Processing Math: 68%
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

2.3 Exercises

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Robot: Automated text replacement (-Svar +Answer))
m (Robot: Automated text replacement (-Lösning +Solution))
Line 20: Line 20:
|width="25%" | <math>x^2+5x+3</math>
|width="25%" | <math>x^2+5x+3</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:1|Solution a|Lösning 2.3:1a|Solution b|Lösning 2.3:1b|Solution c|Lösning 2.3:1c|Solution d|Lösning 2.3:1d}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:1|Solution a|Solution 2.3:1a|Solution b|Solution 2.3:1b|Solution c|Solution 2.3:1c|Solution d|Solution 2.3:1d}}
===Exercise 2.3:2===
===Exercise 2.3:2===
Line 40: Line 40:
|width="33%" | <math>3x^2-10x+8=0</math>
|width="33%" | <math>3x^2-10x+8=0</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:2|Solution a|Lösning 2.3:2a|Solution b|Lösning 2.3:2b|Solution c|Lösning 2.3:2c|Solution d|Lösning 2.3:2d|Solution e|Lösning 2.3:2e|Solution f|Lösning 2.3:2f}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:2|Solution a|Solution 2.3:2a|Solution b|Solution 2.3:2b|Solution c|Solution 2.3:2c|Solution d|Solution 2.3:2d|Solution e|Solution 2.3:2e|Solution f|Solution 2.3:2f}}
===Exercise 2.3:3===
===Exercise 2.3:3===
Line 61: Line 61:
|width="50%" | <math>x(x^2-2x)+x(2-x)=0</math>
|width="50%" | <math>x(x^2-2x)+x(2-x)=0</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:3|Solution a|Lösning 2.3:3a|Solution b|Lösning 2.3:3b|Solution c|Lösning 2.3:3c|Solution d|Lösning 2.3:3d|Solution e|Lösning 2.3:3e|Solution f|Lösning 2.3:3f}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:3|Solution a|Solution 2.3:3a|Solution b|Solution 2.3:3b|Solution c|Solution 2.3:3c|Solution d|Solution 2.3:3d|Solution e|Solution 2.3:3e|Solution f|Solution 2.3:3f}}
===Exercise 2.3:4===
===Exercise 2.3:4===
Line 76: Line 76:
|width="100" | <math>3\ </math> and <math>\ \sqrt{3}</math>
|width="100" | <math>3\ </math> and <math>\ \sqrt{3}</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:4|Solution a|Lösning 2.3:4a|Solution b|Lösning 2.3:4b|Solution c|Lösning 2.3:4c}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:4|Solution a|Solution 2.3:4a|Solution b|Solution 2.3:4b|Solution c|Solution 2.3:4c}}
===Exercise 2.3:5===
===Exercise 2.3:5===
Line 90: Line 90:
|width="100" | The equation <math>\,x^2+4x+b=0\,</math> has one root at <math>\,x=1\,</math>. Determine the value of the constant <math>\,b\,</math>.
|width="100" | The equation <math>\,x^2+4x+b=0\,</math> has one root at <math>\,x=1\,</math>. Determine the value of the constant <math>\,b\,</math>.
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:5|Solution a|Lösning 2.3:5a|Solution b|Lösning 2.3:5b|Solution c|Lösning 2.3:5c}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:5|Solution a|Solution 2.3:5a|Solution b|Solution 2.3:5b|Solution c|Solution 2.3:5c}}
===Exercise 2.3:6===
===Exercise 2.3:6===
Line 103: Line 103:
|width="33%" | <math>x^2-5x+7</math>
|width="33%" | <math>x^2-5x+7</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:6|Solution a|Lösning 2.3:6a|Solution b|Lösning 2.3:6b|Solution c|Lösning 2.3:6c}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:6|Solution a|Solution 2.3:6a|Solution b|Solution 2.3:6b|Solution c|Solution 2.3:6c}}
Line 117: Line 117:
|width="33%" | <math>x^2+x+1</math>
|width="33%" | <math>x^2+x+1</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:7|Solution a|Lösning 2.3:7a|Solution b|Lösning 2.3:7b|Solution c|Lösning 2.3:7c}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:7|Solution a|Solution 2.3:7a|Solution b|Solution 2.3:7b|Solution c|Solution 2.3:7c}}
===Exercise 2.3:8===
===Exercise 2.3:8===
Line 130: Line 130:
|width="33%" | <math>f(x)=x^2-6x+11</math>
|width="33%" | <math>f(x)=x^2-6x+11</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:8|Solution a|Lösning 2.3:8a|Solution b|Lösning 2.3:8b|Solution c|Lösning 2.3:8c}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:8|Solution a|Solution 2.3:8a|Solution b|Solution 2.3:8b|Solution c|Solution 2.3:8c}}
===Exercise 2.3:9===
===Exercise 2.3:9===
Line 143: Line 143:
|width="33%" | <math>y=3x^2-12x+9</math>
|width="33%" | <math>y=3x^2-12x+9</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:9|Solution a|Lösning 2.3:9a|Solution b|Lösning 2.3:9b|Solution c|Lösning 2.3:9c}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:9|Solution a|Solution 2.3:9a|Solution b|Solution 2.3:9b|Solution c|Solution 2.3:9c}}
===Exercise 2.3:10===
===Exercise 2.3:10===
Line 160: Line 160:
|}
|}
-
</div>{{#NAVCONTENT:Answer|Answer 2.3:10|Solution a|Lösning 2.3:10a|Solution b|Lösning 2.3:10b|Solution c|Lösning 2.3:10c|Solution d|Lösning 2.3:10d}}
+
</div>{{#NAVCONTENT:Answer|Answer 2.3:10|Solution a|Solution 2.3:10a|Solution b|Solution 2.3:10b|Solution c|Solution 2.3:10c|Solution d|Solution 2.3:10d}}

