(1) Plot the graphs of the straight lines y = x, y = 1.1x – 0.2
and y = 0.9x – 0.1
What do the graphs tell you about the solutions to the two pairs of simultaneous equations y = x y = 1.1x – 0.2 and y = x y = 0.9x – 0.1 […]
Do you have exactly the right amount of information or more information than you need?
This problem is adapted […]
What is the area of the bigger square edged by dotted line segments of length a?
What is left of that area if you take away a square with edges of length b?
What is the area of the rectangle formed by the yellow […]
Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .
2. What do you notice about the difference between squares of consecutive numbers?
Compare the differences between squares of numbers that differ by 1 […]
Is there more than one?
It is quite easy to find a few solutions. The big challenge is to find all possible solutions.
Can you provide a convincing argument that you have found […]
For what other values of x is A the greatest?
For what values of x is B the greatest ?
For what values of x is C the greatest?
Is there a value of x when neither A nor B […]
How big is the smallest village for which this is true?
Can you describe the population of other villages for which this is true?