentheses and simplify: )333(32 d c

Remove parentheses and simplify: )( 22 ababaa ++

Remove parentheses and simplify: x xy y x )73

2( 43 +


35/89

35

Remove parentheses and simplify: ))(52

( 3aba

Remove parentheses and simplify: )84(41 5 x x

Remove parentheses and simplify: )86(3 34 y y y +

Remove parentheses and simplify: )2( 352 x x x +

Remove parentheses and simplify: )7(2 22 y y y

Remove parentheses and simplify: )9( 224 baaa +

Remove parentheses and simplify: )(52

abbaab

Remove parentheses and simplify: )1003.0(2.0 6ccc

Remove parentheses and simplify: )4( 510 xy x x

Remove parentheses and simplify: )(2 nmmn

Remove parentheses and simplify: ( ) x x x 422

5

Remove parentheses and simplify: )3.0(7.0 n

Remove parentheses and simplify: )100)(06.03.2( x

Remove parentheses and simplify: )206.0(5 y x

Remove parentheses and simplify: )42.0(6.0 + n

4BThe Distributive Law: removing parentheses in multiplication of a binomialby a binomial. No collecting terms needed at the end but numericaloperations or application of exponential laws needed in the process (nooperations on fractions or decimals).


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36

Eliminate parentheses in the following expression. Simplify: )32)(( + aba

Eliminate parentheses in the following expression. Simplify: ))(2( 5cccb ++

Eliminate parentheses in the following expression. Simplify ))(( 2 w zx y x +

Eliminate parentheses in the following expression. Simplify )10)(3( 3aba

Eliminate parentheses in the following expression. Simplify ))(( 2dgcaga

Eliminate parentheses in the following expression. Simplify: )1)(( 23 + yx x x

Eliminate parentheses in the following expression. Simplify: ) 1)(1( + y yx

Eliminate parentheses in the following expression. Simplify )1)(12( 5 baab

Eliminate parentheses in the following expression. Simplify )32)(84( 93 x yx x +

Eliminate parentheses in the following expression. Simplify ) 13)(( 52 + mmm

Eliminate parentheses in the following expression. Simplify: )33)(4( 322 baabba +

Eliminate parentheses in the following expression. Simplify: ))(( 54 cbccb ++

Eliminate parentheses in the following expression. Simplify )2)(3( 32 y x xy y x

Eliminate parentheses in the following expression. Simplify )2)(2( 3 baab

Eliminate parentheses in the following expression. Simplify ) 3)(( 2 ++ y y x

Eliminate parentheses in the following expression. Simplify: )2)(1( 2 xa x ++

Eliminate parentheses in the following expression. Simplify: )2)(3( my xnm ++

Eliminate parentheses in the following expression. Simplify )23)(3( 2 y x y x

Eliminate parentheses in the following expression. Simplify )31)(3( x xy x

Eliminate parentheses in the following expression. Simplify ))(2( v z z


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5BFactorization of an indicated monomial (factorization of an entire term isand thus getting 1 as a term after factorization possible). No operations on

fractions or decimals.

Factor 2 x from the following expression: 235 23 x x x +

Factor a4 from the following expression:484 xaa +

Factor 2 x from the following expression: 253 yx x

Factor 2 xy from the following expression: 33422 34 y x xy y x +

Factor xy2 from the following expression: 222

422 y x xy xy +

Factor 33ba from the following expression: 337343 5 baabba +

Factor xy7 from the following expression: xy y x y x 21147 2335 ++

Factor 337 ba from the following expression: 3373 714 baab

Factor 34ac from the following expression: d acacac 873 12816 +

Factor2

7ab from the following expression:2423

71435 abbaab +

Factor 2 y from the following expression: 42 42 y y x +

Factor 2 x from the following expression: 42 32 x x

Factor y x 22 from the following expression: 372 146 x y y x +

Factor 23abc from the following expression: 222562 6123 cbabcaabc +

Factor 3 z from the following expression: 345 23 z z z +

Factor 2 x from the following expression: 232 x x

Factor ay3 from the following expression: 2423 633 yaay x ya +


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38

Factor ab3 from the following expression: baab 36 5

Factor ba 2 from the following expression: 2723 4 bababa +

Factor32

3 y z from the following expression:2464

93 z y y z

6BSimplification of rational expressions. Factorization of a numerator OR adenominator (but not both) needed.

