5.2 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
                       
                        5.1 Writing formulas 
                        5.2 Mathematical text
                      
                    
                    
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			5.2 Exercises
			
			  From Förberedande kurs i matematik 1
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				Revision as of 08:14, 29 January 2009 (edit)
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 |a)  |a)
- |width="100%" | <math>\tan x(\sin x+1) = 2\tan x\quad ?\quad\sin x+1=2</math> + |width="100%" | <math>\tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1</math>
 |-  |-
 |b)  |b)
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 |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>  |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>
 |}  |}
- </div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution|Solution 5.2:1}} + </div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution a|Solution 5.2:1a|Solution b|Solution 5.2:1b|Solution c|Solution 5.2:1c}}
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 ===Exercise 5.2:9===  ===Exercise 5.2:9===
Current revision


  
  
  
  Theory
  
  
  
  
  Exercises
  
  
  




 Exercise 5.2:1

Which of the arrows ,  or  should you insert between the following equations? (Instead of the question mark.) 



a)
 tanx(sinx+1)=tanx ?sinx+1=1


b)
 x−1=x+1 ?x−1=(x+1)2 


c)
 x2−6x+1=0 ?(x−3)2−9+1=0




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


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Solution a


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Solution b


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Solution c


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 Exercise 5.2:2

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:3

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:4

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:5

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:6

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:7

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:8

Criticize the following excerpt from a solution written by a student.





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 Exercise 5.2:9

Criticize the following excerpt from a solution written by a student.





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Retrieved from "http://wiki.math.se/wikis/2009/bridgecourse1-ImperialCollege/index.php/5.2_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
                       
                        5.1 Writing formulas 
                        5.2 Mathematical text
                      
                    
                    
		       Search
		       
		         

                           
                            
			 
		       
		    
		    
		  
		  
		  
		    
		      Processing Math: Done
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			5.2 Exercises
			
			  From Förberedande kurs i matematik 1
			  (Difference between revisions)
			  			                            Jump to: navigation, search
                          
		          
			
			
			
			
			
			
				Revision as of 08:14, 29 January 2009 (edit)
Tek  (Talk | contribs)
m 
← Previous diff
				Current revision (13:02, 29 January 2009) (edit) (undo)
Tek  (Talk | contribs) 
m 
 
			
		(2 intermediate revisions not shown.)
Line 6:
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 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;  | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}  |}
  + 
  
 ===Exercise 5.2:1===  ===Exercise 5.2:1===
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 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
- |width="100%" | <math>\tan x(\sin x+1) = 2\tan x\quad ?\quad\sin x+1=2</math> + |width="100%" | <math>\tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1</math>
 |-  |-
 |b)  |b)
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 |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>  |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>
 |}  |}
- </div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution|Solution 5.2:1}} + </div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution a|Solution 5.2:1a|Solution b|Solution 5.2:1b|Solution c|Solution 5.2:1c}}
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 ===Exercise 5.2:2===  ===Exercise 5.2:2===
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 ===Exercise 5.2:3===  ===Exercise 5.2:3===
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 ===Exercise 5.2:4===  ===Exercise 5.2:4===
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 ===Exercise 5.2:5===  ===Exercise 5.2:5===
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 ===Exercise 5.2:7===  ===Exercise 5.2:7===
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 ===Exercise 5.2:8===  ===Exercise 5.2:8===
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-  
  
 ===Exercise 5.2:9===  ===Exercise 5.2:9===
Current revision


  
  
  
  Theory
  
  
  
  
  Exercises
  
  
  




 Exercise 5.2:1

Which of the arrows ,  or  should you insert between the following equations? (Instead of the question mark.) 



a)
 tanx(sinx+1)=tanx ?sinx+1=1


b)
 x−1=x+1 ?x−1=(x+1)2 


c)
 x2−6x+1=0 ?(x−3)2−9+1=0




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


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Solution a


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Solution b


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Solution c


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 Exercise 5.2:2

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:3

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:4

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:5

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:6

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:7

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:8

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:9

Criticize the following excerpt from a solution written by a student.





Solution




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Retrieved from "http://wiki.math.se/wikis/2009/bridgecourse1-ImperialCollege/index.php/5.2_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
                       
                        5.1 Writing formulas 
                        5.2 Mathematical text
                      
                    
                    
		       Search
+		      Processing Math: Done
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Hi-Res Fonts for Printing button on the jsMath control panel.

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These may be slow and might not print well.

