1.2 Exercises - Förberedande kurs i matematik 1

                       Welcome to the course
                       
                        About the course 
                        Examinations
                      
                    
                      1. Numerical calculations
                       
                        1.1 Different types of numbers 
                        1.2 Fractions 
                        1.3 Powers
                      
                    
                      2. Algebra
                       
                        2.1 Algebraic expressions 
                        2.2 Linear expressions 
                        2.3 Quadratic expressions
                      
                    
                      3. Roots and logarithms
                       
                        3.1 Roots 
                        3.2 Equations with roots 
                        3.3 Logarithms 
                        3.4 Logarithmic equations
                      
                    
                      4. Trigonometry
                       
                        4.1 Angles and circles 
                        4.2 Functions 
                        4.3 Relations 
                        4.4 Equations
                      
                    
                      5. Written mathematics
                                            
                    
                    
		       Search
		       
		         

                           
                            
			 
		       
		    
		    
		  
		  
		  
		    
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			1.2 Exercises
			
			  From Förberedande kurs i matematik 1
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 {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"  {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
 | style="border-bottom:1px solid #000" width="5px" | &nbsp;  | style="border-bottom:1px solid #000" width="5px" | &nbsp;
- {{Mall:Ej vald flik|[[1.2 Bråkräkning|Teori]]}} + {{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
- {{Mall:Vald flik|[[1.2 Övningar|Övningar]]}} + {{Selected tab|[[1.2 Exercises|Exercises]]}}
 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;  | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}  |}
  
- ===Övning 1.2:1=== +  
  + ===Exercise 1.2:1===
 <div class="ovning">  <div class="ovning">
- Skriv på gemensamt bråkstreck + Express as a single fraction
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 16:
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 |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>  |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
 |c)  |c)
- |width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math> + |width="33%" | <math>\displaystyle \frac{1}{6}-\frac{2}{5}</math>
 |-  |-
 |d)  |d)
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 ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>  ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:1|Lösning a|Lösning 1.2:1a|Lösning b|Lösning 1.2:1b|Lösning c|Lösning 1.2:1c|Lösning d|Lösning 1.2:1d|Lösning e|Lösning 1.2:1e}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:1|Solution a|Solution 1.2:1a|Solution b|Solution 1.2:1b|Solution c|Solution 1.2:1c|Solution d|Solution 1.2:1d|Solution e|Solution 1.2:1e}}
  
  
- ===Övning 1.2:2=== + ===Exercise 1.2:2===
 <div class="ovning">  <div class="ovning">
- Bestäm minsta gemensamma nämnare + Determine the lowest common denominator of  
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 40:
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 || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>  || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:2|Lösning a|Lösning 1.2:2a|Lösning b|Lösning 1.2:2b|Lösning c|Lösning 1.2:2c|Lösning d|Lösning 1.2:2d}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:2|Solution a|Solution 1.2:2a|Solution b|Solution 1.2:2b|Solution c|Solution 1.2:2c|Solution d|Solution 1.2:2d}}
  
  
- ===Övning 1.2:3=== + ===Exercise 1.2:3===
 <div class="ovning">  <div class="ovning">
- Beräkna följande uttryck genom att använda minsta gemensamma nämnare: + Calculate the following by using the lowest common denominator.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>  |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Solution 1.2:3a|Solution b|Solution 1.2:3b}}
  
  
- ===Övning 1.2:4=== + ===Exercise 1.2:4===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat. + Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>  |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:4|Lösning a|Lösning 1.2:4a|Lösning b|Lösning 1.2:4b|Lösning c|Lösning 1.2:4c}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:4|Solution a|Solution 1.2:4a|Solution b|Solution 1.2:4b|Solution c|Solution 1.2:4c}}
  
  
- ===Övning 1.2:5=== + ===Exercise 1.2:5===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat. + Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>  |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:5|Lösning a|Lösning 1.2:5a|Lösning b|Lösning 1.2:5b|Lösning c|Lösning 1.2:5c}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:5|Solution a|Solution 1.2:5a|Solution b|Solution 1.2:5b|Solution c|Solution 1.2:5c}}
  
