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2.2 Exercises

From Förberedande kurs i matematik 1

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       Theory          Exercises      

Exercise 2.2:1

Solve the equations

a) x2=1 b) 2x+1=13
c) 31x1=x d) 5x+7=2x6

Exercise 2.2:2

Solve the equations

a) 65x9x+2=21 b) 78x+345x7=2
c) (x+3)2(x5)2=6x+4 d) (x2+4x+1)2+3x42x2=(2x2+2x+3)2

Exercise 2.2:3

Solve the equations

a) x3x+3x2x+5=0
b) 4x4x712x3=1
c) 1x11x+1x2+21=3x36x1 
d) x2314x+2112x32212x+3112x31=0 

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+4y5=0 in the form y=kx+m.

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 (12).
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 (08).

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+y1=0  and  y2x2=0

Exercise 2.2:7

Sketch the graph of the functions

a) f(x)=3x2 b) f(x)=2x c) f(x)=2

Exercise 2.2:8

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

a) yx b) y3x4 c) 2x+3y6

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=102x.
c) is described by the inequalities  x+y2, \displaystyle \ 2x-y \leq 2\ and \displaystyle \ 2y-x \leq 2\,.