Simplify, if possible. If not possible, write not possible:a

aba 2+

Simplify, if possible. If not possible, write not possible: 22 3 xy y x xy

Simplify, if possible. If not possible, write not possible:ad

d a

+

44

Simplify, if possible. If not possible, write not possible: y x 22

2+

Simplify, if possible. If not possible, write not possible:

x

xz xy

3

+

Simplify, if possible. If not possible, write not possible: x

x x6

33 2+


x x 254

Simplify, if possible. If not possible, write not possible:mnnm

33

Simplify, if possible. If not possible, write not possible:a

abba443

4

Simplify, if possible. If not possible, write not possible:93

3 x x

Simplify, if possible. If not possible, write not possible: 2933

x x x


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39


2 x x x

Simplify, if possible. If not possible, write not possible: bacba

+

++

Simplify, if possible. If not possible, write not possible: 2 xy xy xy+


x3

412

Simplify, if possible. If not possible, write not possible:

uvs

svu

+

2

2

Simplify, if possible. If not possible, write not possible:uv

vuuv2

24 2 +

Simplify, if possible. If not possible, write not possible: yx xy xy

3

2

Simplify, if possible. If not possible, write not possible:4

8124 z y x ++

Simplify, if possible. If not possible, write not possible: z x

z84

8

7BUnderstanding what it means that a number(s) is a solution of a givenequation (relatively complicated evaluation needed). Performing anoperation on fractions or on decimals might be needed.

Ability to rewrite the expression and evaluating it, if possible (one instance of a variable). If evaluation is not possible, recognizing that it is not possible toevaluate. Performing an operation on fractions or on decimals might beneeded.

Circle all of the numbers below that are solutions of the equation x x += 63 .


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40

2= x 2= x

Determine if 2,1 == y x is a solution of the following equation. Show your work.123 = y x .

Determine if 2,1==

y x is a solution of the following equation. Show your work.3= y x

Determine if 2,1 == y x is a solution of the following equation. Show your work.

2=

x y

Does 2,21

== ba make the following statement true or false? Show your work.

1=ab

Does 2,21


1=ab

Does 2,21


41

=ba

Does 2,21


23

=+ ba

Is 0,1 == y x a solution of 22 = xy ? Show your work.

Is 0,1 == y x a solution of 02 = xy ? Show your work.

Is 0,1 == y x a solution of 1= x y ? Show your work.

Is 0,1 == y x a solution of 0= y x

? Show your work.

Is 2,21

== y x a solution of 4= y x

? Show your work.


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41

Is 0,1 == y x a solution of 4= x y

? Show your work.

Is 0,1 == y x a solution of

2

3= x y ? Show your work.

Is 0,1 == y x a solution of x y xy 2= ? Show your work.

Let 4= x . Rewrite the expression replacing the variable with its value and evaluate: 2 x

Let 4= x . Rewrite the expression replacing the variable with its value and evaluate: x)2(

Let 8= x . Rewrite the expression replacing the variable with its value and evaluate: )( 2 x

Let 100= x . Rewrite the expression replacing the variable with its value and evaluate: 2 x

Substitute32

= x in the following expression and then evaluate: x+35

Substitute32

= x in the following expression and then evaluate:51

+ x

Substitute32= x in the following expression and then evaluate:

72+ x

Substitute32

= x in the following expression and then evaluate: x125

Substitute32


Substitute

3

2= x in the following expression and then evaluate: 3 x

Substitute53


Substitute53



42/89

42

Substitute53


2

Substitute53


1

Substitute53


3 x

Substitute72


Substitute72


Substitute 72


Substitute72


Substitute72


Substitute72

= x in the following expression and then evaluate:2 x

Substitute43

= x in the following expression and then evaluate: 2 x

Substitute43


Substitute43

= x in the following expression and then evaluate:

