Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

24x ( 5x)g)xa bi)7(a b)bc ( b e)h)b2x 3j)2xEx.25 Simplify, if possible. Otherwise write “not possible”.2a)b)2x 2y24x 5xc)x3xe)23x 9xa 3bg) 3b aa b ci)a b12x 4k)3xxy xym)3yxo)4uv22 6vu2uv2x2yxy xz3x23x 3xd)6x3 4 4a b 4baf)a2xh)2 52x xxyj)2xy xy 4x12y 8zl)4u 2v sn)s 2v u 2vuxyp)43xy 6x2y2z60
Lesson 6__________________________________________________________________________________Topics: Addition and subtraction of algebraic expressions.__________________________________________________________________________________In this lesson we will learn how and when to perform the operations of addition and subtraction ofalgebraic expressions.Like terms22Consider 3 x 4y z . The expression consists of three terms: 3x , 4y, z . Each term can beviewed as a product of a numerical and non-numerical factor (recall that numerical factors are alsocalled numerical coefficients). And so,3 x has a numerical factor 3, non-numerical factor x22 4y has a numerical factor 4 , non-numerical factor yz has a numerical factor 1, non-numerical factor zLike TermsLike terms are terms that have equal non-numerical factors.What is meant by non-numerical factors being equal is that they are equal (equivalent) as algebraicexpressions. That does not mean that they „look identical‟. You will notice that in the second examplebelow, xy and yx are equivalent even though they do not „look identical‟.Examples:3 a and 7 a are like terms because their non-numerical factors, both a ‟s, are equivalent.4 xy and 3yxare like terms because xy and yx are equivalent.2x and3x are not like terms since2x is not equivalent toAnother way of looking at like terms is that two terms are alike if they can be written as expressions3 2that have the same variables with the same exponents. For example, 5x y and 4 yx 3 y are like terms,because yx 33 24 y can be written as 4xy , and thus both expressions consist of the variable x raised tothe third power and variable y raised to the second power. It should be stressed once again, that beinglike terms does not mean ‘looking identical’.3x .Example 6.1 Circle all expressions that are like2 34yxyx 3 y23 y3 2x .0 .2( xy)2y2 32xySolution:We should circle3yx y2x y2123 23 2 x y ).2 3 4yx (because2 3 3 2 4yx 4xy ) andyx 3 y2(because61
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Math 017MaterialsWithExercises
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TABLE OF CONTENTSLesson 1Variables
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Lesson 1___________________________
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e) „minus x ‟ or „the opposit
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For example,Evaluate 5 x when x 10
Page 11 and 12: 3xd) x( y)e) 2f) 2x yz w(t)Ex.4 T
Page 13 and 14: Ex.16 Let x 3. Rewrite the express
Page 15 and 16: e) x5f) x2Ex.28 Substitute“undefi
Page 17 and 18: Lesson 2___________________________
Page 19: Solution:Please, notice the use of
Page 22 and 23: g)i)4( a 2)h)8y (x)4(ab)j) ( a d)
Page 24 and 25: 1 2Ex.19 If possible, evaluate when
Page 26 and 27: Lesson 3___________________________
Page 28 and 29: Commutative Propertyof Additionx y
Page 30 and 31: 2 x 2 xFor example, and thus als
Page 32 and 33: Example 3.10 Determine which of the
Page 34 and 35: Exercises with Answers (For answers
Page 36 and 37: Ex.16 Write the following expressio
Page 38 and 39: s) ( 0.2xy)( 0.3z)t)4x1Ex.24 Is 1
Page 40 and 41: Lesson 4___________________________
Page 42 and 43: Numerical coefficientsNumerical Coe
Page 44 and 45: For your convenience, we will displ
Page 46 and 47: 9 818081a) 9 98097 6 76134 4 4 4
Page 48 and 49: Ex.8Simplify by raising to the indi
Page 50 and 51: 73a 2xxi) 2aj)2( 42a)x(3xk)4x2 ) 3
Page 52 and 53: Lesson 5___________________________
Page 54 and 55: FactorizationThe Distributive Law l
Page 56 and 57: Simplification of algebraic fractio
Page 58 and 59: Mistake 5.1When factoring 3 from 3x
Page 60 and 61: Ex.13 Factor2a) 5 a from the follow
Page 64 and 65: Adding and subtracting like termsIf
Page 66 and 67: ) This should be written as 4x 2
Page 68 and 69: Ex.4 Circle all terms that are like
Page 70 and 71: 682 122k) 6 ( d a) a dl) 3a1(4a
Page 72 and 73: Lesson 7___________________________
Page 74 and 75: For instance, the area of a rectang
Page 76 and 77: a) a b 2bc) a bd) ae)b)aba 22a a
Page 78 and 79: Ex.24 Express the expressiona) m s
Page 80 and 81: A solution, the solution set, and w
Page 82 and 83: ■ Solve the following equation 3x
Page 84 and 85: sides (subtracting 4 x from both si
Page 86 and 87: Mistake 8.2While solving an equatio
Page 88 and 89: Ex.12 Determine whether the followi
Page 90: Lesson 9___________________________
Page 94 and 95: xy x 1 yFactor x .x( y 1)1yDivide
Page 96 and 97: a) b b) a c) tEx.15. SolveEx.16. So
Page 98 and 99: For each number you should check if
Page 100 and 101: ■ Solve the inequality 4x 9 1.
Page 102 and 103: ■ Solve the following inequality
Page 104 and 105: Ex.10 Graph the following number se
Page 106 and 107: d) z 3e) z 13 Ex.22 Knowing x 1
Page 108 and 109: Example 11.2 The expression( 22 2x
Page 110 and 111: Solution:a) To match the form y mx
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a x and b 3 , so now we can rewri
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Ex.9 For each of the following expr
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114xc) y 5d) y 3x 2 0e) 3y 6x1f
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APPENDIX A:Lesson 1ANSWERS TO EXERC
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49C 3255 2(L+W)62mc75a) a b expon
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3(m n)a(x1)g)h)2tx19s s s sThe opp
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52233x1 2 x5 3 1513 a) m ( 2m) 2mb
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c) Numerator: one term, 3ab (with t
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18 a) 9 b) 3 c) 3 d) 3e) 6 f) 279
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11 a) x 1 b)12 a) x abcx a b42 b
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c) x 2d) a 7e) x 10f) a 225 a)
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x or 4x ( 7) 0; a 4; b 7g) x (
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3. Let m = ─3. Evaluate the follo
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1. Write the following statements a
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6. Solve the following equations:8.
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8. Factor the following expressions
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3 ;b) x 3 y 6 xy 2 A xy 28. a) x
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Math 017 Materials With Exercises

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