  
- ===Övning 1.2:6=== + ===Exercise 1.2:6===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math> + Simplify  
- </div>{{#NAVCONTENT:Svar|Svar 1.2:6|Lösning |Lösning 1.2:6}} + <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
  + </div>{{#NAVCONTENT:Answer|Answer 1.2:6|Solution |Solution 1.2:6}}
Current revision


  
  
  
  Theory
  
  
  
  
  Exercises
  
  
  




 Exercise 1.2:1

Express as a single fraction



a)
 47+711
b)
 72−51
c)
 61−52


d)
 31+41+51
e)
78+43−34




Answer | 
Solution a | 
Solution b | 
Solution c | 
Solution d | 
Solution e




Answer


Answer 1.2:1  Loading...



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Solution a


Solution 1.2:1a  Loading...



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Solution b


Solution 1.2:1b  Loading...



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Solution c


Solution 1.2:1c  Loading...



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Solution d


Solution 1.2:1d  Loading...



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Solution e


Solution 1.2:1e  Loading...



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 Exercise 1.2:2

Determine the lowest common denominator of  



a)
 61+110
b)
 41−81


c)
 112−114
d)
 245+175




Answer | 
Solution a | 
Solution b | 
Solution c | 
Solution d




Answer


Answer 1.2:2  Loading...



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Solution a


Solution 1.2:2a  Loading...



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Solution b


Solution 1.2:2b  Loading...



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Solution c


Solution 1.2:2c  Loading...



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Solution d


Solution 1.2:2d  Loading...



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 Exercise 1.2:3

Calculate the following by using the lowest common denominator.



a)
 320+750−110
b)
 124+140−116




Answer | 
Solution a | 
Solution b




Answer


Answer 1.2:3  Loading...



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Solution a


Solution 1.2:3a  Loading...



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Solution b


Solution 1.2:3b  Loading...



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 Exercise 1.2:4

Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.



a)
 53710
b)
 8372
c)
 31041−51




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


Answer 1.2:4  Loading...



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Solution a


Solution 1.2:4a  Loading...



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Solution b


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Solution c


Solution 1.2:4c  Loading...



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 Exercise 1.2:5

Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.



a)
 271−115
b)
 31−2121+31
c)
 \displaystyle \displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


Answer 1.2:5  Loading...



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Solution a


Solution 1.2:5a  Loading...



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Solution b


Solution 1.2:5b  Loading...



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Solution c


Solution 1.2:5c  Loading...



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 Exercise 1.2:6

Simplify  
\displaystyle \ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}




Answer | 
Solution




Answer


Answer 1.2:6  Loading...



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Solution


Solution 1.2:6  Loading...



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Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/1.2_Exercises"
                       Welcome to the course
                       
                        About the course 
                        Examinations
                      
                    
                      1. Numerical calculations
                       
                        1.1 Different types of numbers 
                        1.2 Fractions 
                        1.3 Powers
                      
                    
                      2. Algebra
                       
                        2.1 Algebraic expressions 
                        2.2 Linear expressions 
                        2.3 Quadratic expressions
                      
                    
                      3. Roots and logarithms
                       
                        3.1 Roots 
                        3.2 Equations with roots 
                        3.3 Logarithms 
                        3.4 Logarithmic equations
                      
                    
                      4. Trigonometry
                       
                        4.1 Angles and circles 
                        4.2 Functions 
                        4.3 Relations 
                        4.4 Equations
                      
                    
                      5. Written mathematics
                                            
                    
                    
		       Search
		       
		         

                           
                            
			 
		       
		    
		    
		  
		  
		  
		    
		      Processing Math: 88%
To print higher-resolution math symbols, click the

Hi-Res Fonts for Printing button on the jsMath control panel.

No jsMath TeX fonts found -- using image fonts instead.

These may be slow and might not print well.