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			5.2 Exercises
			
			  From Förberedande kurs i matematik 1
			  (Difference between revisions)
			  			                            Jump to: navigation, search
                          
		          
			
			
			
			
			
			
				Revision as of 08:14, 29 January 2009 (edit)
Tek  (Talk | contribs)
m 
← Previous diff
				Current revision (13:02, 29 January 2009) (edit) (undo)
Tek  (Talk | contribs) 
m 
 
			
		(2 intermediate revisions not shown.)
Line 6:
Line 6:
 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;  | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}  |}
  + 
  
 ===Exercise 5.2:1===  ===Exercise 5.2:1===
Line 12:
Line 13:
 {| width="100%" cellspacing="10px"  {| width="100%" cellspacing="10px"
 |a)  |a)
- |width="100%" | <math>\tan x(\sin x+1) = 2\tan x\quad ?\quad\sin x+1=2</math> + |width="100%" | <math>\tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1</math>
 |-  |-
 |b)  |b)
Line 20:
Line 21:
 |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>  |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>
 |}  |}
- </div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution|Solution 5.2:1}} + </div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution a|Solution 5.2:1a|Solution b|Solution 5.2:1b|Solution c|Solution 5.2:1c}}
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 ===Exercise 5.2:2===  ===Exercise 5.2:2===
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 </div>{{#NAVCONTENT:Solution|Solution 5.2:2}}  </div>{{#NAVCONTENT:Solution|Solution 5.2:2}}
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 ===Exercise 5.2:3===  ===Exercise 5.2:3===
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 [[Image:ex5_2_3_orig.png||center]]  [[Image:ex5_2_3_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:3}}  </div>{{#NAVCONTENT:Solution|Solution 5.2:3}}
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 ===Exercise 5.2:4===  ===Exercise 5.2:4===
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 ===Exercise 5.2:5===  ===Exercise 5.2:5===
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 ===Exercise 5.2:6===  ===Exercise 5.2:6===
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 ===Exercise 5.2:7===  ===Exercise 5.2:7===
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 </div>{{#NAVCONTENT:Solution|Solution 5.2:7}}  </div>{{#NAVCONTENT:Solution|Solution 5.2:7}}
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 ===Exercise 5.2:8===  ===Exercise 5.2:8===
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 </div>{{#NAVCONTENT:Solution|Solution 5.2:8}}  </div>{{#NAVCONTENT:Solution|Solution 5.2:8}}
-  
  
 ===Exercise 5.2:9===  ===Exercise 5.2:9===
Current revision


  
  
  
  Theory
  
  
  
  
  Exercises
  
  
  




 Exercise 5.2:1

Which of the arrows ,  or  should you insert between the following equations? (Instead of the question mark.) 



a)
 tanx(sinx+1)=tanx ?sinx+1=1


b)
 x−1=x+1 ?x−1=(x+1)2 


c)
 x2−6x+1=0 ?(x−3)2−9+1=0




Answer | 
Solution a | 
Solution b | 
Solution c




Answer


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Solution b


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Solution c


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 Exercise 5.2:2

Criticize the following excerpt from a solution written by a student.





Solution




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 Exercise 5.2:3

Criticize the following excerpt from a solution written by a student.





Solution




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Criticize the following excerpt from a solution written by a student.





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 Exercise 5.2:5

Criticize the following excerpt from a solution written by a student.





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Criticize the following excerpt from a solution written by a student.





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Criticize the following excerpt from a solution written by a student.





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 Exercise 5.2:9

Criticize the following excerpt from a solution written by a student.





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Retrieved from "http://wiki.math.se/wikis/2009/bridgecourse1-ImperialCollege/index.php/5.2_Exercises"
 To print higher-resolution math symbols, click the

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@@ Line 6: / Line 6: @@
 | style="border-bottom:1px solid #000"  width="100%"| &nbsp;
 |}
 ===Exercise 5.2:1===
@@ Line 12: / Line 13: @@
 {| width="100%" cellspacing="10px"
 |a)
-|width="100%" | <math>\tan x(\sin x+1) = 2\tan x\quad ?\quad\sin x+1=2</math>
+|width="100%" | <math>\tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1</math>
 |-
 |b)
@@ Line 20: / Line 21: @@
 |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>
 |}
-</div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution|Solution 5.2:1}}
+</div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution a|Solution 5.2:1a|Solution b|Solution 5.2:1b|Solution c|Solution 5.2:1c}}
 ===Exercise 5.2:2===
@@ Line 28: / Line 28: @@
 [[Image:ex5_2_2_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:2}}
 ===Exercise 5.2:3===
@@ Line 35: / Line 34: @@
 [[Image:ex5_2_3_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:3}}
 ===Exercise 5.2:4===
@@ Line 42: / Line 40: @@
 [[Image:ex5_2_4_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:4}}
 ===Exercise 5.2:5===
@@ Line 49: / Line 46: @@
 [[Image:ex5_2_5_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:5}}
 ===Exercise 5.2:6===
@@ Line 56: / Line 52: @@
 [[Image:ex5_2_6_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:6}}
 ===Exercise 5.2:7===
@@ Line 63: / Line 58: @@
 [[Image:ex5_2_7_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:7}}
 ===Exercise 5.2:8===
@@ Line 70: / Line 64: @@
 [[Image:ex5_2_8_orig.png||center]]
 </div>{{#NAVCONTENT:Solution|Solution 5.2:8}}
 ===Exercise 5.2:9===
-  Theory
+  Exercises
-a)
+ tanx(sinx+1)=tanx ?sinx+1=1
-b)
+ x−1=x+1 ?x−1=(x+1)2
-c)
+ x2−6x+1=0 ?(x−3)2−9+1=0