ASSET 2_AnswerKey - Learning Center- 1 ASSET 2 Elementary...

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Learning Center-- 1 ASSET 2 Elementary Algebra Review 1) A . Natural or Counting numbers : ... 6 , 5 , 4 , 3 , 2 , 1 B. Integers : ... 3 , 2 , 1 , 0 , 1 , 2 , 3 ... C. Irrational Numbers : 2 , Π D . Whole Numbers : ... 4 , 3 , 2 , 1 , 0 E . Rational Numbers : ... 3 , 2 , 1 , 2 / 1 , 0 , 1 , 2 , 3 ... F. Real numbers: Π , 2 , 3 2 , 0 , 5 11 , 3 ... 2) A. -5 2 = -(5*5) = -(25) = -25 -25 B. (5 x 10 -12 )(7 x 10 10 ) = 35 x 10 -2 = 3.5 x 10 -1 3.5 x 10 -1 The exponent tells how many times 5 is multiplied to itself. Multiply the numbers and add the exponents. The decimal must always be placed after the first number. When the decimal moves the exponent changes. C. (5 x 10 -2 )+(7 x 10 2 ) = .0005 (2+2=4) = .0005x 10 2 + 7 x 10 2 = 7.0005 x 10 2 7 x 10 2 or 700.05 D. ( ) ( ) 2 5 4 3 6 2 i ÷ = ( ) ( ) 2 5 4 9 6 i ÷ = ( ) i 10 5 6 ÷ = i 10 30 = 2 10 30 10 30 i i i i i = = 10 30 i = 10 10 10 30 ÷ ÷ i = 3 i 3 i E. 2(7-4) + 8 =2(3) + 8 =6 + 8 = 14 14 One can only add when the exponents are the same. Convert the lowest exponent to match the highest exponent by moving the decimal over the sum of the two exponents. Follow the order of operations. Because i represents 1 , the denominator must be rationalized. When i is squared it becomes -1. Next reduce the fraction. Follow the order of operations.
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Learning Center-- 2 F. 7 + [8(2-3 2 ) – 5] =7 + [8(2-9) – 5] =7 + [8(-7) – 5] =7 + (-56 – 5) =7 +(-61) = - 54 - 54 G. 2x 2 - 7x + 2; solve when x = -3 =2(-3) 2 - 7(-3) + 2 =2(9) + 21 + 2 =18 + 23 =41 41 H. 5b 2 -2b+1 solve when b = -3 5(-3) 2 -2(-3)+1 =5(9)+6+1 =45+7 =52 52 I. 3x 2 y+2xy-5y Solve when x = -2; y = 3; =3(-2) 2 (3)+2(3)(-2)-5(3) =3(4)(3)+6(-2)-15 =3(12)-12-15 =36-12-15 =9 9 Follow the order of operations. Substitute x with -3 and solve. Substitute b with – 3 and solve. Substitute and solve. J. x y y x + 2 12 Solve when: X = -2; y = 3 2 3 3 ) 2 ( 2 12 + = 2 3 3 ) 4 ( 1 12 + = 2 3 6 6 3 ) 4 ( 6 6 1 12 6 6 = 6 9 6 8 6 72 + = 6 71 6 71 3) A . 7x -3 = 3 7 x 3 7 x B. (3x 3 )(7x 5 ) (3x 3 )(7x 5 ) =21x 8 21x 8 C. (5x 2 )( 3x 7 ) =(5x 2 )(3x 7 ) =15x 5 = 5 15 x 5 15 x Substitute and solve Find a common denominator. Move the x with the negative exponent into the denominator and change the sign. Multiply the numbers and then add the numbers. x n * x m = x n+m x 2 * x 3 = x 5 See the previous two problems. 1 1 2 3
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Learning Center-- 3 D. ( )( ) 3 3 4 12 x x ( )( ) 3 3 4 12 x x =48x 0 =48(1) =48 48 E. 2 5 10 35 x x 2 5 10 35 x x = 2 5 10 5 35 5 x x ÷ ÷ = 2 5 2 7 x x = 2 * 7 2 5 x x = 2 7 3 x 2 7 3 x F. 3 3 2 8 12 y x xy 3 3 2 8 12 y x xy = 3 3 2 8 4 12 4 y x xy ÷ ÷ = 3 3 2 2 3 y x xy = 2 3 3 2 3 y y x x = 5 4 2 3 y x 5 4 2 3 y x See the previous problems for instructions. x 0 = 1 Divide the numbers and subtract the exponents. The sum of the exponents must always be a positive number. m n x x = x n-m 3 2 x x = 2 3 1 x = x 1 See the previous problem for instruction. G. 3 2 2 3 6 3 y x y x 3 2 2 3 6 3 y x y x = 3 1 2 2 3 6 3 3 3 ÷ ÷ y y x x = 3 1 1 2 1 y x = 3 3 3 3 3 * 1 3 * 1 3 * 1 3 * 1 2 1 2 1 y x y x = = 8 3 3 y x 8 3 3 y x H.
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ASSET 2_AnswerKey - Learning Center- 1 ASSET 2 Elementary...

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