Use the jsMath control panel to get additional information.jsMath Control PanelHide this Message

jsMath

		        
			
			1.2 Exercises
			
			  From Förberedande kurs i matematik 1
			  (Difference between revisions)
			  			                            Jump to: navigation, search
                          
		          
			
			
			
			
			
			
				Revision as of 18:07, 27 March 2008 (edit)
Tek  (Talk | contribs)
← Previous diff
				Current revision (11:49, 22 October 2008) (edit) (undo)
Eakc07  (Talk | contribs) 
 
			
		(14 intermediate revisions not shown.)
Line 2:
Line 2:
 {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"  {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
 | style="border-bottom:1px solid #000" width="5px" | &nbsp;  | style="border-bottom:1px solid #000" width="5px" | &nbsp;
- {{Mall:Ej vald flik|[[1.2 Bråkräkning|Teori]]}} + {{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
- {{Mall:Vald flik|[[1.2 Övningar|Övningar]]}} + {{Selected tab|[[1.2 Exercises|Exercises]]}}
 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;  | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}  |}
  
- ===Övning 1.2:1=== +  
  + ===Exercise 1.2:1===
 <div class="ovning">  <div class="ovning">
- Skriv på gemensamt bråkstreck + Express as a single fraction
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 16:
Line 17:
 |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>  |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
 |c)  |c)
- |width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math> + |width="33%" | <math>\displaystyle \frac{1}{6}-\frac{2}{5}</math>
 |-  |-
 |d)  |d)
Line 23:
Line 24:
 ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>  ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:1|Lösning a|Lösning 1.2:1a|Lösning b|Lösning 1.2:1b|Lösning c|Lösning 1.2:1c|Lösning d|Lösning 1.2:1d|Lösning e|Lösning 1.2:1e}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:1|Solution a|Solution 1.2:1a|Solution b|Solution 1.2:1b|Solution c|Solution 1.2:1c|Solution d|Solution 1.2:1d|Solution e|Solution 1.2:1e}}
  
  
- ===Övning 1.2:2=== + ===Exercise 1.2:2===
 <div class="ovning">  <div class="ovning">
- Bestäm minsta gemensamma nämnare + Determine the lowest common denominator of  
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 40:
Line 41:
 || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>  || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:2|Lösning a|Lösning 1.2:2a|Lösning b|Lösning 1.2:2b|Lösning c|Lösning 1.2:2c|Lösning d|Lösning 1.2:2d}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:2|Solution a|Solution 1.2:2a|Solution b|Solution 1.2:2b|Solution c|Solution 1.2:2c|Solution d|Solution 1.2:2d}}
  
  
- ===Övning 1.2:3=== + ===Exercise 1.2:3===
 <div class="ovning">  <div class="ovning">
- Beräkna följande uttryck genom att använda minsta gemensamma nämnare: + Calculate the following by using the lowest common denominator.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 52:
Line 53:
 |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>  |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Solution 1.2:3a|Solution b|Solution 1.2:3b}}
  
  
- ===Övning 1.2:4=== + ===Exercise 1.2:4===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat. + Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 66:
Line 67:
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>  |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:4|Lösning a|Lösning 1.2:4a|Lösning b|Lösning 1.2:4b|Lösning c|Lösning 1.2:4c}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:4|Solution a|Solution 1.2:4a|Solution b|Solution 1.2:4b|Solution c|Solution 1.2:4c}}
  
  
- ===Övning 1.2:5=== + ===Exercise 1.2:5===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat. + Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
Line 80:
Line 81:
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>  |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:5|Lösning a|Lösning 1.2:5a|Lösning b|Lösning 1.2:5b|Lösning c|Lösning 1.2:5c}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:5|Solution a|Solution 1.2:5a|Solution b|Solution 1.2:5b|Solution c|Solution 1.2:5c}}
  
  
- ===Övning 1.2:6=== + ===Exercise 1.2:6===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math> + Simplify  
- </div>{{#NAVCONTENT:Svar|Svar 1.2:6|Lösning |Lösning 1.2:6}} + <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
  + </div>{{#NAVCONTENT:Answer|Answer 1.2:6|Solution |Solution 1.2:6}}
Current revision


  
  
  
  Theory
  
  
  
  
  Exercises
  
  
  




 Exercise 1.2:1

Express as a single fraction



a)
 47+711
b)
 72−51
c)
 61−52


d)
 31+41+51
e)
78+43−34




Answer | 
Solution a | 
Solution b | 
Solution c | 
Solution d | 
Solution e




Answer


Answer 1.2:1  Loading...



