2.3 Exercises
From Förberedande kurs i matematik 1
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Revision as of 10:41, 10 September 2008
| Theory | Exercises |
Exercise 2.3:1
Complete the square of the expressions
| a) | | b) | | c) | | d) | |
Answer | Solution a | Solution b | Solution c | Solution d
Loading...Exercise 2.3:2
Solve the following second order equations by completing the square
| a) | | b) | | c) | |
| d) | | e) | | f) | |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 2.3:3
Solve the following equations directly
| a) | | b) | |
| c) | | d) | |
| e) | | f) | |
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) | |
| b) |  3 3 |
| c) | 3 |
Answer | Solution a | Solution b | Solution c
Exercise 2.3:5
| a) | Determine a second-degree equation which only has |
| b) | Determine a value of |
| c) | The equation |
Answer | Solution a | Solution b | Solution c
Exercise 2.3:6
Determine the smallest value that the following polynomial can take
| a) | | b) | | c) | |
Answer | Solution a | Solution b | Solution c
Exercise 2.3:7
Determine the largest value that the following polynomials can take.
| a) | | 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
