Signs of a solution

12 questions

1. A value has been rounded to 2.8 to 2 significant figures. What is the lower bound of this value?
2. A value has been rounded to 2.8 to 2 significant figures. What is the upper bound of this value?
3. What is the value of x^3-2x+5 when x=2?
4. What is the value of x^3-2x+5 when x=-2?
5. Match the letter representing each graph to the equation of the graph.
6. Using the iterative formula x_{n+1}=\sqrt[3]{4(x_n)^2-1} and x_0=5 there is a solution to x^3-4x^2+1=0 correct to 2 significant figures when x=___ .
7. Using the table of values shown for the equation y=x^3-4x+2 which of these statements are definitely true?
8. Between which sets of values is there definitely a solution to x^3-5x-1=0 ?
9. When might a change in sign not indicate there is a solution between two values?
10. The image shows Jacob's workings to test his approximate solution to the equation x^3-2x=0. What do you think his solution was?
11. To see if x=-1.4 is a solution to the equation x^3-2x=0 to 2 significant figures which values should we test to see if there is a change in sign?
12. Which of these are solutions to -x^2+3x-1=0 correct to the stated degree of accuracy?

License: OGL