2.2 Exercises
From Förberedande kurs i matematik 1
| Theory | Exercises |
Exercise 2.2:1
Solve the equations
| a) | \displaystyle x-2=-1 | b) | \displaystyle 2x+1=13 |
| c) | \displaystyle \displaystyle\frac{1}{3}x-1=x | d) | \displaystyle 5x+7=2x-6 |
Answer
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Solution a
Solution b
Solution c
Solution d
Exercise 2.2:2
Solve the equations
| a) | \displaystyle \displaystyle\frac{5x}{6}-\displaystyle\frac{x+2}{9}=\displaystyle\frac{1}{2} | b) | \displaystyle \displaystyle\frac{8x+3}{7}-\displaystyle\frac{5x-7}{4}=2 |
| c) | \displaystyle (x+3)^2-(x-5)^2=6x+4 | d) | \displaystyle (x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2 |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 2.2:3
Solve the equations
| a) | \displaystyle \displaystyle\frac{x+3}{x-3}-\displaystyle\frac{x+5}{x-2}=0 |
| b) | \displaystyle \displaystyle\frac{4x}{4x-7}-\displaystyle\frac{1}{2x-3}=1 |
| c) | \displaystyle \left(\displaystyle\frac{1}{x-1}-\frac{1}{x+1}\right)\left(x^2+\frac{1}{2}\right)=\displaystyle\frac{6x-1}{3x-3} |
| d) | \displaystyle \left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0 |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 2.2:4
| a) | Write the equation for the line \displaystyle \,y=2x+3\, in the form \displaystyle \,ax+by=c\,. |
| b) | Write the equation for the line \displaystyle 3x+4y-5=0 in the form \displaystyle \,y=kx+m\,. |
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