32

1

x

Substitute43


1

Substitute43


x

Substitute43



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43

Substitute 2.0= x in the following expression and then evaluate: 21.3+ x

Substitute 2.0= x in the following expression and then evaluate: x01.35

Substitute 2.0= x in the following expression and then evaluate:4 x

Substitute 2.0= x in the following expression and then evaluate: x40


Substitute 2.0= x in the following expression and then evaluate:04.0 x

Substitute 6.0= x in the following expression and then evaluate: 5 .4 x

Substitute 6.0= x in the following expression and then evaluate: x 7.2




Substitute 6.0= x in the following expression and then evaluate: 3 x

Substitute 5.1= x in the following expression and then evaluate: 08.0 x

Substitute 5.1= x in the following expression and then evaluate: 4 .03 + x

Substitute 5.1= x in the following expression and then evaluate: 15.0 x



8B


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44

Recognizing equivalent expressions by applying the followinga) the order of terms of an expression can be changedb) the order of factors of an expression can be changedc)

acb

ac

ab

= d)c

abcb

ac

ab 1== e)

ba

ba

ba

=

=

Circle all expressions that are equal to z y x 452 + : y z x 542 + x z y 245 ++ z x y 425 ++

Rewrite the expression )( ba yx + in two equivalent forms by multiplying its factors in adifferent order.

Rewrite the following expression in its equivalent form as a single fraction: a116

Rewrite the following expression in its equivalent form as a single fraction: y x

2

Rewrite the following expression in its equivalent form as a single fraction: )1(31 2 +a

Rewrite the following expression in its equivalent form as a single fraction:2

22

+ x

b x

a

Fill in the blanks to make a true statement: _____3 = x y x

Fill in the blanks to make a true statement: ____13

= y y

x

Fill in the blanks to make a true statement: _____1

=+

y yba

Circle all expressions that are equivalent to cb2

cb 2

,cb

c

2, )2(

1b

c ,

cb 2+

Circle all expressions that are equivalent to m

1m

,1m

, )1(m ,m1


45/89

45

Circle all expressions that are equivalent to :nm

mn , )( nm , nm , mn + ,

Circle all expressions that are equivalent to 9

2 xy

xy92

,9

2xy

,91

2 xy ,

Circle all expressions that are equivalent to 9

2 xy

291

xy , 29

xy, y

x9

2

Circle all expressions that are equivalent to d bca ++ .d bcaacbd d cbad cba +++++ ,,,

Circle all expressions that are equivalent toba

.

,1

,1

,a

bb

aba

Circle all expressions that are equivalent toba .

,,22

ba

ba

ba

Circle all expressions that are equivalent to abc

cab )( 1

cba bca

Circle all expressions that are equivalent to abc

1bca

cab )( cab

Circle all expressions that are equivalent to6

5 x.


46/89

46

65

x, ,

65

x x561


5 x.

,12

10,65,

65 x

x x

Circle all expressions that are equivalent to 2 x .

2 x

, x2 , x2 ,

Circle all expressions that are equivalent to 2 x .2 x ,

8

4 x,

2

x

Circle all expressions that are equivalent to a83 + .a11 , 38 +a , 83 + a , a+11 ,


3 ba .

63ab

, ,6

3),3(

61

ba

ba


3 ba

61

)3(,6

3,

663

baabba

+

Circle all expressions that are equivalent to33nm

.

,31

31

,3

,33

nmnmmn

By placing the minus sign differently, write the following expression in two additional

equivalent ways.ba2


47/89

47

By placing the minus sign differently, write the following expression in two additional

equivalent ways.d

ac2

2

Rewrite the following expression as of a single fraction:4

74

nm

Rewrite the following expression as of a single fraction:t

nt m 27


224

5 2

cn

cm


31

s

t ss

m

Using the rule for multiplication of fractions, rewrite the following expression in its equivalent

form as a single fraction: nm

3


form as a single fraction:

4b

a


form as a single fraction:

4b

a

Using the rule for multiplication of fractions, rewrite the following expression in its equivalentform as a single fraction:

nt

s )4(


form as a single fraction:1

4

na

Write the following expressions in its equivalent form as a single fraction: y x34

32

+

Write the following expressions in its equivalent form as a single fraction: y x31

32

Write the following expressions in its equivalent form as a single fraction:3

731

2y

x

Write the following expressions in its equivalent form as a single fraction: yt

xt

13


48/89

48

Write the following expressions in its equivalent form as a single fraction:t

yt

x32 +

Write the following expression in its equivalent form as a single fraction:t k

nt k +

+

21

9BExpanding exponential expression; Rewriting expressions using exponentialnotation whenever possible. Understanding that the exponent pertains only tothe closest expression.

Evaluation of exponential expressions raised to the zero-th power.

Identifying bases, exponents and numerical coefficients of exponentialexpressions.

