Other tags that relate to Function Pyramids
Surds. Mathematical reasoning & proof. Logarithmic functions. Making and proving conjectures. Working systematically. Chemistry. Modular arithmetic. Powers & roots. Functions and their inverses. Biology.There are 17 results
Broad Topics > Functions and Graphs > Logarithmic functions
Function Pyramids
Age 16 to 18 Challenge Level:
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
Harmonically
Age 16 to 18 Challenge Level:
Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
Equation Attack
Age 16 to 18 Challenge Level:
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.
Complex Sine
Age 16 to 18 Challenge Level:
Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.
Tuning and Ratio
Age 16 to 18 Challenge Level:
Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?
Big, Bigger, Biggest
Age 16 to 18 Challenge Level:
Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?
Power Match
Age 16 to 18 Challenge Level:
Can you locate these values on this interactive logarithmic scale?
What Do Functions Do for Tiny X?
Age 16 to 18 Challenge Level:
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How Does Your Function Grow?
Age 16 to 18 Challenge Level:
Compares the size of functions f(n) for large values of n.
Extreme Dissociation
Age 16 to 18 Challenge Level:
In this question we push the pH formula to its theoretical limits.
Blood Buffers
Age 16 to 18 Challenge Level:
Investigate the mathematics behind blood buffers and derive the form of a titration curve.
Drug Stabiliser
Age 16 to 18 Challenge Level:
How does the half-life of a drug affect the build up of medication in the body over time?
Sierpinski Triangle
Age 16 to 18 Challenge Level:
What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.
NRICH is part of the family of activities in the Millennium Mathematics Project.