Math 017 Materials With Exercises

More documents

Recommendations

Info

$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

a) b b) a c) tEx.15. SolveEx.16. Solvex 6 for x , and then evaluate, if 1a3aa .2 mn 2 for n , and then evaluate, if 43mnmm .Ex.17. If b represents the base of a triangle, h is the height, and A is the area of the triangle, thenbhthe following is true: A .2a) Solve the above formula for hb) Find the height of a triangle with base b 2 inches and the area A 4 square inchesEx.18. If L represents the length of a rectangle and W its width, then the perimeter P of therectangle is given by the formula P 2(L W)a) Solve the above formula for W .b) Find the value of W when P 4,and L 1.c) Find the width of a rectangle with perimeter 10 inches and length equal to 3 inches.94
Lesson 10__________________________________________________________________________________Topics: Linear Inequalities; Graphing sets of the type x a , x a on a number line.__________________________________________________________________________________We will now be discussing inequalities.Meaning and symbolic notation for ‘less (greater) than’, ‘less (greater) than or equal to’Recall thatx < 2 means that a number x is less than 2x > 2 means that a number x is greater than 2.Notice, that x 2 has exactly the same meaning as 2 x , and x 2 the same as 2 x (just as 1 2has exactly the same meaning as 2 > 1).The following symbols are also in usex ≤ 2 means that a number x is less than or equal to 2x ≥ 2 means that a number x is greater than or equal to 2.Again, x 2 is equivalent to 2 x, x 2 is equivalent to 2 x.The only difference between „ x 2‟ and „ x 2‟ is that 2 satisfies the first inequality but does notsatisfy the second one (2 is not less than 2). Similarly, 2 satisfies ‘ x 2’, but does not satisfy ‘ x 2 ’.Example 10.1 Describe the following set of numbers using inequality signs.a) All numbers x that are positiveb) All numbers x that are non-negativec) All numbers x that are at most equal to 9d) All numbers x that are at least equal to 9e) All numbers x that are not less than 9Solution:a) x 0 (zero should not be included)b) x 0 (zero should be included)c) x 9 (at most means that amount or less)d) x 9 (at least means that amount or higher)e) x 9 (not less than includes the given number and higher)Example 10.2 Determine which of the following numbers satisfies the condition x 2. 4, 2.1, 2, 0.9, 0, 1Solution:95
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 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 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 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 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 136 and 137: 3. Let m = ─3. Evaluate the follo
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
show all

Math 017 Materials With Exercises

Create successful ePaper yourself

Delete template?

Save as template?