Expand (i.e. write without using exponential notation). Do not simplify. 2)(bca

Expand (i.e. write without using exponential notation). Do not simplify. 35 A

Rewrite using exponential notation whenever it is possible: mmm7

Rewrite using exponential notation whenever it is possible: aaaaaa

Rewrite using exponential notation whenever it is possible: zzzz

z z z

Rewrite using exponential notation whenever it is possible: z z z

z z z++

))()((

Evaluate 0)2( x

Evaluate 02 x

Evaluate 07 )8(4 m

In the following expression, identify base, exponent and numerical coefficient: 273a Base___________ exponent__________ numerical coefficient_______________

In the following expression, identify base, exponent and numerical coefficient:9

x yz


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49

Base___________ exponent__________ numerical coefficient_______________

In the following expression, identify base, exponent and numerical coefficient: 4 x Base___________ exponent__________ numerical coefficient_______________

In the following expression, identify base, exponent and numerical coefficient: 32 3 x


In the following expression, identify base, exponent and numerical coefficient: 2)( bca Base___________ exponent__________ numerical coefficient_______________

In the following expression, identify base, exponent and numerical coefficient:m

y x



)( 7 y x +



3

4

3

+

w

z x



)( 5ab


Write using exponential notation whenever it is possible: aaaa 3333

Write using exponential notation whenever it is possible: xyxyxxx

Write using exponential notation whenever it is possible: aaaaa

Write using exponential notation whenever it is possible: yyx xxy

Write using exponential notation whenever it is possible: ))()(( bababa +++


50/89

50

Write using exponential notation whenever it is possible: )2)(2)(2)(2( 3333 t t t t

Write using exponential notation whenever it is possible: mnnm ++

Write using exponential notation whenever it is possible: k n

kkk

Write using exponential notation whenever it is possible: x x x

x2

Write using exponential notation whenever it is possible: )3)(3)(3( x x x +

Write using exponential notation whenever it is possible:

ba

ba

ba 2

22


x x x

333

Write using exponential notation whenever it is possible:)2)(2)(2(

1wvwvvw +++


m

y xm y

m x

Write using exponential notation whenever it is possible: nmnmnm +++ ))((

Write using exponential notation whenever it is possible: ))()(( pmnnm pn pm +++

Write the following expression without using exponential notation: 3)( m

Write the following expression without using exponential notation: 3m

Write the following expression without using exponential notation: 3)( xy

Write the following expression without using exponential notation: 32a

Write the following expression without using exponential notation: 2)( ba +

Write the following expression without using exponential notation: 2ba +

Simplify by raising to the indicated power: 0)3( x

Simplify by raising to the indicated power: 03 x


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51

Simplify by raising to the indicated power: 3 x0

Simplify by raising to the indicated power: 0)( cba +

Simplify by raising to the indicated power: 0abc

Simplify by raising to the indicated power: 0)(abc

Simplify by raising to the indicated power: 0cab +

Simplify by raising to the indicated power: 000 cba

10BDetermining if rational expressions can be simplified and simplifying them.Factorization not needed.

Simplify, if possible. If not possible, write not possible: yx xy

93


aba

Simplify, if possible. If not possible, write not possible: acba

2)(2

Simplify, if possible. If not possible, write not possible: z

zv4

4

Simplify, if possible. If not possible, write not possible: x xy

912

Simplify, if possible. If not possible, write not possible:ababc

82


42

nmn


205

y xy


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52


ba x25

)(15

Simplify, if possible. If not possible, write not possible:cb

cba

)(2

Simplify, if possible. If not possible, write not possible:b

ebbc )( +


x x )5(4 2

Simplify, if possible. If not possible, write not possible:)(7 ba

ba+

+


x2

32 +

Simplify, if possible. If not possible, write not possible: x y x

124 32

Simplify, if possible. If not possible, write not possible:abba

+

+

33

Simplify, if possible. If not possible, write not possible:ab

cab

Simplify, if possible. If not possible, write not possible: x y

y x+

+

3)3(2

Simplify, if possible. If not possible, write not possible: xyz

z x72 2

Simplify, if possible. If not possible, write not possible:)(9

3k mn +

11BCollecting like terms: more than one type of like terms in the expression(fractions and decimals used but not as coefficients of variables).