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Solution a


Solution 1.2:1a  Loading...



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Solution b


Solution 1.2:1b  Loading...



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Solution c


Solution 1.2:1c  Loading...



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Solution d


Solution 1.2:1d  Loading...



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Solution e


Solution 1.2:1e  Loading...



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 Exercise 1.2:2

Determine the lowest common denominator of  



a)
 61+110
b)
 41−81


c)
 112−114
d)
 245+175




Answer | 
Solution a | 
Solution b | 
Solution c | 
Solution d




Answer


Answer 1.2:2  Loading...



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Solution a


Solution 1.2:2a  Loading...



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Solution b


Solution 1.2:2b  Loading...



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Solution c


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Solution d


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 Exercise 1.2:3

Calculate the following by using the lowest common denominator.



a)
 320+750−110
b)
 124+140−116




Answer | 
Solution a | 
Solution b




Answer


Answer 1.2:3  Loading...



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Solution b


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 Exercise 1.2:4

Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.



a)
 53710
b)
 8372
c)
 31041−51




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


Answer 1.2:4  Loading...



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Solution a


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Solution c


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 Exercise 1.2:5

Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.



a)
 271−115
b)
 31−2121+31
c)
 \displaystyle \displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


Answer 1.2:5  Loading...



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Solution c


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 Exercise 1.2:6

Simplify  
\displaystyle \ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}




Answer | 
Solution




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Answer 1.2:6  Loading...



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Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/1.2_Exercises"
-                      Welcome to the course
                       
                        About the course 
                        Examinations
                      
                    
                      1. Numerical calculations
                       
                        1.1 Different types of numbers 
                        1.2 Fractions 
                        1.3 Powers
                      
                    
                      2. Algebra
                       
                        2.1 Algebraic expressions 
                        2.2 Linear expressions 
                        2.3 Quadratic expressions
                      
                    
                      3. Roots and logarithms
                       
                        3.1 Roots 
                        3.2 Equations with roots 
                        3.3 Logarithms 
                        3.4 Logarithmic equations
                      
                    
                      4. Trigonometry
                       
                        4.1 Angles and circles 
                        4.2 Functions 
                        4.3 Relations 
                        4.4 Equations
                      
                    
                      5. Written mathematics
                                            
                    
                    
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			1.2 Exercises
			
			  From Förberedande kurs i matematik 1
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 {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"  {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
 | style="border-bottom:1px solid #000" width="5px" | &nbsp;  | style="border-bottom:1px solid #000" width="5px" | &nbsp;
- {{Mall:Ej vald flik|[[1.2 Bråkräkning|Teori]]}} + {{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
- {{Mall:Vald flik|[[1.2 Övningar|Övningar]]}} + {{Selected tab|[[1.2 Exercises|Exercises]]}}
 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;  | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}  |}
  
- ===Övning 1.2:1=== +  
  + ===Exercise 1.2:1===
 <div class="ovning">  <div class="ovning">
- Skriv på gemensamt bråkstreck + Express as a single fraction
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>  |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
 |c)  |c)
- |width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math> + |width="33%" | <math>\displaystyle \frac{1}{6}-\frac{2}{5}</math>
 |-  |-
 |d)  |d)
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 ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>  ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:1|Lösning a|Lösning 1.2:1a|Lösning b|Lösning 1.2:1b|Lösning c|Lösning 1.2:1c|Lösning d|Lösning 1.2:1d|Lösning e|Lösning 1.2:1e}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:1|Solution a|Solution 1.2:1a|Solution b|Solution 1.2:1b|Solution c|Solution 1.2:1c|Solution d|Solution 1.2:1d|Solution e|Solution 1.2:1e}}
  
  
- ===Övning 1.2:2=== + ===Exercise 1.2:2===
 <div class="ovning">  <div class="ovning">
- Bestäm minsta gemensamma nämnare + Determine the lowest common denominator of  
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>  || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:2|Lösning a|Lösning 1.2:2a|Lösning b|Lösning 1.2:2b|Lösning c|Lösning 1.2:2c|Lösning d|Lösning 1.2:2d}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:2|Solution a|Solution 1.2:2a|Solution b|Solution 1.2:2b|Solution c|Solution 1.2:2c|Solution d|Solution 1.2:2d}}
  