Revision as of 11:21, 9 September 2008

       Theory          Exercises      

Exercise 2.3:1

Complete the square of the expressions

a) x2−2x b) x2+2x−1 c) 5+2x−x2 d) x2+5x+3

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

Exercise 2.3:2

Solve the following second order equations by completing the square

a) x2−4x+3=0 b) y2+2y−15=0 c) y2+3y+4=0
d) 4x2−28x+13=0 e) 5x2+2x−3=0 f) 3x2−10x+8=0

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

Exercise 2.3:3

Solve the following equations directly

a) x(x+3)=0 b) (x−3)(x+5)=0
c) 5(3x−2)(x+8)=0 d) x(x+3)−x(2x−9)=0
e) (x+3)(x−1)−(x+3)(2x−9)=0 f) x(x2−2x)+x(2−x)=0

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

Exercise 2.3:4

Determine a second-degree equation which has roots

a) −1  and  2
b) 1+3   and  1−3 
c) 3  and  3 

Answer | Solution a | Solution b | Solution c

Exercise 2.3:5

a) Determine a second-degree equation which only has −7 as a root.
b) Determine a value of x which makes the expression 4x2−28x+48 negative.
c) The equation x2+4x+b=0 has one root at x=1. Determine the value of the constant b.

Answer | Solution a | Solution b | Solution c

Exercise 2.3:6

Determine the smallest value that the following polynomial can take

a) x2−2x+1 b) x2−4x+2 c) x2−5x+7

Answer | Solution a | Solution b | Solution c


Exercise 2.3:7

Determine the largest value that the following polynomials can take.

a) 1−x2 b) \displaystyle -x^2+3x-4 c) \displaystyle x^2+x+1

Answer | Solution a | Solution b | Solution c

Exercise 2.3:8

Sketch the graph of the following functions

a) \displaystyle f(x)=x^2+1 b) \displaystyle f(x)=(x-1)^2+2 c) \displaystyle f(x)=x^2-6x+11

Answer | Solution a | Solution b | Solution c

Exercise 2.3:9

Find all the points where the x-axis and the following curves intersect.

a) \displaystyle y=x^2-1 b) \displaystyle y=x^2-5x+6 c) \displaystyle y=3x^2-12x+9

Answer | Solution a | Solution b | Solution c

Exercise 2.3:10

In the xy-plane, draw in all the points whose coordinates \displaystyle \,(x,y)\, satisfy

a) \displaystyle y \geq x^2\ and \displaystyle \ y \leq 1 b) \displaystyle y \leq 1-x^2\ and \displaystyle \ x \geq 2y-3
c) \displaystyle 1 \geq x \geq y^2 d) \displaystyle x^2 \leq y \leq x

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

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/2.3_Exercises"