Simplify by collecting like terms: a xa x + 43


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53

Simplify by collecting like terms: 61257 ++ y y y

Simplify by collecting like terms: 323232 64 baabba

Simplify by collecting like terms: 8.02.0 x x

Simplify by collecting like terms: yx y y xy ++31

32

Simplify by collecting like terms: x x y x 2883 +

Simplify by collecting like terms: abba 7235

Simplify by collecting like terms: 13242 ++ abbaab

Simplify by collecting like terms: j j j 243 22 +

Simplify by collecting like terms: 323232 64 baabba

Simplify by collecting like terms: 4.0522.0 + z z z

Simplify by collecting like terms: 343 x x x +

Simplify by collecting like terms: 1221

++ x x

Simplify by collecting like terms: y x x y 473 ++

Simplify by collecting like terms:52472 m

Simplify by collecting like terms: babaab + 9.07.0

Simplify by collecting like terms: x yx x y x 532 44 +

Simplify by collecting like terms: cd dccd ++31

32

Simplify by collecting like terms: 3.222+

aa Simplify by collecting like terms: y x y x 22 ++

12B


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54

Solving linear equations with a variable on both sides. No fractions orparentheses involved. No solution or all real numbers as a solutionpossible. No operations on decimals needed.

Solve the following equation: x x 453 =

Solve the following equation: x x += 1554

Solve the following equation: 98 = x x

Solve the following equation: aa =+2

Solve the following equation: j j j 243 =

Solve the following equation: mm = 472

Solve the following equation: z z z += 1


Solve the following equation: 124 += x x


Solve the following equation: x x = 73

Solve the following equation: x x 453=

Solve the following equation: x x 324 =+



Solve the following equation: 5266 +=+ x x

Solve the following equation: x x =+ 21930

Solve the following equation: x x x 233 =++




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13BSolving linear inequalities (no parentheses, no fractions, no decimals involved;if a variables is only on one side its coefficient will be negative). No solutionor all real numbers as a solution possible.

Solve the following inequality: x x

Solve the following inequality: x x <


Solve the following inequality: 12 >+ x


Solve the following inequality: x328 <


Solve the following inequality: 5214 x x



Solve the following inequality: 21 >+ x

Solve the following inequality: 98 > x x

Solve the following inequality: 453 >+ a

Solve the following inequality: 11313 + aaa

Solve the following inequality: 2325 ++ x x

Solve the following inequality: aa 623 + x x



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56

14BThe difference of squares factorization (formula not given).

Factor the following expression: 136 2 x

Factor the following expression: 09.02 x

Factor the following expression: 24 nm

Factor the following expression: 2941

x

Factor the following expression: 22 100a y


y x

Factor the following expression: 22 6425 t s

Factor the following expression: 01.022

ba

Factor the following expression: 22 81nm

Factor the following expression: 22 9)2( aa

Factor the following expression: 22 364 y x


2

x

Factor the following expression: 221 nm

Factor the following expression:2594 x

Factor the following expression:161

9 4 m

Factor the following expression: 22 )7(25 y x

Factor the following expression: 166 x


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57

Factor the following expression: 404.0 s

Factor the following expression: 124 s

Factor the following expression: 425 10 x

15BRewriting algebraic expression in terms of another variable. Only a directsubstitution needed; relatively easy simplification.

Rewrite the expression2

3ain terms of x , given that xa 2= (i.e. substitute x2 for a ) Simplify.

Express P2 in terms of m , when mP = (i. e. substitute m for P ). Write your final answerwithout parentheses.

Express P2 in terms of m , when mmP = 2 (i. e. substitute mm 2 for P ). Write yourfinal answer without parentheses.

Express 3 A in terms of x , when x A 2= (i.e. substitute 2 x for A). Write your answer withoutparentheses. Simplify.

Express 3 A in terms of x , when x A = (i.e. substitute x for A). Write your answer withoutparentheses. Simplify.

Rewrite the expression131

xa

in terms of x , if it is given that xa 3= (i.e. substitute 3 x for a ).

Simplify.

Express 3 A in terms of x , when 7 x A = (i.e. substitute 7 x for A). Write your answer withoutparentheses. Simplify.

Express 3 A in terms of x , when 3 x A = (i.e. substitute 3 x for A). Write your answer withoutparentheses. Simplify.

Write the expression ba 2+ in terms of x , if xa 5= and xb = (i.e. substitute x5 for a and x for b ). Eliminate parentheses and simplify.


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58

Write the expression aa 42 + in terms of x , if 2= xa (i.e. substitute 2 x for a ). Eliminateparentheses and simplify.

