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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) 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 \displaystyle \,(2,3)\, and\displaystyle \,(3,0)\,.
b) Determine the equation for the straight line that has slope \displaystyle \,-3\, and goes through the point \displaystyle \,(1,-2)\,.
c) Determine the equation for the straight line that goes through the point \displaystyle \,(-1,2)\, and is parallel to the line \displaystyle \,y=3x+1\,.
d) Determine the equation for the straight line that goes through the point \displaystyle \,(2,4)\, and is perpendicular to the line \displaystyle \,y=2x+5\,.
e) Determine the slope, \displaystyle \,k\,, for the straight line that cuts the x-axis at the point \displaystyle \,(5,0)\, and y-axis at the point \displaystyle \,(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) \displaystyle y=3x+5\ and the x-axis b) \displaystyle y=-x+5\ and the y-axis
c) \displaystyle 4x+5y+6=0\ and the y-axis d) \displaystyle x+y+1=0\ and \displaystyle \ x=12
e) \displaystyle 2x+y-1=0\ and \displaystyle \ 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) \displaystyle f(x)=3x-2 b) \displaystyle f(x)=2-x c) \displaystyle f(x)=2

Answer | Solution a | Solution b | Solution c

Exercise 2.2:8

In the xy-plane, shade in the section whose coordinates \displaystyle \,(x,y)\, satisfy

a) \displaystyle y \geq x b) \displaystyle y < 3x -4 c) \displaystyle 2x+3y \leq 6

Answer | Solution a | Solution b | Solution c

Exercise 2.2:9

Calculate the area of the triangle which

a) has corners at the points \displaystyle \,(1,4)\,, \displaystyle \,(3,3)\, and \displaystyle \,(1,0)\,.
b) is bordered by the lines \displaystyle \ x=2y\,, \displaystyle \ y=4\ and \displaystyle \ y=10-2x\,.
c) is described by the inequalities \displaystyle \ x+y \geq -2\,, \displaystyle \ 2x-y \leq 2\ and \displaystyle \ 2y-x \leq 2\,.

Answer | Solution a | Solution b | Solution c

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