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2.2 Übungen

Aus Online Mathematik Brückenkurs 1

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Vorlage:Ej vald flik Vorlage:Vald flik

 

Exercise 2.2:1

Solve the equations

a) x−2=−1 b) 2x+1=13
c) 31x−1=x d) 5x+7=2x−6

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

Exercise 2.2:2

Solve the equations

a) 65x−9x+2=21 b) 78x+3−45x−7=2
c) (x+3)2−(x−5)2=6x+4 d) (x2+4x+1)2+3x4−2x2=(2x2+2x+3)2

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

Exercise 2.2:3

Solve the equations

a) x−3x+3−x−2x+5=0
b) 4x4x−7−12x−3=1
c) 1x−1−1x+1x2+21=3x−36x−1 
d) x2−314x+21−12x−322−12x+3112x−31=0 

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

Exercise 2.2:4

a) Write the equation for the line y=2x+3 in the form ax+by=c.
b) Write the equation for the line 3x+4y−5=0 in the form y=kx+m.

Answer | Solution a | Solution b

Exercise 2.2:5

a) Determine the equation for the straight line that goes between the points (23) and(30).
b) Determine the equation for the straight line that has slope −3 and goes through the point (1−2).
c) Determine the equation for the straight line that goes through the point (−12) and is parallel to the line y=3x+1.
d) Determine the equation for the straight line that goes through the point (24) and is perpendicular to the line y=2x+5.
e) Determine the slope, k, for the straight line that cuts the x-axis at the point (50) and y-axis at the point (0−8).

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

Exercise 2.2:6

Find the points of intersection between the pairs of lines in the following

a) y=3x+5  and the x-axis b) y=−x+5  and the y-axis
c) 4x+5y+6=0  and the y-axis d) x+y+1=0  and  x=12
e) 2x+y−1=0  and  y−2x−2=0

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

Exercise 2.2:7

Sketch the graph of the functions

a) f(x)=3x−2 b) f(x)=2−x c) f(x)=2

Answer | Solution a | Solution b | Solution c

Exercise 2.2:8

In the xy-plane, fill in all the points whose coordinates (xy) satisfy

a) yx b) y3x−4 c) 2x+3y6

Answer | Solution a | Solution b | Solution c

Exercise 2.2:9

Calculate the area of the triangle which

a) has corners at the points (14), (33) and (10).
b) is bordered by the lines  x=2y,  y=4  and  y=10−2x.
c) is described by the inequalities  x+y−2,  2x−y2  and  2y−x2.

Answer | Solution a | Solution b | Solution c

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/2.2_%C3%9Cbungen“