Express y x y x

+

in terms of a and b if ba x += , ba y = (i.e. substitute ba + for x and

ba for y and simplify). . Eliminate parentheses and simplify.

Express the following expression in terms of x (i. e. substitute x for y). Simplify the newexpression:

y x y x

+

if x y =

Let 14,2 =+= xQ xP . Express QP + in terms of x (i.e. substitute 2+ x for P and 14 x for Q ). Write your final answer without parentheses, in a simplified form.

Let 14,2 =+= xQ xP . Express QP in terms of x (i.e. substitute 2+ x for P and 14 x for Q ). Write your final answer without parentheses, in a simplified form.

Let 4,2 =+= Q xP . Express PQ in terms of x (i.e. substitute 2+ x for P and 4 for Q ).Write your final answer without parentheses, in a simplified form.

Let 14 = xQ . Express 2Q in terms of x (i.e. substitute 14 x for Q ). Write your final answer

without parentheses, in a simplified form.

Let 2+= x A , x B 4= . Express B A + in terms of x (i.e. substitute 2+ x for A and x4 for B). Write the expression without parentheses. Simplify.

Let 2+= x A , x B 4= . Express AB in terms of x (i.e. substitute 2+ x for A and x4 for B). Write the expression without parentheses. Simplify.

Express AB A 2 in terms of x , if x B x A == , (i.e. substitute x for A and x for B). Writeyour answer without parentheses. Simplify.

Let 3 xP = and 22 x R = . Write the expression PR in terms of x (i.e. substitute 3 x for P and 22 x for R). Simplify.

Let 3 xP = and 22 x R = . Express the expression RP

in terms of x (i.e. substitute 3 x for P

and 22 x for R). Simplify.


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Rewrite the expression 22 ba in terms of x , if xa 5= and 1=b (i.e. substitute x5 for a and1 for b). Write the new expression without parentheses. Simplify.

Rewrite the expression 22 ba in terms of x , if xa = and xb = (i.e. substitute x for a and x for b). Write the new expression without parentheses. Simplify.

Rewrite the expression 22 ba in terms of a, if .ba = (i.e. substitute b for a ). Simplify.

Rewrite the expression ba 2 in terms of x , if 43 , xb xa == (i.e. substitute 3 x for a and 4 x forb). Write the new expression without parentheses. Simplify.

Rewrite the expression ba 2 in terms of a, if .ba = (i.e. substitute b for a ). Simplify.

Let2

,3x

D xC == . Express the expression CD in terms of x (i.e. substitute x3 for C and

2 x

for D ). Simplify.

Let2

,3x

D xC == . Write the expression DC in terms of x (i.e. substitute x3 for C and

2 x

for D ). Simplify.

Rewrite the expression 22 2 baba + in terms of x , if xba == ,1 , i.e. substitute 1 for a and x for b. Simplify.

Rewrite the expression 22 2 baba + in terms of x , if xb xa 2,3 == , i.e. substitute 3x for aand 2 x for b. Simplify.

Rewrite the expression 22 2 baba + in terms of x , if xb x

a == ,2

, i.e. substitute2 x

for a

and x for b. Simplify.

Rewrite the expression 22 2 baba + in terms of x , if xba == , i.e. substitute x for a and forb. Simplify

Express y x 2 in terms of s , if 3s x = , s y 2= , i.e. substitute 3s for x and s2 for y .Simplify, if possible.


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Express y x 2 in terms of s , if 3s x = , s y 2= . i.e. substitute 3s for x and s2 for y . Simplify,if possible.

Express 32 y x + in terms of s , if 3s x = , s y 2= . i.e. substitute 3s for x and s2 for y .Simplify, if possible.

Express4

2 xyin terms of s , if 3s x = , s y 2= . i.e. substitute 3s for x and s2 for y . Simplify,

if possible.

Express ab in terms of x , if 5

126,

1265

== b x

a , i.e. substitute1265 x

for a and5

126for b .

Simplify.

Express zt

z x

in terms of y, if , y z x

= y zt

2= , i.e. substitute , y for z x

and y2 for zt

.

Simplify.

Express22

zt

z x

in terms of y, if ,3 y z x

= y zt

2= , i.e. substitute ,3 y for z x

and y2 for

zt

. Simplify.