  
- ===Övning 1.2:3=== + ===Exercise 1.2:3===
 <div class="ovning">  <div class="ovning">
- Beräkna följande uttryck genom att använda minsta gemensamma nämnare: + Calculate the following by using the lowest common denominator.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>  |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Solution 1.2:3a|Solution b|Solution 1.2:3b}}
  
  
- ===Övning 1.2:4=== + ===Exercise 1.2:4===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat. + Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>  |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:4|Lösning a|Lösning 1.2:4a|Lösning b|Lösning 1.2:4b|Lösning c|Lösning 1.2:4c}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:4|Solution a|Solution 1.2:4a|Solution b|Solution 1.2:4b|Solution c|Solution 1.2:4c}}
  
  
- ===Övning 1.2:5=== + ===Exercise 1.2:5===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat. + Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
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 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>  |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
 |}  |}
- </div>{{#NAVCONTENT:Svar|Svar 1.2:5|Lösning a|Lösning 1.2:5a|Lösning b|Lösning 1.2:5b|Lösning c|Lösning 1.2:5c}} + </div>{{#NAVCONTENT:Answer|Answer 1.2:5|Solution a|Solution 1.2:5a|Solution b|Solution 1.2:5b|Solution c|Solution 1.2:5c}}
  
  
- ===Övning 1.2:6=== + ===Exercise 1.2:6===
 <div class="ovning">  <div class="ovning">
- F&ouml;renkla <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math> + Simplify  
- </div>{{#NAVCONTENT:Svar|Svar 1.2:6|Lösning |Lösning 1.2:6}} + <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
  + </div>{{#NAVCONTENT:Answer|Answer 1.2:6|Solution |Solution 1.2:6}}
Current revision


  
  
  
  Theory
  
  
  
  
  Exercises
  
  
  




 Exercise 1.2:1

Express as a single fraction



a)
 47+711
b)
 72−51
c)
 61−52


d)
 31+41+51
e)
78+43−34




Answer | 
Solution a | 
Solution b | 
Solution c | 
Solution d | 
Solution e




Answer


Answer 1.2:1  Loading...



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Solution a


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Solution b


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Solution c


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Solution d


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Solution e


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 Exercise 1.2:2

Determine the lowest common denominator of  



a)
 61+110
b)
 41−81


c)
 112−114
d)
 245+175




Answer | 
Solution a | 
Solution b | 
Solution c | 
Solution d




Answer


Answer 1.2:2  Loading...



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Solution a


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Solution b


Solution 1.2:2b  Loading...



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Solution c


Solution 1.2:2c  Loading...



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Solution d


Solution 1.2:2d  Loading...



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 Exercise 1.2:3

Calculate the following by using the lowest common denominator.



a)
 320+750−110
b)
 124+140−116




Answer | 
Solution a | 
Solution b




Answer


Answer 1.2:3  Loading...



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Solution a


Solution 1.2:3a  Loading...



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Solution b


Solution 1.2:3b  Loading...



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 Exercise 1.2:4

Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.



a)
 53710
b)
 8372
c)
 31041−51




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


Answer 1.2:4  Loading...



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Solution a


Solution 1.2:4a  Loading...



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Solution b


Solution 1.2:4b  Loading...



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Solution c


Solution 1.2:4c  Loading...



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 Exercise 1.2:5

Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.



a)
 271−115
b)
 31−2121+31
c)
 \displaystyle \displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


Answer 1.2:5  Loading...



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Solution a


Solution 1.2:5a  Loading...



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Solution b


Solution 1.2:5b  Loading...



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Solution c


Solution 1.2:5c  Loading...



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 Exercise 1.2:6

Simplify  
\displaystyle \ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}




Answer | 
Solution




Answer


Answer 1.2:6  Loading...



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Solution 1.2:6  Loading...



