Arithmetics. Homeworks

Page 1

Arithmetics Homeworks

OpenMaths.com 1.1.1

Ver 01:05/05/2010



NOTA La clasificación decimal de todos los temas de este manual tienen implícito el comienzo 1.1.1 correspondiente a 1

SCIENCE

1.1

MATHEMATICS

1.1.1

ARITHMETICS

COPYLEFT Este material así como los applets, powerpoints, videos y archivos de sonido asociados, puede ser distribuido bajo los términos y condiciones definidos en Open Publication License versión 1.0 o posterior (La versión más reciente está disponible en http://www.opencontent.org/openpub/). El contenido está sujeto a constantes cambios sin previo aviso. Su fin es didáctico y solo pretende la universalización de la cultura. Está escrito en base a la colaboración de las miles de personas que componen nuestra comunidad OpenUepc. Se ha exigido a los autores que referencien todas las fuentes utilizadas y figuran al final del texto. Cualquier distribución del mismo debe mencionar a OpenUepc como fuente. Miguel Pérez Fontenla miguelperez@edu.xunta.es INDICE AUTORES

Iniciado por: Miguel Pérez Fontenla 05/05/2010



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1 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify −

1 2 3 2 − −  −   2 3 4 6

−1

(Answer : -3)

2.- Perform and simplify

11 ' + 1' 1 − 3'21

3.- Express these square roots in the simplest possible terms

600 ;

968

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2 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach 1 −2  1  3   2  −   0'13 6  2   1.- Perform and simplify  − 1  0 ' 1 9  4 −1      3   

( Answer : 2 )

2.- Perform and simplify

27 3 9 ⋅ 81−1  1 3 −3  3 6   

( Answer : 3 )

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3 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify the following expression:

Answer:

4

3 ⋅ 4 9 ⋅ 3 27 −1 3 −2 ⋅ 9 3 ⋅ 81−1

3

 1 2 3 1  − + 0' 2 −  9 2.- Calculate and simplify the following expression:  3 4 5 +   − 1  2  3 1      −  9    3  4  5

Answer:

3

 10     23 

1'3

4

3.- Check if it is true or false the following identity: 013 '  1 =  0' 6  0'2 

−1

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4 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify the following expression:

Answer:

6

88 ⋅ 0'176

140 9

1.Perform and simplify 13  3  7 4 2 1     − 1   1    − 2  2'3 +  −  + − −    6  4  21 5 15 3     6   3 

Answer:

2 3

the

following

expression:

89 270

3.- Perform the following arithmetic operation, symplifying the final answer:

(4 + (12 − 2 3 ) + (15 − 05 ) 2 ) ÷ (14 − ( −2) 2 )

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5 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

−1

 −1  3 1.- Check if it is true or false   = −3  27 

2.- Write in one only index of three the following expression:

3 3 3

−2

3 .- Perform and simplify

(−1) 4 ÷ ( 25 )3  ÷ (− 53 ) 2 − 5−1 

(Answer : 16/625)

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6 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Work out the final value of the following arithmetic expression: 2 − 3 ⋅ 2 4 ⋅ 25  2 − 3 ⋅ 2  ÷ 2 0  2 2 ⋅ 2 −5  2 ⋅2 

−1

2.- Write in one only index of three the following expression::

3 2

15625

(Answer: 5)

3.- Perform and simplify the following expression rationalising previously the denominators of these thractions 1 1 + 3+ 2 2− 3

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7 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.Perform and simplifythe 2 2 3 4 ⋅ 3 − 2(−3) − 5 ⋅ 3 + 6 ⋅ 3(−2)

following

arithmetic

expression

2.-

following

arithmetic

expression:

Perform

 108 3 ⋅ 625 4 ⋅ 3 −3    25 7 ⋅ 6 6  

Answer:

and

simplifythe

−1

1 5

3.- Exptress this surd in the simplest possible terms

4

3111696 . .