16B Simplifying algebraic expressions by removing parentheses first, andthen collecting like terms. Performing an operation on fractions or ondecimals might be needed (no expressions of the form 2)( ba )

Eliminate parentheses and simplify by collecting like terms: t t 4)5(2 +

Eliminate parentheses and simplify by collecting like terms: )4()2(3 55 x x

Eliminate parentheses and simplify by collecting like terms: qq 21)8)(6( +

Eliminate parentheses and simplify by collecting like terms: ) 4)(3( + aa

Eliminate parentheses and simplify by collecting like terms: )12(5

2 x

x

Eliminate parentheses and simplify by collecting like terms: ) 4()3(2 + aa


2 x

x

Eliminate parentheses and simplify by collecting like terms: )3(452 y x y x +


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Eliminate parentheses and simplify by collecting like terms: )3(73 ++ xy yx xy

Eliminate parentheses and simplify by collecting like terms: ) 333()136( 2334 + x x x x

Eliminate parentheses and simplify by collecting like terms: )32(1.0 aa

Eliminate parentheses and simplify by collecting like terms: )(23 bcaabccb ++


31

baba

Eliminate parentheses and simplify by collecting like terms: d aad )21

32

(6

Eliminate parentheses and simplify by collecting like terms: ) 24(13 22 + aa

Eliminate parentheses and simplify by collecting like terms: )54

4(93 baba

Eliminate parentheses and simplify by collecting like terms: qqq 52)62( +

Eliminate parentheses and simplify by collecting like terms: x x x + ))(1(

Eliminate parentheses and simplify by collecting like terms: x x )1(

Eliminate parentheses and simplify by collecting like terms: 1)3(2 + t t

Eliminate parentheses and simplify by collecting like terms: )3.0(32.0 + y y

Eliminate parentheses and simplify by collecting like terms: aa 12)26( +

Eliminate parentheses and simplify by collecting like terms: )18(274 +++ aaa

17BCollecting like terms (if possible) involving operations on fractions, ordecimals.

If possible, collect like terms. If not possible, write not possible 24.003.0 x x +

If possible, collect like terms. If not possible, write not possible 2273

21

aa

If possible, collect like terms. If not possible, write not possible mmn 7.05.0

If possible, collect like terms. If not possible, write not possible baab

61

3


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If possible, collect like terms. If not possible, write not possible:64mm

If possible, collect like terms. If not possible, write not possible:

38

2

38

2 mm+

If possible, collect like terms. If not possible, write not possible: cbaabc 08.07.0

If possible, collect like terms. If not possible, write not possible: baab 2.8

If possible, collect like terms. If not possible, write not possible:223

112 33 ss

If possible, collect like terms. If not possible, write not possible: x x72

31

If possible, collect like terms. If not possible, write not possible : 22 72.0 nmmn

If possible, collect like terms. If not possible, write not possible: yx xy 5.03.0


297 x

x


2x

x +

If possible, collect like terms. If not possible, write not possible: x x

32

5


21 +

If possible, collect like terms. If not possible, write not possible: x xy 17.024.0


21

If possible, collect like terms. If not possible, write not possible : 43 105.0 cc

If possible, collect like terms. If not possible, write not possible: 22 8.04.0 yx y x

18BSolving linear equations (inequalities) when the removal of parentheses isneeded; no fractions involved. No solution or all real numbers as asolution is a possibility. Operations on decimals might be needed.


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Solve the following equation: )1(423 = x x

Solve the following equation: x x x 11)32(6 =+

Solve the following equation: )12()3(=++

x x x

Solve the following equation: )1.0(32.0)3(2.0 x x x +=+

Solve the following equation: x x x =+ 47)14(2

Solve the following equation: )1()2(4 y y +=

Solve the following equation: )1(20 x+=

Solve the following equation: ( ) 1234=

x

Solve the following equation: )5(26 += x

Solve the following equation: 1.0)3.0(27.0 = x x

Solve the following equation: ( ) 66423 += mm

Solve the following inequality: )5(26 + x

Solve the following inequality:

)4(31113 ++>+ x x

Solve the following inequality: )25(714 x x x +

Solve the following inequality: )2(61 >+ x x

Solve the following inequality: )5(214 x x

Solve the following inequality: 23)2(3 ++ x x

Solve the following inequality: 166)52(3 +>+ x x

Solve the following inequality: ( ) aa 65323


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19BSolving equations for a given variable. Factorization of this variable might beneeded in the process. Variable might be on both sides of the equation.Variable could be in the denominator. No simplification needed at the end.More than one operation might be needed in the process.

