The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
If a sum invested gains 10% each year how long before it has doubled its value?
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Looking at small values of functions. Motivating the existence of the Maclaurin expansion.
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
