Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

For instance, the area of a rectangle is equal to the product LW where L represents its length and Wits width. Let us consider a rectangle with the length and width equal to each other. Recall that thistype of a rectangle is called a square. Let a denote the side of the square. We have W a,L a . Wecan express the area of a square in terms of a . To this end, we replace both W and L with a :2LW aa aAnd thus the area of a square is equal to the square of its side.Now, if for example, we would like to fine the area of a square, whose side is 2 inches long, wedetermine that a 2 (side is 2 inches long), and the area can be found by evaluatinga2 2 2 4The area of the square is 4 (actually 4 in 2 ).Example 7.5 Ifx z, express the following expressions in terms of z.2a) x b) xSolution:2 2 2a) x ( z) zb) x (z) z22Example 7.6 Express ( m n)(m mn n ) in terms ofa) x , if m 2, and n 3x.b) m , if n m.Solution:a) We replace m with 2, and n with 3 x , and simplify.22222( m n)(m mn n ) (2 3x)(2 2(3x) (3x)) (2 3x)(4 6x 3 x2 (2 3x)(4 6x 9x)b) We replace n with m , and simplify.22222 2 22( m n)(m mn n ) ( m m)(m mm m ) 2m(m m m ) 2mm 2m2)3Example 7.7 If2A vandB 2 2v, express ( A B)(A B ) in terms of v .Solution:We must find an equivalent form of the above expression expressed only in terms of2and B . We will remove parentheses.22 2 2( A B)(A B) A AB BA B A B .22Now, we can replace A with v , B with 2 v to get2 2( A B)(A B) A B v 2v v.2AEx.1 If x2 10, evaluate the following.<strong>Exercises</strong> with Answers (For answers see Appendix A)72
2 1a) 2x b) 30 5Ex.2 If A 3, evaluate the following.5a) 2Ab)c)5 2 2Ad)a bEx.3 Evaluate the following expressions, if 2.ca ba) 2cb)c)2 a b c a b c Ex.4 If x y 2, evaluate.2a) 7x 7yb)c) x yd)32 x c) 3x2 2 ( 2A3 23AA5 ) 2x y 7 7( x y)2Ex.5If1 A27, evaluate.a) 1 Ab)c)1 A1A1d)2AEx.6 Evaluate the following expressions, if 2a b c 7.a) c b 2ab) 2 a b cc) ( 2a b c)d) 2a ( c b)e) a b c aEx.7 Evaluate the following expressions, if GHJ 1.1a) JHGb) GHJc) G ( 2) H(1)Jd)G3(HJ)3aEx.8 Evaluate the following expressions, if 3.b73
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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
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3xd) x( y)e) 2f) 2x yz w(t)Ex.4 T
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Ex.16 Let x 3. Rewrite the express
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e) x5f) x2Ex.28 Substitute“undefi
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Lesson 2___________________________
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Solution:Please, notice the use of
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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 62 and 63: 24x ( 5x)g)xa bi)7(a b)bc ( b e)
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 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
Page 112 and 113: a x and b 3 , so now we can rewri
Page 114 and 115: Ex.9 For each of the following expr
Page 116 and 117: 114xc) y 5d) y 3x 2 0e) 3y 6x1f
Page 118 and 119: APPENDIX A:Lesson 1ANSWERS TO EXERC
Page 120 and 121: 49C 3255 2(L+W)62mc75a) a b expon
Page 122 and 123: 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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