Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.

jsMath

1.3 Exercises

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
Current revision (11:50, 22 October 2008) (edit) (undo)
 
(16 intermediate revisions not shown.)
Line 1: Line 1:
__NOTOC__
__NOTOC__
 +
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
 +
| style="border-bottom:1px solid #000" width="5px" |  
 +
{{Not selected tab|[[1.3 Powers|Theory]]}}
 +
{{Selected tab|[[1.3 Exercises|Exercises]]}}
 +
| style="border-bottom:1px solid #000" width="100%"|  
 +
|}
 +
-
===Övning 1.3:1===
+
===Exercise 1.3:1===
<div class="ovning">
<div class="ovning">
-
Ber&auml;kna
+
Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 14: Line 21:
|width="25%"| <math>\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}</math>
|width="25%"| <math>\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 1.3:1|Lösning a|Lösning 1.3:1a|Lösning b|Lösning 1.3:1b|Lösning c|Lösning 1.3:1c|Lösning d|Lösning 1.3:1d}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.3:1|Solution a|Solution 1.3:1a|Solution b|Solution 1.3:1b|Solution c|Solution 1.3:1c|Solution d|Solution 1.3:1d}}
-
===Övning 1.3:2===
+
===Exercise 1.3:2===
<div class="ovning">
<div class="ovning">
-
Skriv som en potens av <math>2</math>
+
Write each of the following as a power of <math>2</math>
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="33%"| <math>2\cdot4\cdot8</math>
|width="33%"| <math>2\cdot4\cdot8</math>
|b)
|b)
-
|width="33%"| <math>0{,}25</math>
+
|width="33%"| <math>0\textrm{.}25</math>
|c)
|c)
|width="33%"| <math>1</math>
|width="33%"| <math>1</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 1.3:2|Lösning a|Lösning 1.3:2a|Lösning b|Lösning 1.3:2b|Lösning c|Lösning 1.3:2c}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.3:2|Solution a|Solution 1.3:2a|Solution b|Solution 1.3:2b|Solution c|Solution 1.3:2c}}
-
===Övning 1.3:3===
+
===Exercise 1.3:3===
<div class="ovning">
<div class="ovning">
-
Skriv som en potens av <math>3</math>
+
Write each of the following as a power of <math>3</math>
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 46: Line 53:
|width="20%"| <math>\displaystyle \frac{3}{9^2}</math>
|width="20%"| <math>\displaystyle \frac{3}{9^2}</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 1.3:3|Lösning a|Lösning 1.3:3a|Lösning b|Lösning 1.3:3b|Lösning c|Lösning 1.3:3c|Lösning d|Lösning 1.3:3d|Lösning e|Lösning 1.3:3e}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.3:3|Solution a|Solution 1.3:3a|Solution b|Solution 1.3:3b|Solution c|Solution 1.3:3c|Solution d|Solution 1.3:3d|Solution e|Solution 1.3:3e}}
-
===Övning 1.3:4===
+
===Exercise 1.3:4===
<div class="ovning">
<div class="ovning">
-
Ber&auml;kna
+
Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 65: Line 72:
||<math>625\cdot(5^{8}+5^{9})^{-1}</math>
||<math>625\cdot(5^{8}+5^{9})^{-1}</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 1.3:4|Lösning a|Lösning 1.3:4a|Lösning b|Lösning 1.3:4b|Lösning c|Lösning 1.3:4c|Lösning d|Lösning 1.3:4d|Lösning e|Lösning 1.3:4e}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.3:4|Solution a|Solution 1.3:4a|Solution b|Solution 1.3:4b|Solution c|Solution 1.3:4c|Solution d|Solution 1.3:4d|Solution e|Solution 1.3:4e}}
 +
 
 +
 
 +
===Exercise 1.3:5===
 +
<div class="ovning">
 +
Calculate
 +
{| width="100%" cellspacing="10px"
 +
|a)
 +
|width="33%" | <math>4^{1/2}</math>
 +
|b)
 +
|width="33%" | <math>4^{-1/2}</math>
 +
|c)
 +
|width="33%" | <math>9^{3/2}</math>
 +
|-
 +
|d)
 +
|| <math>\left(47^{2/3} \right) ^{3}</math>
 +
|e)
 +
||<math>3^{1\textrm{.}4}\cdot3^{0\textrm{.}6}</math>
 +
|f)
 +
||<math>\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}</math>
 +
|}
 +
</div>{{#NAVCONTENT:Answer|Answer 1.3:5|Solution a|Solution 1.3:5a|Solution b|Solution 1.3:5b|Solution c|Solution 1.3:5c|Solution d|Solution 1.3:5d|Solution e|Solution 1.3:5e|Solution f|Solution 1.3:5f}}
 +
 
 +
 
 +
===Exercise 1.3:6===
 +
<div class="ovning">
 +
In each of the following cases, determine which is the larger of the two numbers.
 +
{| width="100%" cellspacing="10px"
 +
|a)
 +
|width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </math>
 +
|b)
 +
|width="33%" | <math>0\textrm{.}5^{-3}\ </math> and <math>\ 0\textrm{.}4^{-3} </math>
 +
|c)
 +
|width="33%" | <math>0\textrm{.}2^5\ </math> and <math>\ 0\textrm{.}2^{7} </math>
 +
|-
 +
|d)
 +
|| <math>400^{1/3}\ </math> and <math>\ \bigl(5^{1/3}\bigr)^{4} </math>
 +
|e)
 +
||<math>125^{1/2}\ </math> and <math>\ 625^{1/3} </math>
 +
|f)
 +
||<math>2^{56}\ </math> and <math>\ 3^{40} </math>
 +
|}
 +
</div>{{#NAVCONTENT:Answer|Answer 1.3:6|Solution a|Solution 1.3:6a|Solution b|Solution 1.3:6b|Solution c|Solution 1.3:6c|Solution d|Solution 1.3:6d|Solution e|Solution 1.3:6e|Solution f|Solution 1.3:6f}}

Current revision

       Theory          Exercises      


Exercise 1.3:1

Calculate

a) 2332 b) 3592 c) (5)3 d) 323 


Exercise 1.3:2

Write each of the following as a power of 2

a) 248 b) 0.25 c) 1


Exercise 1.3:3

Write each of the following as a power of 3

a) 31 b) 243 c) 92 d) 127 e) 392


Exercise 1.3:4

Calculate

a) 2927 b) 31393272 c) 51254(52)6
d) 223(2)4 e) 625(58+59)1


Exercise 1.3:5

Calculate

a) 412  b) 412  c) 932 
d) 47233  e) 31.430.6 f) 12513227132912 


Exercise 1.3:6

In each of the following cases, determine which is the larger of the two numbers.

a) 25613   and  20013  b) 0.53  and  0.43 c) 0.25  and  0.27
d) 40013   and  5134  e) 12512   and  62513  f) 256  and  340