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8 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.Perform and simplify 9 48 − 12 − 2 27 + 3 75

the

following

arithmetic

expression:

1.Perform and simplify the following 13  3  7 4 2 1    − 1   1   − 2  2'3 +  −  + − −   6  4  21 5 15 3    6   3 

arithmetic

expression:

2. Perform -3 { 4 -3 [ 4-3 (4-3)] -4 } -3

Solución:

89 270

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9 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify the following arithmetic expression

[(

) ⋅ ( −76 ) 2 ⋅ ( 53 − 23 ) 0 ⋅ (4 13 ⋅ 2 15 ) −1 ]

−2 3 3

−160 ) 7007

(Answer

2.- Check if it is true or false the folllowing equality

−3 3

34

= −3

−1 3

3.- Work out and simplify the following arithmetic expression 1 8−4 4+ 2 (Answer

75 9

5 3) 3

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10 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify the following arithmetic expression 23 81 +

13 2 3 − 3 24 3 5

833 3 ) 15

(Answer

2.- Rewrite this surd in the simplest possible form

27 x 4 y 2 z 3

3.- Write in one only index of 2 the following expression 3

4 ⋅ 3 2 ⋅ 3 16 2 8

= 2x

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11 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify the following arithmetic expression

3 −2 ⋅ 4 3 ⋅ 4 −2 9 − 2 ⋅ 2 − 2 ⋅ 3 −3 2.- Rationalise the denominator of this fraction

2− 3 1+ 2

3.- Write in one only index of 3 the following expression

3

(

27

)

−1

= 3x

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12 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform and simplify

6!  8!  +  5!  7! 

−1

(Answer : -5’875)

2.- Expand completely using the binomial theorem

(

3.- Calculate the value of the following logarithms:

(SM 1º Bach)

a) e)

log 2

log

1 8 8

2 2

b)

log 1 9

f)

log

1 3 3

1 9

2+2 8

c)

log

1 1000

g)

log

(2 2 )

9

(SM 1º Bach)

d)

log 1 27 3

3

2

).

h)

log 1 3 64 2

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13 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

 4  4  4  4 1.- Perform   +   +   +    0  1  2  3

Answer : 15

(

2.- Calculate the last term in the expand of 2a 2 b − 3a 3

)

7

Example Study the following example:

“Knowing that log 2 = 0,3010 and log 3 = 0,4770, calculate log 2,4.”

24 23 ⋅ 3 = log = log 2 3 ⋅ 3 − log 10 = 3 log 2 + log 3 − log 10 = ... 10 10 ... = 3 ⋅ 0'3010 + 0'4770 − 1 = 0,3801

(

log 2,4 = log

)

Now, work out the following exercise:

3.- If you know that log 2 = 0,3010 and log 3 = 0,4770, calculate the decimal logarithms of: (SM 1º Bach) a) Log 0,72

b) Log 250

c)

log

18

d)

log

4

6

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14 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach

1.- Perform

n! (n + 2)! + (n − 1)! n!

2.- Express by intervals and draw them on the real line, the following sets:

{x ∈ ℜ / 2 x + 6 < 1}  1 x ∈ ℜ / x − < 2  1  x ∈ ℜ / x ≤  3 

1  4

3.- Calculate the following arithmetic expression

 7,25 ⋅ 1012 − 1012   log 2  10  1,25 ⋅ 10 

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15 SUBJECT: Mathematics. Theme: Arithmetic Group 1st Bach 1.- Carry out, using logarithms, NOT the calculator, the future value Cf of a capital of 1200 € with a 3% per year of compound interest during 4 years if the capitalization is every month. r   C f = C 0 1 +   12 

12⋅t

2.- Calculate the value of x if 2 ⋅ 10 6 = x12

3.- Rationalize

3 6+2 2 3 3+2

4.- Calculate x if log x = log 12 + log 25 − 2 log 6

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