Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

3. Let m = ─3. Evaluate the following expressions if _______________________________________possible (otherwise, write “undefined”): 5a2 m 5 m 18. Write in three different ways.a) m b) c)d) 3 2m2b2 m 3______________________________________________________________________________________ 9. Determine which of the following expressions are24. Evaluate uv if possible (otherwise, write2aequivalent to2 1“undefined”), when u and v .b3 31 2a(1 1a2, 2a b, 2a, (1 1a) b,_______________________________________ b b bbm ___________________________________________5. Evaluate n if possible (otherwise, writep10. Determine which of the following expressions areequivalent to“undefined”), when m 0.1,n 0.02, p 1.mn k :k mn nm k mn ( k)m(n k) k mn___________________________________________________________6. Let F be a variable representing the temperature. __________________________________________Use F to write the following statement as an algebraic 11. Replace with expressions such that theexpression:five-ninth times the difference of F and 32.resulting statement is true. Use parentheses whenneeded.___________________________________________a) xyz yz7. Perform all numerical operations if possible (ifAperforming a numerical operation is not possible,b) A 7 write “not possible”).10b2 2x3 9ya b a) b) 2 3cc) x (3) d) c) ( a b) 53 5c ce) 2x 3 (2 5) 4nf) 24 ( 5)_____________________________________________________________________________________Sample Test 3 (Lesson 1-3)_____________________________________________________________________________________1. Use the letter x to represent a number and write thefollowing statements as algebraic expressions.a) Half of a number is subtracted from 7.b) Twice a number is added to 5, and then theresult is multiplied by 3.c) The number is tripled, and then squared.___________________________________________2. Write the opposite (do not simplify).x ya) 2x + 3y b)x y_________________________________________3. Name the operation that should be performed first.23 x y b) x yz c) 4x d) 4x 2a) ___________________________________________4. If possible (otherwise, write “undefined”), evaluate─3xy when a) x = 6 and y = 253b) x 6 and y 4 c) x = 0.1 and y = 0.2.5. If possible (otherwise, write “undefined”), evaluatex when a) x = 6 and y = 2y53b) x 6 and y 4 c) x = 0.1 and y = 0.2.___________________________________________6. If possible (otherwise, write “undefined”), evaluatexwhen1 xa) x 0 b) x 1 c) x 1___________________________________________x y7. State which expressions are equivalent to2x ya) x y 2 b) x y2 c) 2 2 y x 1d)e) ( x y)2 2134Sample Tests
8. Replace X with expressions such that the resultingstatement is true. Use parentheses when needed.a) x 2 y 3z 3z 2y Xa Xb) 3 by ym n nc) X .v v9. Perform all possible numerical operations. If noneis possible, write “not possible”a) 5 6 2xb) 6(2x)c) 6 2xd) 2 53 6x e) 2 5 x3 6___________________________________________2210. Show that ( x) is not equivalent to x by2evaluating both expressions when x 3_____________________________________________________________________________________Sample Test 1 (Lesson 4-6)_____________________________________________________________________________________1. Write the following statements as an algebraicexpression using parentheses where appropriate, andthen remove parentheses:a) The product of A and B A 3b) The opposite of x 2_______________________________________35 32. Factor 2a from the expression 8ab 10a.___________________________________________2 4 23. Factor from the expression a 7 7 7_______________________________________4. If possible, add (or subtract) the followingexpressions. If not possible, write “not possible”.12a) 2hk kh b) ab ab22x 1c) mn nmn d) x3 6__________________________________________5. Collect like terms in 4yx y 3xy 8y 7y,1and then evaluate it when x 2,y .4_______________________________________6. Remove parentheses and then collect like terms1a) 7b (3b 6)b) 4x ( x 2)32c) ( 3x b)d) 2x2 (2x1)(x 2)7. Simplify, if possible (assume that all denominatorsare different from zero). If not possible, write “notpossible”.ax b xy 3a)b)axx2( a b)2c c)d) 2xyb a xyx 2e)2 x_______________________________________8. Write as a single exponential expression. For eachexpression, identify the numerical coefficient.5( a)7 2 3a) b) x ( 2x) 32abc)33a2ab___________________________________________9. Evaluate the following expressions:4520a) b) 3a432___________________________________________10. Find such X that the following is true:Xa) 4 7 2 1 b) 3X 1 9 5_____________________________________________________________________________________Sample Test 2 (Lesson 4-6)_____________________________________________________________________________________Sample Tests 135
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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)
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1 2Ex.19 If possible, evaluate when
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Lesson 3___________________________
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Commutative Propertyof Additionx y
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2 x 2 xFor example, and thus als
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Example 3.10 Determine which of the
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Exercises with Answers (For answers
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Ex.16 Write the following expressio
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s) ( 0.2xy)( 0.3z)t)4x1Ex.24 Is 1
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Lesson 4___________________________
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Numerical coefficientsNumerical Coe
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For your convenience, we will displ
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9 818081a) 9 98097 6 76134 4 4 4
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Ex.8Simplify by raising to the indi
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73a 2xxi) 2aj)2( 42a)x(3xk)4x2 ) 3
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Lesson 5___________________________
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FactorizationThe Distributive Law l
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Simplification of algebraic fractio
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Mistake 5.1When factoring 3 from 3x
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Ex.13 Factor2a) 5 a from the follow
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24x ( 5x)g)xa bi)7(a b)bc ( b e)
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Adding and subtracting like termsIf
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) This should be written as 4x 2
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Ex.4 Circle all terms that are like
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682 122k) 6 ( d a) a dl) 3a1(4a
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Lesson 7___________________________
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For instance, the area of a rectang
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a) a b 2bc) a bd) ae)b)aba 22a a
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Ex.24 Express the expressiona) m s
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A solution, the solution set, and w
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■ Solve the following equation 3x
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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
Page 124 and 125: 52233x1 2 x5 3 1513 a) m ( 2m) 2mb
Page 126 and 127: c) Numerator: one term, 3ab (with t
Page 128 and 129: 18 a) 9 b) 3 c) 3 d) 3e) 6 f) 279
Page 130 and 131: 11 a) x 1 b)12 a) x abcx a b42 b
Page 132 and 133: c) x 2d) a 7e) x 10f) a 225 a)
Page 134 and 135: x or 4x ( 7) 0; a 4; b 7g) x (
Page 138 and 139: 1. Write the following statements a
Page 140 and 141: 6. Solve the following equations:8.
Page 142 and 143: 8. Factor the following expressions
Page 144 and 145: ___________________________________
Page 146: 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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