Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

Help available: You can find help in the Learning Lab for math in room B2-36 weekdays and inroom B1-28 Monday- Thursday evenings and Saturdays on Main Campus. During fall and springsemesters, free, peer tutoring is available beginning with the second week of classes for all currentCCP students and free, weekly workshops begin in the third week of the semester. The peer tutors areexperienced CCP students who have taken many of the courses in which they tutor. <strong>Math</strong> specialistsalso tutor as well as lead workshops. Check at Regional Centers for days and times of services. Also,during summer sessions, offerings may vary.2July 2012
Lesson 1__________________________________________________________________________________Topics: Variables and algebraic expressions; Evaluation of algebraic expressions.__________________________________________________________________________________Variables and algebraic expressions as symbolic representations of numbersSuppose that you thought of a number but you did not tell me what it was. I can think about yournumber as a number x . The symbol x is an example of a variable.VariableA variable is a symbol that represents an unknown number.The choice of the name of a variable is arbitrary. One can as well call it n , m or . We treatvariables as if they were numbers. We can, for example, add numbers to variables: m 3, orsubtract other variables from them:m . We can multiply them: 4 m ; divide: ; raise to anymgiven power:2m ; and then, if we wish, add all of the expressions together:resulting expressions are called algebraic expressions. 24 m m . ThemAlgebraic ExpressionAn algebraic expression is a number, variable or combination ofthe two connected by some mathematical operations likeaddition, subtraction, multiplication, division, or exponentiation.Notice that numbers and variables are also examples of algebraic expressions. We can refer to 3,x , ory as algebraic expressions. Just like 4 5,2 5,or 3 2 1 are numbers (written in a „complicated‟ way,but numbers), algebraic expressions 4 m,x y or a n b are symbolic representations of numbers.Both variables and algebraic expressions can be thought of as unknown numbers.Correct language and conventions used when forming algebraic expressionsAlgebraic expressions are read using the same terminology as in arithmetic. For example, A 5 can be2read as “A plus 5” or “the sum of A and 5”; y can be read as “ y raised to the second power” or “ ysquared”; x is read “minus x ” or “the opposite of x ”. The following convention is commonlyadopted to indicate multiplication of a number and a variable, or multiplication of variables.To denote the operation of multiplication, the sign of multiplication between a number and avariable or between two variables or expressions does not have to be explicitly displayed, so forexample,2A means 2 times Axy means x times y,y(a+b) means y times the quantity a+b3
Page 1 and 2: Math 017MaterialsWithExercises
Page 3: TABLE OF CONTENTSLesson 1Variables
Page 7 and 8: e) „minus x ‟ or „the opposit
Page 9 and 10: 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
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Mistake 5.1When factoring 3 from 3x
Page 60 and 61:
Ex.13 Factor2a) 5 a from the follow
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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
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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
Page 72 and 73:
Lesson 7___________________________
Page 74 and 75:
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
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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
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■ Solve the inequality 4x 9 1.
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■ Solve the following inequality
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Ex.10 Graph the following number se
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d) z 3e) z 13 Ex.22 Knowing x 1
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Example 11.2 The expression( 22 2x
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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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___________________________________
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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