(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?
Click here to download the MATCHLESS worksheet.
Click here to download the AIMSSEC Teacher Notes for MATCHLESS
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?
Click here to download the […]
Note: The symbols may be slightly different. Use the subtle differences in the images in working out your answer.
This puzzle is adapted from puzzlebrain.com.
Copy this pattern. You could use toothpicks or paper sticks or draw the pattern on isometric paper (download here).
Make or draw the next 3 patterns in the sequence. How would you explain to someone else on the telephone how to do this when you could not point to the diagram?