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Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/1.2_Exercises"
 To print higher-resolution math symbols, click the

Hi-Res Fonts for Printing button on the jsMath control panel.
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@@ Line 2: / Line 2: @@
 {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
 | style="border-bottom:1px solid #000" width="5px" | &nbsp;
-{{Mall:Ej vald flik|[[1.2 Bråkräkning|Teori]]}}
+{{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
-{{Mall:Vald flik|[[1.2 Övningar|Övningar]]}}
+{{Selected tab|[[1.2 Exercises|Exercises]]}}
 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}
-===Övning 1.2:1===
+===Exercise 1.2:1===
 <div class="ovning">
-Skriv på gemensamt bråkstreck
+Express as a single fraction
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 16: / Line 17: @@
 |width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
 |c)
-|width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
+|width="33%" | <math>\displaystyle \frac{1}{6}-\frac{2}{5}</math>
 |-
 |d)
@@ Line 23: / Line 24: @@
 ||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
 |}
-</div>{{#NAVCONTENT:Svar|Svar 1.2:1|Lösning a|Lösning 1.2:1a|Lösning b|Lösning 1.2:1b|Lösning c|Lösning 1.2:1c|Lösning d|Lösning 1.2:1d|Lösning e|Lösning 1.2:1e}}
+</div>{{#NAVCONTENT:Answer|Answer 1.2:1|Solution a|Solution 1.2:1a|Solution b|Solution 1.2:1b|Solution c|Solution 1.2:1c|Solution d|Solution 1.2:1d|Solution e|Solution 1.2:1e}}
-===Övning 1.2:2===
+===Exercise 1.2:2===
 <div class="ovning">
-Bestäm minsta gemensamma nämnare
+Determine the lowest common denominator of
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 40: / Line 41: @@
 || <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
 |}
-</div>{{#NAVCONTENT:Svar|Svar 1.2:2|Lösning a|Lösning 1.2:2a|Lösning b|Lösning 1.2:2b|Lösning c|Lösning 1.2:2c|Lösning d|Lösning 1.2:2d}}
+</div>{{#NAVCONTENT:Answer|Answer 1.2:2|Solution a|Solution 1.2:2a|Solution b|Solution 1.2:2b|Solution c|Solution 1.2:2c|Solution d|Solution 1.2:2d}}
-===Övning 1.2:3===
+===Exercise 1.2:3===
 <div class="ovning">
-Beräkna följande uttryck genom att använda minsta gemensamma nämnare:
+Calculate the following by using the lowest common denominator.
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 52: / Line 53: @@
 |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
 |}
-</div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b}}
+</div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Solution 1.2:3a|Solution b|Solution 1.2:3b}}
-===Övning 1.2:4===
+===Exercise 1.2:4===
 <div class="ovning">
-F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.
+Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 66: / Line 67: @@
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
 |}
-</div>{{#NAVCONTENT:Svar|Svar 1.2:4|Lösning a|Lösning 1.2:4a|Lösning b|Lösning 1.2:4b|Lösning c|Lösning 1.2:4c}}
+</div>{{#NAVCONTENT:Answer|Answer 1.2:4|Solution a|Solution 1.2:4a|Solution b|Solution 1.2:4b|Solution c|Solution 1.2:4c}}
-===Övning 1.2:5===
+===Exercise 1.2:5===
 <div class="ovning">
-F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.
+Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 80: / Line 81: @@
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
 |}
-</div>{{#NAVCONTENT:Svar|Svar 1.2:5|Lösning a|Lösning 1.2:5a|Lösning b|Lösning 1.2:5b|Lösning c|Lösning 1.2:5c}}
+</div>{{#NAVCONTENT:Answer|Answer 1.2:5|Solution a|Solution 1.2:5a|Solution b|Solution 1.2:5b|Solution c|Solution 1.2:5c}}
-===Övning 1.2:6===
+===Exercise 1.2:6===
 <div class="ovning">
-F&ouml;renkla <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
+Simplify
-</div>{{#NAVCONTENT:Svar|Svar 1.2:6|Lösning |Lösning 1.2:6}}
+<math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle  + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle  - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
+</div>{{#NAVCONTENT:Answer|Answer 1.2:6|Solution |Solution 1.2:6}}
-  Theory
+  Exercises
-a)
+−52
-d)
++43−34
-a)
+−81
-c)
++175
-a)
++140−116
-a)
+−51
-a)
+ \displaystyle \displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}