1 out of 3
Relate these algebraic expressions to geometrical diagrams.
1 out of 3
For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
1 out of 3
This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
1 out of 3
Can you hit the target functions using a set of input functions and a little calculus and algebra?
1 out of 3
Derive an equation which describes satellite dynamics.
1 out of 3
Can you fit polynomials through these points?
2 out of 3
Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
2 out of 3
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
2 out of 3
A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?
2 out of 3
Can you find the value of this function involving algebraic fractions for x=2000?
