Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

Ex.33 If possible, evaluate x y when3 2a) x , y 5 32 9b) x , y 7 14c) x 0.2,y 1.08Ex.34 If possible, evaluate xy when2 22a) x , y 11 99b) x 4,y 10c) x 0.2,y 0. 01Ex.35 If possible, evaluate yx when2a) x ,11b)y229910y 0.x 4,y c) x 0.2, 01mEx.36 If possible, evaluate ( x) whena) x 10,m 7b) x 2,m 41c) x ,2m 3d) x 0.1,m 5Ex.37 Use the letter x to represent a number and write the following statements as algebraic1expressions. Then evaluate each expression when x .2a) A number doubledb) Three fourths of a numberc) A number raised to the second powerEx.38 Evaluate t , when t 1,t 1Based on your results, which of the following are true?a) t is always positiveb) t is always negativec) t may be positive or negative depending on the value of t14
Lesson 2__________________________________________________________________________________Topics: Algebraic expressions and their evaluations; Order of operations.__________________________________________________________________________________Recall the order of operations.The order of operationsWhen evaluating arithmetic expressions, the order of operations is1) Perform all operations in parentheses first.2) Do any work with exponents.3) Perform all multiplications and divisions, working from left to right.4) Perform all additions and subtractions, working from left to right.If a numerical expression includes a fraction bar, perform all calculations above and belowthe fraction bar before dividing the top by the bottom number.Let x be an unknown number. If we increase the number by 1, the resulting number can berepresented by x 1. Now, suppose that after adding 1, we multiply some other number, called y , bythe result of the addition. We may now write the expression y ( x 1). Let us analyze why we mustplace parentheses around x 1. If an algebraic expression involves more than one mathematicaloperation, then the order of operations is followed. Thus, if we simply write yx 1(without usingparentheses), we would only be multiplying y and x, rather than y times the entire quantity x 1.According to the order of operations, using parentheses in y ( x 1)indicates that we add 1 to x first,and then multiply the result by y. Expressions yx 1and y ( x 1)have entirely different meanings,and only y ( x 1)correctly represents the result of operations performed in this example.The order of operations is used when algebraic expressions are evaluated.2For example, let us evaluate 2 x x when x 3.2 x 2 x replace each x with 3223 3 raise 3 to the second power2 9 3 multiply it by 218 3 subtract 3 from the result15Example 2.1 Rewrite the following expressions and circle the arithmetic operation together with itsoperands that has to be performed first. Write the name of the operation next to yourexpression.4a) 3 5yb) 2xSolution:15
Page 1 and 2: Math 017MaterialsWithExercises
Page 3 and 4: TABLE OF CONTENTSLesson 1Variables
Page 5 and 6: Lesson 1___________________________
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: e) x5f) x2Ex.28 Substitute“undefi
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 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
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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
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Mistake 8.2While solving an equatio
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Ex.12 Determine whether the followi
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Lesson 9___________________________
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xy x 1 yFactor x .x( y 1)1yDivide
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a) b b) a c) tEx.15. SolveEx.16. So
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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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___________________________________
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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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