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
| 1
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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 . .
| 7
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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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U⌀ℕℤℚ∊ℝℂℙℐΩ⇐⇒⇔⇏∊∉∈∅⇾≈≔⇎⇝≡ℤ≤≥≲≳≴≵≮≯∀⇒∊≠∅⊂⟇·∊∃ A⨯Bεαβηθλµξσφφδεε ·∅U∩∪∼∿⊂⊃⊆⊇⊄⋂⋃⊅∧∨U⤳≮≠|∂∆√±∞ǀǁƟƩǃξχ∘6⊕⊗⊛⋅♫♯ ⨁⨂✘✔×
ℕ
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