Solve for x : bca

x=

+

Solve for x : ba x =+2

Solve for x : cbax =

Solve for x : 0= cbxax

Solve for x : b x

a=

Solve for the indicated variable: 4=+ bax for a

Solve for the indicated variable: au

m=

2

for u .

Solve for the indicated variable: st y x 32 +=+ for y .

Solve for the indicated variable: 1= A AX for A.

Solve for the indicated variable: xsy x 23 =+ for y.

Solve for the indicated variable: vst v +=3 for v .

Solve for x : x a = .

Solve for x : xbyax 3= .

Solve for m : k n

m+= 4

22

Solve for b : cab =

Solve for b: cabc = 12

Solve for x : a x

nm=

2


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Solve for s: t ssx =

Solve for x : 12 = xax

Solve the following equation ed y x

+= for y .

20BWriting phrases as algebraic expressions (involving 2 operations).

Use the letter x to represent a number and write the following as algebraic expression:Seven more than one third of a number

Use the letter x to represent a number and write the following as algebraic expression:A quantity decreased by 9, and then multiplied by A

Use the letter x to represent a number and write the following as algebraic expression:A number cubed, and then decreased by y

Write a direct translation of the following phrases as an algebraic expression.Multiply 3 by x , and then add y.

Write a direct translation of the following phrases as an algebraic expression.Multiply the sum of a and b by 4.

Write a direct translation of the following phrases as an algebraic expression. Do not simplify.The opposite of x , then raise it to the sixth power.

Write a direct translation of the following phrases as an algebraic expression. Do not simplify.Subtract 3 from y, and then multiply it by z .

Write a direct translation of the following phrases as an algebraic expression.Raise x to the third power, and then multiply by 9.

Write a direct translation of the following phrases as an algebraic expression. Do not simplify.

Multiply x by 9, and then raise the result to the third power.Write a direct translation of the following phrases as an algebraic expression.

The difference of a and b, then divided by c

Write a direct translation of the following phrases as an algebraic expression.Divide 3 by y, and then add x

Write a direct translation of the following phrases as an algebraic expression.


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Raise x to the third power, raise y to the seventh power, and then add them together

Let C be a variable representing the temperature in Celsius. Write the following phrase as analgebraic expression: Nine fifths of the Celsius temperature plus 32.

Let m represents mass, and c speed of light. Use m and c to write the following phrase as analgebraic expression: the product of mass and the square of speed of light.

Use the letter X to represent a number and write the following as an algebraic expression:A number decreased by 7, and then the result is doubled.

Use the letter Y to represent a number and write the following as an algebraic expression:The opposite of a number, then raised to one hundred and twenty first power

Use the letter C to represent a number and write the following as an algebraic expression:A number, first divided by 2, and then raised to the third power.

Use the letter s to represent a number and write the following as an algebraic expression:Multiply a number by 9, and then subtract it from c.

Use the letter m to represent a number and write the following as an algebraic expression:The difference between a number and 4, then multiplied by y.

Use the letter X of your choice to represent a number and write the following as an algebraicexpression: Take one fourth of a number, and then subtract 5.

21BIdentifying linear equations and writing them in a standard form.Recognizing the value of parameters in the representation.

Rewriting algebraic expressions to match a prescribed format and identifyingthe values of given variables.

Determine if the following equation is linear in one variable. If it is not linear, write not linear.If it is linear, express it in the form 0=+ bax , 0a . Determine the values of a and b in your

representation: 014

= x

Determine if the following equation is linear in one variable. If so, express it in the form0=+ bax , 0a . Determine the values of a and b in your representation: x x 327 =+


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Determine if the following equation is linear in one variable. If it is not linear, write not linear.If it is linear, express it in the form 0=+ bax , 0a . Determine the values of a and b in yourrepresentation: 22)3(2 x x x =+

Determine if the following equation is linear in one variable. If it is not linear, write not linear.If it is linear, express it in the form 0=+ bax , 0a . Determine the values of a and b in yourrepresentation: 013 2 = x

Write the expression 222 )1()2( r y x =++ in the form: 222 )()( r q y p x =++ Whatare the values of p and q?

Write the following expression in the form 2 A , where A is any algebraic expression. Identify A : 281 x

Write the following expression in the form 2 A , where A is any algebraic expression. Identify A : 8 x

Write the following expression in the f

017 Final Exam Topics

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